diff --git a/src/sage/algebras/lie_conformal_algebras/fermionic_ghosts_lie_conformal_algebra.py b/src/sage/algebras/lie_conformal_algebras/fermionic_ghosts_lie_conformal_algebra.py index 004718d4a5f..6c4418e4751 100644 --- a/src/sage/algebras/lie_conformal_algebras/fermionic_ghosts_lie_conformal_algebra.py +++ b/src/sage/algebras/lie_conformal_algebras/fermionic_ghosts_lie_conformal_algebra.py @@ -72,7 +72,7 @@ class FermionicGhostsLieConformalAlgebra(GradedLieConformalAlgebra): sage: R.structure_coefficients() Finite family {('a', 'c'): ((0, K),), ('b', 'd'): ((0, K),), ('c', 'a'): ((0, K),), ('d', 'b'): ((0, K),)} """ - def __init__(self,R,ngens=2,names=None,index_set=None): + def __init__(self, R, ngens=2, names=None, index_set=None): """ Initialize ``self``. diff --git a/src/sage/algebras/orlik_terao.py b/src/sage/algebras/orlik_terao.py index 60c3c60e6db..26b3c49b443 100644 --- a/src/sage/algebras/orlik_terao.py +++ b/src/sage/algebras/orlik_terao.py @@ -557,7 +557,7 @@ class OrlikTeraoInvariantAlgebra(FiniteDimensionalInvariantModule): defines the action we want, but since the groundset is `\{0,1,2\}` we first add `1` and then subtract `1`:: - sage: def on_groundset(g,x): + sage: def on_groundset(g, x): ....: return g(x+1)-1 Now that we have defined an action we can create the invariant, and @@ -625,7 +625,7 @@ def __init__(self, R, M, G, action_on_groundset=None, *args, **kwargs): ....: [0,0,-1,0,-1,-1]]) sage: M = Matroid(A); sage: G = SymmetricGroup(6) - sage: def on_groundset(g,x): return g(x+1)-1 + sage: def on_groundset(g, x): return g(x+1)-1 sage: import __main__; __main__.on_groundset = on_groundset sage: OTG = M.orlik_terao_algebra(QQ, invariant = (G,on_groundset)) sage: TestSuite(OTG).run() @@ -687,7 +687,7 @@ def construction(self): sage: A = matrix([[1,1,0],[-1,0,1],[0,-1,-1]]) sage: M = Matroid(A) sage: G = SymmetricGroup(3) - sage: def on_groundset(g,x): + sage: def on_groundset(g, x): ....: return g(x+1)-1 sage: OTG = M.orlik_terao_algebra(QQ, invariant=(G,on_groundset)) sage: OTG.construction() is None @@ -718,7 +718,7 @@ def _basis_action(self, g, f): sage: M.groundset() frozenset({0, 1, 2}) sage: G = SymmetricGroup(3) - sage: def on_groundset(g,x): + sage: def on_groundset(g, x): ....: return g(x+1)-1 sage: OTG = M.orlik_terao_algebra(QQ, invariant=(G,on_groundset)) sage: def act(g): diff --git a/src/sage/algebras/steenrod/steenrod_algebra.py b/src/sage/algebras/steenrod/steenrod_algebra.py index 7e4c3dc014f..540cb6ee92d 100644 --- a/src/sage/algebras/steenrod/steenrod_algebra.py +++ b/src/sage/algebras/steenrod/steenrod_algebra.py @@ -2533,7 +2533,7 @@ def an_element(self): return self.monomial(((1, 2),)) return self.term(((), (((1,2), 1),)), GF(p)(p-1)) - def pst(self,s,t): + def pst(self, s, t): r""" The Margolis element `P^s_t`. diff --git a/src/sage/algebras/steenrod/steenrod_algebra_bases.py b/src/sage/algebras/steenrod/steenrod_algebra_bases.py index 06f9a5b87ad..9d37290ef3e 100644 --- a/src/sage/algebras/steenrod/steenrod_algebra_bases.py +++ b/src/sage/algebras/steenrod/steenrod_algebra_bases.py @@ -887,7 +887,7 @@ def degree_dictionary(n, basis): deg = 2**s * (2**t - 1) return dict - def sorting_pair(s,t,basis): # pair used for sorting the basis + def sorting_pair(s, t, basis): # pair used for sorting the basis if basis.find('wood') >= 0 and basis.find('z') >= 0: return (-s-t,-s) elif basis.find('wood') >= 0 or basis.find('wall') >= 0 or \ diff --git a/src/sage/algebras/steenrod/steenrod_algebra_mult.py b/src/sage/algebras/steenrod/steenrod_algebra_mult.py index 053290bc5ed..c3ae7c181f9 100644 --- a/src/sage/algebras/steenrod/steenrod_algebra_mult.py +++ b/src/sage/algebras/steenrod/steenrod_algebra_mult.py @@ -204,7 +204,7 @@ # Milnor, p=2 -def milnor_multiplication(r,s): +def milnor_multiplication(r, s): r""" Product of Milnor basis elements r and s at the prime 2. @@ -372,7 +372,7 @@ def multinomial(list): # Milnor, p odd -def milnor_multiplication_odd(m1,m2,p): +def milnor_multiplication_odd(m1, m2, p): r""" Product of Milnor basis elements defined by m1 and m2 at the odd prime p. @@ -568,7 +568,7 @@ def milnor_multiplication_odd(m1,m2,p): return result -def multinomial_odd(list,p): +def multinomial_odd(list, p): r""" Multinomial coefficient of list, mod p. @@ -635,7 +635,7 @@ def multinomial_odd(list,p): # Adem relations, Serre-Cartan basis, admissible sequences -def binomial_mod2(n,k): +def binomial_mod2(n, k): r""" The binomial coefficient `\binom{n}{k}`, computed mod 2. @@ -665,7 +665,7 @@ def binomial_mod2(n,k): return 0 -def binomial_modp(n,k,p): +def binomial_modp(n, k, p): r""" The binomial coefficient `\binom{n}{k}`, computed mod `p`. diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py index 745d5fcbbe7..14fe466ccd9 100644 --- a/src/sage/arith/misc.py +++ b/src/sage/arith/misc.py @@ -4171,7 +4171,7 @@ def multinomial_coefficients(m, n): return r -def kronecker_symbol(x,y): +def kronecker_symbol(x, y): """ The Kronecker symbol `(x|y)`. diff --git a/src/sage/arith/multi_modular.pyx b/src/sage/arith/multi_modular.pyx index 1d5e9a46221..6488eb22761 100644 --- a/src/sage/arith/multi_modular.pyx +++ b/src/sage/arith/multi_modular.pyx @@ -196,11 +196,11 @@ cdef class MultiModularBasis_base(): while True: if len(known_primes) >= self._num_primes: raise RuntimeError("there are not enough primes in the interval [%s, %s] to complete this multimodular computation" % (self._l_bound, self._u_bound)) - p = random_prime(self._u_bound, lbound =self._l_bound) + p = random_prime(self._u_bound, lbound=self._l_bound) if p not in known_primes: return p - def extend_with_primes(self, plist, partial_products = None, check=True): + def extend_with_primes(self, plist, partial_products=None, check=True): """ Extend the stored list of moduli with the given primes in ``plist``. diff --git a/src/sage/calculus/integration.pyx b/src/sage/calculus/integration.pyx index f746f8aa04a..179e5751894 100644 --- a/src/sage/calculus/integration.pyx +++ b/src/sage/calculus/integration.pyx @@ -498,7 +498,7 @@ def monte_carlo_integral(func, xl, xu, size_t calls, algorithm='plain', (4.0, 0.0) sage: monte_carlo_integral(lambda u,v: u*v, [0,0], [2,2], 10000) # abs tol 0.1 (4.0, 0.0) - sage: def f(x1,x2,x3,x4): return x1*x2*x3*x4 + sage: def f(x1, x2, x3, x4): return x1*x2*x3*x4 sage: monte_carlo_integral(f, [0,0], [2,2], 1000, params=[0.6,2]) # abs tol 0.2 (4.8, 0.0) @@ -522,7 +522,7 @@ def monte_carlo_integral(func, xl, xu, size_t calls, algorithm='plain', ValueError: The function to be integrated depends on 2 variables (x, y), and so cannot be integrated in 3 dimensions. Please fix additional variables with the 'params' argument - sage: def f(x,y): return x*y + sage: def f(x, y): return x*y sage: monte_carlo_integral(f, [0,0,0], [2,2,2], 100) Traceback (most recent call last): ... diff --git a/src/sage/calculus/ode.pxd b/src/sage/calculus/ode.pxd index 2de37b91764..fad66432a9e 100644 --- a/src/sage/calculus/ode.pxd +++ b/src/sage/calculus/ode.pxd @@ -1,4 +1,4 @@ cdef class ode_system: - cdef int c_j(self,double , double *, double *,double *) noexcept + cdef int c_j(self, double , double *, double *, double *) noexcept - cdef int c_f(self,double t, double* , double* ) noexcept + cdef int c_f(self, double t, double* , double* ) noexcept diff --git a/src/sage/calculus/ode.pyx b/src/sage/calculus/ode.pyx index 646b937e2e4..2addf3e7f81 100644 --- a/src/sage/calculus/ode.pyx +++ b/src/sage/calculus/ode.pyx @@ -313,11 +313,11 @@ class ode_solver(): from sage.libs.gsl.all cimport * cdef class van_der_pol(sage.calculus.ode.ode_system): - cdef int c_f(self,double t, double *y,double *dydt): + cdef int c_f(self, double t, double *y, double *dydt): dydt[0]=y[1] dydt[1]=-y[0]-1000*y[1]*(y[0]*y[0]-1) return GSL_SUCCESS - cdef int c_j(self, double t,double *y,double *dfdy,double *dfdt): + cdef int c_j(self, double t, double *y, double *dfdy, double *dfdt): dfdy[0]=0 dfdy[1]=1.0 dfdy[2]=-2.0*1000*y[0]*y[1]-1.0 diff --git a/src/sage/calculus/riemann.pyx b/src/sage/calculus/riemann.pyx index 385aa7a09f8..455567371eb 100644 --- a/src/sage/calculus/riemann.pyx +++ b/src/sage/calculus/riemann.pyx @@ -65,7 +65,7 @@ ctypedef np.complex128_t COMPLEX_T cdef FLOAT_T PI = pi cdef FLOAT_T TWOPI = 2*PI -cdef COMPLEX_T I = complex(0,1) +cdef COMPLEX_T I = complex(0, 1) cdef class Riemann_Map: r""" @@ -1263,7 +1263,7 @@ cpdef complex_to_spiderweb(np.ndarray[COMPLEX_T, ndim = 2] z_values, return rgb -cpdef complex_to_rgb(np.ndarray[COMPLEX_T, ndim = 2] z_values): +cpdef complex_to_rgb(np.ndarray[COMPLEX_T, ndim=2] z_values): r""" Convert from a (Numpy) array of complex numbers to its corresponding matrix of RGB values. For internal use of :meth:`~Riemann_Map.plot_colored` diff --git a/src/sage/calculus/tests.py b/src/sage/calculus/tests.py index ac76b5e4f70..2879dda115d 100644 --- a/src/sage/calculus/tests.py +++ b/src/sage/calculus/tests.py @@ -16,7 +16,7 @@ :: - sage: def christoffel(i,j,k,vars,g): + sage: def christoffel(i, j, k, vars, g): ....: s = 0 ....: ginv = g^(-1) ....: for l in range(g.nrows()): diff --git a/src/sage/calculus/transforms/dwt.pyx b/src/sage/calculus/transforms/dwt.pyx index fdb68153a8b..c004b00715c 100644 --- a/src/sage/calculus/transforms/dwt.pyx +++ b/src/sage/calculus/transforms/dwt.pyx @@ -103,11 +103,11 @@ cdef class DiscreteWaveletTransform(GSLDoubleArray): """ Discrete wavelet transform class. """ - def __cinit__(self,size_t n,size_t stride, wavelet_type, size_t wavelet_k): + def __cinit__(self, size_t n, size_t stride, wavelet_type, size_t wavelet_k): self.wavelet = NULL self.workspace = NULL - def __init__(self,size_t n,size_t stride, wavelet_type, size_t wavelet_k): + def __init__(self, size_t n, size_t stride, wavelet_type, size_t wavelet_k): if not is2pow(n): raise NotImplementedError("discrete wavelet transform only implemented when n is a 2-power") GSLDoubleArray.__init__(self,n,stride) diff --git a/src/sage/calculus/var.pyx b/src/sage/calculus/var.pyx index 4967bb9bd9a..853c5c493ff 100644 --- a/src/sage/calculus/var.pyx +++ b/src/sage/calculus/var.pyx @@ -255,7 +255,7 @@ def function(s, **kwds): sage: foo(x).conjugate() 2*x - sage: def deriv(self, *args,**kwds): print("{} {}".format(args, kwds)); return args[kwds['diff_param']]^2 + sage: def deriv(self, *args, **kwds): print("{} {}".format(args, kwds)); return args[kwds['diff_param']]^2 sage: foo = function("foo", nargs=2, derivative_func=deriv) sage: foo(x,y).derivative(y) (x, y) {'diff_param': 1} diff --git a/src/sage/categories/category.py b/src/sage/categories/category.py index b534f7be794..feb1b2cb393 100644 --- a/src/sage/categories/category.py +++ b/src/sage/categories/category.py @@ -173,7 +173,7 @@ class Category(UniqueRepresentation, SageObject): ....: pass ....: ....: class ElementMethods:# holds the generic operations on elements - ....: def gcd(x,y): + ....: def gcd(x, y): ....: # Euclid algorithms ....: pass ....: diff --git a/src/sage/categories/category_with_axiom.py b/src/sage/categories/category_with_axiom.py index 766ec9b64cb..014ac68d369 100644 --- a/src/sage/categories/category_with_axiom.py +++ b/src/sage/categories/category_with_axiom.py @@ -1695,7 +1695,7 @@ class ``Sets.Finite``), or in a separate file (typically in a class ) -def uncamelcase(s,separator=" "): +def uncamelcase(s, separator=" "): """ EXAMPLES:: diff --git a/src/sage/categories/classical_crystals.py b/src/sage/categories/classical_crystals.py index 42dc02bdb2f..b8b05f17b55 100644 --- a/src/sage/categories/classical_crystals.py +++ b/src/sage/categories/classical_crystals.py @@ -328,11 +328,11 @@ def __iter__(self): sage: fb4 = lambda a,b,c,d: crystals.Tableaux(['B',4],shape=[a+b+c+d,b+c+d,c+d,d]) sage: fd4 = lambda a,b,c,d: crystals.Tableaux(['D',4],shape=[a+b+c+d,b+c+d,c+d,d]) sage: fd5 = lambda a,b,c,d,e: crystals.Tableaux(['D',5],shape=[a+b+c+d+e,b+c+d+e,c+d+e,d+e,e]) - sage: def fd4spinplus(a,b,c,d): + sage: def fd4spinplus(a, b, c, d): ....: C = crystals.Tableaux(['D',4],shape=[a+b+c+d,b+c+d,c+d,d]) ....: D = crystals.SpinsPlus(['D',4]) ....: return crystals.TensorProduct(C,D,generators=[[C[0],D[0]]]) - sage: def fb3spin(a,b,c): + sage: def fb3spin(a, b, c): ....: C = crystals.Tableaux(['B',3],shape=[a+b+c,b+c,c]) ....: D = crystals.Spins(['B',3]) ....: return crystals.TensorProduct(C,D,generators=[[C[0],D[0]]]) diff --git a/src/sage/categories/crystals.py b/src/sage/categories/crystals.py index c822bbd50fc..ddcdf6bb44d 100644 --- a/src/sage/categories/crystals.py +++ b/src/sage/categories/crystals.py @@ -1177,7 +1177,7 @@ def plot(self, **options): sage: print(C.plot()) Graphics object consisting of 17 graphics primitives """ - return self.digraph().plot(edge_labels=True,vertex_size=0,**options) + return self.digraph().plot(edge_labels=True, vertex_size=0, **options) def plot3d(self, **options): """ diff --git a/src/sage/categories/discrete_valuation.py b/src/sage/categories/discrete_valuation.py index 77267664bb2..39ed8ae8148 100644 --- a/src/sage/categories/discrete_valuation.py +++ b/src/sage/categories/discrete_valuation.py @@ -196,7 +196,7 @@ def is_unit(self): """ return self.valuation() == 0 - def gcd(self,other): + def gcd(self, other): """ Return the greatest common divisor of ``self`` and ``other``, normalized so that it is a power of the distinguished @@ -209,7 +209,7 @@ def gcd(self,other): else: return self.parent().uniformizer() ** val - def lcm(self,other): + def lcm(self, other): """ Return the least common multiple of ``self`` and ``other``, normalized so that it is a power of the distinguished diff --git a/src/sage/categories/distributive_magmas_and_additive_magmas.py b/src/sage/categories/distributive_magmas_and_additive_magmas.py index 830c6c77c8c..cd736a5d15c 100644 --- a/src/sage/categories/distributive_magmas_and_additive_magmas.py +++ b/src/sage/categories/distributive_magmas_and_additive_magmas.py @@ -16,7 +16,7 @@ class DistributiveMagmasAndAdditiveMagmas(CategoryWithAxiom): """ - The category of sets `(S,+,*)` with `*` distributing on `+`. + The category of sets `(S, +, *)` with `*` distributing on `+`. This is similar to a ring, but `+` and `*` are only required to be (additive) magmas. diff --git a/src/sage/categories/finite_dimensional_modules_with_basis.py b/src/sage/categories/finite_dimensional_modules_with_basis.py index ee5b6490346..4b91c642074 100644 --- a/src/sage/categories/finite_dimensional_modules_with_basis.py +++ b/src/sage/categories/finite_dimensional_modules_with_basis.py @@ -212,7 +212,7 @@ def annihilator_basis(self, S, action=operator.mul, side='right'): sage: # needs sage.graphs sage.modules sage: x,y,a,b = F.basis() - sage: def scalar(u,v): + sage: def scalar(u, v): ....: return vector([sum(u[i]*v[i] for i in F.basis().keys())]) sage: F.annihilator_basis([x + y, a + b], scalar) (x - y, a - b) @@ -496,7 +496,7 @@ def twisted_invariant_module(self, G, chi, sage: # needs sage.combinat sage.groups sage.modules sage: M = CombinatorialFreeModule(QQ, [1,2,3]) sage: G = SymmetricGroup(3) - sage: def action(g,x): return(M.term(g(x))) # permute coordinates + sage: def action(g, x): return(M.term(g(x))) # permute coordinates sage: T = M.twisted_invariant_module(G, [2,0,-1], ....: action_on_basis=action) sage: import __main__; __main__.action = action diff --git a/src/sage/categories/finitely_generated_lambda_bracket_algebras.py b/src/sage/categories/finitely_generated_lambda_bracket_algebras.py index 7d028630658..4a7ca22d50f 100644 --- a/src/sage/categories/finitely_generated_lambda_bracket_algebras.py +++ b/src/sage/categories/finitely_generated_lambda_bracket_algebras.py @@ -51,7 +51,7 @@ def ngens(self): """ return len(self.gens()) - def gen(self,i): + def gen(self, i): r""" The ``i``-th generator of this Lie conformal algebra. diff --git a/src/sage/categories/group_algebras.py b/src/sage/categories/group_algebras.py index e83de9263d3..72f3dd7251b 100644 --- a/src/sage/categories/group_algebras.py +++ b/src/sage/categories/group_algebras.py @@ -238,7 +238,7 @@ def coproduct_on_basis(self, g): g = self.term(g) return tensor([g, g]) - def antipode_on_basis(self,g): + def antipode_on_basis(self, g): r""" Return the antipode of the element ``g`` of the basis. @@ -263,7 +263,7 @@ def antipode_on_basis(self,g): """ return self.term(~g) - def counit_on_basis(self,g): + def counit_on_basis(self, g): r""" Return the counit of the element ``g`` of the basis. @@ -283,7 +283,7 @@ def counit_on_basis(self,g): """ return self.base_ring().one() - def counit(self,x): + def counit(self, x): r""" Return the counit of the element ``x`` of the group algebra. diff --git a/src/sage/categories/magmas_and_additive_magmas.py b/src/sage/categories/magmas_and_additive_magmas.py index 4b612606aee..24a6955abac 100644 --- a/src/sage/categories/magmas_and_additive_magmas.py +++ b/src/sage/categories/magmas_and_additive_magmas.py @@ -19,7 +19,7 @@ class MagmasAndAdditiveMagmas(Category_singleton): """ - The category of sets `(S,+,*)` with an additive operation '+' and + The category of sets `(S, +, *)` with an additive operation '+' and a multiplicative operation `*` EXAMPLES:: diff --git a/src/sage/categories/modules_with_basis.py b/src/sage/categories/modules_with_basis.py index 7b51d82c7ba..489f2f97dbb 100644 --- a/src/sage/categories/modules_with_basis.py +++ b/src/sage/categories/modules_with_basis.py @@ -1395,7 +1395,7 @@ def random_element(self, n=2): we can find a random element in a trivial module:: sage: class Foo(CombinatorialFreeModule): # needs sage.modules - ....: def _element_constructor_(self,x): + ....: def _element_constructor_(self, x): ....: if x in self: ....: return x ....: else: @@ -2535,7 +2535,7 @@ def apply_multilinear_morphism(self, f, codomain=None): and `f` the bilinear morphism `(a,b) \mapsto b \otimes a` from `A \times B` to `B \otimes A`:: - sage: def f(a,b): + sage: def f(a, b): ....: return tensor([b,a]) Now, calling applying `f` on `a \otimes b` returns the same @@ -2564,7 +2564,7 @@ def apply_multilinear_morphism(self, f, codomain=None): Mind the `0` in the sums above; otherwise `f` would not return `0` in `\ZZ`:: - sage: def f(a,b): + sage: def f(a, b): ....: return sum(a.coefficients()) * sum(b.coefficients()) sage: type(f(A.zero(), B.zero())) # needs sage.modules <... 'int'> diff --git a/src/sage/categories/morphism.pyx b/src/sage/categories/morphism.pyx index 34bcd1ca5f5..28e89a36299 100644 --- a/src/sage/categories/morphism.pyx +++ b/src/sage/categories/morphism.pyx @@ -619,7 +619,7 @@ cdef class SetMorphism(Morphism): sage: from sage.categories.morphism import SetMorphism sage: R. = QQ[] - sage: def foo(x,*args,**kwds): + sage: def foo(x, *args, **kwds): ....: print('foo called with {} {}'.format(args, kwds)) ....: return x sage: f = SetMorphism(Hom(R,R,Rings()), foo) diff --git a/src/sage/categories/regular_crystals.py b/src/sage/categories/regular_crystals.py index 506be6ba4ec..0459c0e0695 100644 --- a/src/sage/categories/regular_crystals.py +++ b/src/sage/categories/regular_crystals.py @@ -587,7 +587,7 @@ def demazure_operator_simple(self, i, ring=None): l.append(element) return - C.sum_of_monomials(l) - def stembridgeDelta_depth(self,i,j): + def stembridgeDelta_depth(self, i, j): r""" Return the difference in the `j`-depth of ``self`` and `e_i` of ``self``, where `i` and `j` are in the index set of the @@ -610,7 +610,7 @@ def stembridgeDelta_depth(self,i,j): return 0 return -self.e(i).epsilon(j) + self.epsilon(j) - def stembridgeDelta_rise(self,i,j): + def stembridgeDelta_rise(self, i, j): r""" Return the difference in the `j`-rise of ``self`` and `e_i` of ``self``, where `i` and `j` are in the index set of the @@ -633,7 +633,7 @@ def stembridgeDelta_rise(self,i,j): return 0 return self.e(i).phi(j) - self.phi(j) - def stembridgeDel_depth(self,i,j): + def stembridgeDel_depth(self, i, j): r""" Return the difference in the `j`-depth of ``self`` and `f_i` of ``self``, where `i` and `j` are in the index set of the @@ -656,7 +656,7 @@ def stembridgeDel_depth(self,i,j): return 0 return -self.epsilon(j) + self.f(i).epsilon(j) - def stembridgeDel_rise(self,i,j): + def stembridgeDel_rise(self, i, j): r""" Return the difference in the `j`-rise of ``self`` and `f_i` of ``self``, where `i` and `j` are in the index set of the @@ -679,7 +679,7 @@ def stembridgeDel_rise(self,i,j): return 0 return self.phi(j)-self.f(i).phi(j) - def stembridgeTriple(self,i,j): + def stembridgeTriple(self, i, j): r""" Let `A` be the Cartan matrix of the crystal, `x` a crystal element, and let `i` and `j` be in the index set of the crystal. diff --git a/src/sage/categories/semirings.py b/src/sage/categories/semirings.py index 624a867608a..6ba7dbec342 100644 --- a/src/sage/categories/semirings.py +++ b/src/sage/categories/semirings.py @@ -17,10 +17,10 @@ class Semirings(CategoryWithAxiom): """ The category of semirings. - A semiring `(S,+,*)` is similar to a ring, but without the + A semiring `(S, +, *)` is similar to a ring, but without the requirement that each element must have an additive inverse. In other words, it is a combination of a commutative additive monoid - `(S,+)` and a multiplicative monoid `(S,*)`, where `*` distributes + `(S, +)` and a multiplicative monoid `(S, *)`, where `*` distributes over `+`. .. SEEALSO:: diff --git a/src/sage/categories/sets_cat.py b/src/sage/categories/sets_cat.py index 9d63ac2fa30..ba13c6bc9a4 100644 --- a/src/sage/categories/sets_cat.py +++ b/src/sage/categories/sets_cat.py @@ -1750,8 +1750,8 @@ def _sympy_(self): class ElementMethods: ## Should eventually contain the basic operations which are no math ## latex, hash, ... - ##def equal(x,y): - ##def =(x,y): + ##def equal(x, y): + ##def =(x, y): # Used by Element._test_category _dummy_attribute = None diff --git a/src/sage/categories/supercrystals.py b/src/sage/categories/supercrystals.py index 09b924e0ad6..59fbf9241df 100644 --- a/src/sage/categories/supercrystals.py +++ b/src/sage/categories/supercrystals.py @@ -54,7 +54,7 @@ def tensor(self, *crystals, **options): Crystal of BKK tableaux of shape [2, 1] of gl(2|3)] sage: G = T.digraph() sage: H = S.digraph() - sage: G.is_isomorphic(H, edge_labels= True) + sage: G.is_isomorphic(H, edge_labels=True) True """ cartan_type = self.cartan_type() diff --git a/src/sage/coding/code_bounds.py b/src/sage/coding/code_bounds.py index 4bb33d9565f..892445c75bc 100644 --- a/src/sage/coding/code_bounds.py +++ b/src/sage/coding/code_bounds.py @@ -361,7 +361,7 @@ def gilbert_lower_bound(n, q, d): return ans -def plotkin_upper_bound(n,q,d, algorithm=None): +def plotkin_upper_bound(n, q, d, algorithm=None): r""" Return the Plotkin upper bound. @@ -400,7 +400,7 @@ def plotkin_upper_bound(n,q,d, algorithm=None): return int(d/( d - t * fact)) * q**(n - fact) -def griesmer_upper_bound(n,q,d,algorithm=None): +def griesmer_upper_bound(n, q, d, algorithm=None): r""" Return the Griesmer upper bound. @@ -456,7 +456,7 @@ def griesmer_upper_bound(n,q,d,algorithm=None): return q**(k-1) -def elias_upper_bound(n,q,d,algorithm=None): +def elias_upper_bound(n, q, d, algorithm=None): r""" Return the Elias upper bound. @@ -486,7 +486,7 @@ def ff(n, d, w, q): return int(bnd) -def hamming_upper_bound(n,q,d): +def hamming_upper_bound(n, q, d): r""" Return the Hamming upper bound. diff --git a/src/sage/coding/code_constructions.py b/src/sage/coding/code_constructions.py index be1c087c280..ecee1cd349f 100644 --- a/src/sage/coding/code_constructions.py +++ b/src/sage/coding/code_constructions.py @@ -329,7 +329,7 @@ def walsh_matrix(m0): ##################### main constructions ##################### -def DuadicCodeEvenPair(F,S1,S2): +def DuadicCodeEvenPair(F, S1, S2): r""" Construct the "even pair" of duadic codes associated to the "splitting" (see the docstring for ``_is_a_splitting`` @@ -379,7 +379,7 @@ def DuadicCodeEvenPair(F,S1,S2): return C1,C2 -def DuadicCodeOddPair(F,S1,S2): +def DuadicCodeOddPair(F, S1, S2): """ Construct the "odd pair" of duadic codes associated to the "splitting" S1, S2 of n. @@ -435,7 +435,7 @@ def DuadicCodeOddPair(F,S1,S2): return C1,C2 -def ExtendedQuadraticResidueCode(n,F): +def ExtendedQuadraticResidueCode(n, F): r""" The extended quadratic residue code (or XQR code) is obtained from a QR code by adding a check bit to the last coordinate. (These @@ -500,7 +500,7 @@ def from_parity_check_matrix(H): return Cd.dual_code() -def QuadraticResidueCode(n,F): +def QuadraticResidueCode(n, F): r""" A quadratic residue code (or QR code) is a cyclic code whose generator polynomial is the product of the polynomials @@ -544,7 +544,7 @@ def QuadraticResidueCode(n,F): return QuadraticResidueCodeOddPair(n,F)[0] -def QuadraticResidueCodeEvenPair(n,F): +def QuadraticResidueCodeEvenPair(n, F): r""" Quadratic residue codes of a given odd prime length and base ring either don't exist at all or occur as 4-tuples - a pair of @@ -610,7 +610,7 @@ def QuadraticResidueCodeEvenPair(n,F): return DuadicCodeEvenPair(F,Q,N) -def QuadraticResidueCodeOddPair(n,F): +def QuadraticResidueCodeOddPair(n, F): r""" Quadratic residue codes of a given odd prime length and base ring either don't exist at all or occur as 4-tuples - a pair of @@ -696,7 +696,7 @@ def random_linear_code(F, length, dimension): return LinearCode(G) -def ToricCode(P,F): +def ToricCode(P, F): r""" Let `P` denote a list of lattice points in `\ZZ^d` and let `T` denote the set of all diff --git a/src/sage/coding/codecan/codecan.pyx b/src/sage/coding/codecan/codecan.pyx index 47311e16260..ceb197f7890 100644 --- a/src/sage/coding/codecan/codecan.pyx +++ b/src/sage/coding/codecan/codecan.pyx @@ -619,7 +619,7 @@ cdef class PartitionRefinementLinearCode(PartitionRefinement_generic): S = SemimonomialTransformationGroup(self._matrix.base_ring(), self._n) S_n = SymmetricGroup(self._n) - self._transporter = S(perm= S_n(self._to_best.sage())) + self._transporter = S(perm=S_n(self._to_best.sage())) self._transporter, self._best_candidate, remaining_inner_group = self._compute_group_element(self._transporter, algorithm_type) # compute the other components of the automorphism group generators diff --git a/src/sage/coding/guruswami_sudan/gs_decoder.py b/src/sage/coding/guruswami_sudan/gs_decoder.py index 54a624375bd..a5bf1cf345f 100644 --- a/src/sage/coding/guruswami_sudan/gs_decoder.py +++ b/src/sage/coding/guruswami_sudan/gs_decoder.py @@ -375,7 +375,7 @@ def guruswami_sudan_decoding_radius(C=None, n_k=None, l=None, s=None): """ n,k = n_k_params(C, n_k) - def get_tau(s,l): + def get_tau(s, l): "Return the decoding radius given this s and l" if s <= 0 or l <= 0: return -1 diff --git a/src/sage/coding/linear_code.py b/src/sage/coding/linear_code.py index a9e3813b474..3e9d388c434 100644 --- a/src/sage/coding/linear_code.py +++ b/src/sage/coding/linear_code.py @@ -1261,7 +1261,7 @@ def genus(self): gammaC = n+1-k-d return gammaC - def is_permutation_equivalent(self,other,algorithm=None): + def is_permutation_equivalent(self, other, algorithm=None): """ Return ``True`` if ``self`` and ``other`` are permutation equivalent codes and ``False`` otherwise. diff --git a/src/sage/combinat/cluster_algebra_quiver/quiver.py b/src/sage/combinat/cluster_algebra_quiver/quiver.py index 7e07835b935..d9b73e655a9 100644 --- a/src/sage/combinat/cluster_algebra_quiver/quiver.py +++ b/src/sage/combinat/cluster_algebra_quiver/quiver.py @@ -1533,7 +1533,7 @@ def mutation_sequence(self, sequence, show_sequence=False, fig_size=1.2 ): from sage.plot.plot import Graphics from sage.plot.text import text - def _plot_arrow( v, k, center=(0,0) ): + def _plot_arrow( v, k, center=(0, 0) ): return text(r"$\longleftrightarrow$",(center[0],center[1]), fontsize=25) + text(r"$\mu_"+str(v)+"$",(center[0],center[1]+0.15), fontsize=15) \ + text("$"+str(k)+"$",(center[0],center[1]-0.2), fontsize=15) diff --git a/src/sage/combinat/combination.py b/src/sage/combinat/combination.py index 49de0da4ab7..c3597e86611 100644 --- a/src/sage/combinat/combination.py +++ b/src/sage/combinat/combination.py @@ -642,7 +642,7 @@ def from_rank(r, n, k): TESTS:: sage: from sage.combinat.combination import from_rank - sage: def _comb_largest(a,b,x): + sage: def _comb_largest(a, b, x): ....: w = a - 1 ....: while binomial(w,b) > x: ....: w -= 1 diff --git a/src/sage/combinat/crystals/fast_crystals.py b/src/sage/combinat/crystals/fast_crystals.py index e427c6b48aa..5f4ca47249f 100644 --- a/src/sage/combinat/crystals/fast_crystals.py +++ b/src/sage/combinat/crystals/fast_crystals.py @@ -271,7 +271,7 @@ def digraph(self): """ return self._digraph - def cmp_elements(self, x,y): + def cmp_elements(self, x, y): r""" Return ``True`` if and only if there is a path from `x` to `y` in the crystal graph. diff --git a/src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py b/src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py index 9ba9e3c1e0a..4afc713c225 100644 --- a/src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py +++ b/src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py @@ -222,7 +222,7 @@ def __eq__(self, other): """ return isinstance(self, type(other)) and self.value == other.value - def __lt__(self,other): + def __lt__(self, other): """ Return ``True`` if ``self`` comes before ``other`` and ``False`` otherwise. diff --git a/src/sage/combinat/crystals/infinity_crystals.py b/src/sage/combinat/crystals/infinity_crystals.py index a7f98a369fb..c6331093d87 100644 --- a/src/sage/combinat/crystals/infinity_crystals.py +++ b/src/sage/combinat/crystals/infinity_crystals.py @@ -296,7 +296,7 @@ class Element(InfinityCrystalOfTableauxElement): Elements in `\mathcal{B}(\infty)` crystal of tableaux. """ - def phi(self,i): + def phi(self, i): r""" Return `\varphi_i` of ``self``. diff --git a/src/sage/combinat/crystals/littelmann_path.py b/src/sage/combinat/crystals/littelmann_path.py index c9fa7cb7933..7e2f9fe5aca 100644 --- a/src/sage/combinat/crystals/littelmann_path.py +++ b/src/sage/combinat/crystals/littelmann_path.py @@ -1455,7 +1455,7 @@ def weight(self): alpha = WLR.simple_roots() return -WLR.sum(alpha[i] for i in self.to_highest_weight()[1]) - def phi(self,i): + def phi(self, i): r""" Return `\varphi_i` of ``self``. diff --git a/src/sage/combinat/crystals/star_crystal.py b/src/sage/combinat/crystals/star_crystal.py index 02427149ed4..bc80a7a650c 100644 --- a/src/sage/combinat/crystals/star_crystal.py +++ b/src/sage/combinat/crystals/star_crystal.py @@ -61,7 +61,7 @@ class StarCrystal(UniqueRepresentation, Parent): is the highest weight vector in `B(\infty)`; - if `\Psi_i(b) = f_i^mb_i(0) \otimes b_0`, then - `\Psi_i(f_i^*b) =f_i^{m+1}b_i(0) \otimes b_0` + `\Psi_i(f_i^*b) = f_i^{m+1}b_i(0) \otimes b_0` and `\varepsilon_i(b^*) = m`; - the image of `\Psi_i` is `\{f_i^mb_i(0)\otimes b : @@ -124,7 +124,7 @@ def _repr_(self): class Element(ElementWrapper): - def e(self,i): + def e(self, i): r""" Return the action of `e_i^*` on ``self``. @@ -152,7 +152,7 @@ def e(self,i): return None return P(P._pullback[i]( P._tens[i](image[0].e(i),image[1]) )) - def f(self,i): + def f(self, i): r""" Return the action of `f_i^*` on ``self``. diff --git a/src/sage/combinat/crystals/tensor_product_element.pyx b/src/sage/combinat/crystals/tensor_product_element.pyx index 607dcc2a8dc..05b17350004 100644 --- a/src/sage/combinat/crystals/tensor_product_element.pyx +++ b/src/sage/combinat/crystals/tensor_product_element.pyx @@ -998,7 +998,7 @@ cdef class CrystalOfTableauxElement(TensorProductOfRegularCrystalsElement): return crystal(self.to_tableau().promotion_inverse(cartan_type.rank())) cdef class InfinityCrystalOfTableauxElement(CrystalOfTableauxElement): - def e(self,i): + def e(self, i): r""" Return the action of `\widetilde{e}_i` on ``self``. diff --git a/src/sage/combinat/designs/bibd.py b/src/sage/combinat/designs/bibd.py index 49c930ccb38..09785c3d1da 100644 --- a/src/sage/combinat/designs/bibd.py +++ b/src/sage/combinat/designs/bibd.py @@ -521,7 +521,7 @@ def steiner_triple_system(n): return BIBD(n, sts, name=name,check=False) -def BIBD_from_TD(v,k,existence=False): +def BIBD_from_TD(v, k, existence=False): r""" Return a BIBD through TD-based constructions. @@ -894,7 +894,7 @@ def BIBD_from_PBD(PBD, v, k, check=True, base_cases=None): return bibd -def _relabel_bibd(B,n,p=None): +def _relabel_bibd(B, n, p=None): r""" Relabel the BIBD on `n` points and blocks of size k such that `\{0,...,k-2,n-1\},\{k-1,...,2k-3,n-1\},...,\{n-k,...,n-2,n-1\}` are blocks @@ -1223,7 +1223,7 @@ def _get_r_s_t_u(v): return r,s,t,u -def PBD_from_TD(k,t,u): +def PBD_from_TD(k, t, u): r""" Return a `(kt,\{k,t\})`-PBD if `u=0` and a `(kt+u,\{k,k+1,t,u\})`-PBD otherwise. @@ -1294,7 +1294,7 @@ def BIBD_5q_5_for_q_prime_power(q): return B -def BIBD_from_arc_in_desarguesian_projective_plane(n,k,existence=False): +def BIBD_from_arc_in_desarguesian_projective_plane(n, k, existence=False): r""" Return a `(n,k,1)`-BIBD from a maximal arc in a projective plane. @@ -1430,7 +1430,7 @@ class PairwiseBalancedDesign(GroupDivisibleDesign): modified in place (each block is sorted, and the whole list is sorted). Your ``blocks`` object will become the instance's internal data. """ - def __init__(self, points, blocks, K=None, lambd=1, check=True, copy=True,**kwds): + def __init__(self, points, blocks, K=None, lambd=1, check=True, copy=True, **kwds): r""" Constructor. @@ -1498,7 +1498,7 @@ class BalancedIncompleteBlockDesign(PairwiseBalancedDesign): sage: b=designs.balanced_incomplete_block_design(9,3); b (9,3,1)-Balanced Incomplete Block Design """ - def __init__(self, points, blocks, k=None, lambd=1, check=True, copy=True,**kwds): + def __init__(self, points, blocks, k=None, lambd=1, check=True, copy=True, **kwds): r""" Constructor. diff --git a/src/sage/combinat/designs/database.py b/src/sage/combinat/designs/database.py index 19eb9d26165..ad86c612e86 100644 --- a/src/sage/combinat/designs/database.py +++ b/src/sage/combinat/designs/database.py @@ -69,7 +69,7 @@ cyclic_shift = lambda l,i : l[-i:]+l[:-i] -def _MOLS_from_string(s,k): +def _MOLS_from_string(s, k): r""" Return MOLS from a string. @@ -3829,13 +3829,13 @@ def DM_52_6_1(): from itertools import product - def t1(i,R): + def t1(i, R): if i > 1: return t1(1,t1(i-1,R)) ((x1,y1),(x2,y2),(x3,y3),(x4,y4),(x5,y5),(x6,y6)) = R return [(z*x3, 3*y3), (z*x1, 3*y1), (z*x2, 3*y2), (z*x6, 3*y6), (z*x4, 3*y4), (z*x5, 3*y5)] - def t2(i,R): + def t2(i, R): if i > 1: return t2(1,t2(i-1,R)) ((x1,y1),(x2,y2),(x3,y3),(x4,y4),(x5,y5),(x6,y6)) = R diff --git a/src/sage/combinat/designs/designs_pyx.pyx b/src/sage/combinat/designs/designs_pyx.pyx index c862821330e..790111d4326 100644 --- a/src/sage/combinat/designs/designs_pyx.pyx +++ b/src/sage/combinat/designs/designs_pyx.pyx @@ -350,7 +350,7 @@ def is_orthogonal_array(OA, int k, int n, int t=2, verbose=False, terminology='O return True -def is_group_divisible_design(groups,blocks,v,G=None,K=None,lambd=1,verbose=False): +def is_group_divisible_design(groups, blocks, v, G=None, K=None, lambd=1, verbose=False): r""" Check that input is a Group Divisible Design on `\{0, \ldots, v-1\}`. @@ -469,7 +469,7 @@ def is_group_divisible_design(groups,blocks,v,G=None,K=None,lambd=1,verbose=Fals print("{} does not belong to [0,...,{}]".format(x, n-1)) return False - cdef unsigned short * matrix = sig_calloc(n*n,sizeof(unsigned short)) + cdef unsigned short * matrix = sig_calloc(n*n, sizeof(unsigned short)) if matrix is NULL: raise MemoryError @@ -534,7 +534,7 @@ def is_group_divisible_design(groups,blocks,v,G=None,K=None,lambd=1,verbose=Fals return True if not guess_groups else (True, groups) -def is_pairwise_balanced_design(blocks,v,K=None,lambd=1,verbose=False): +def is_pairwise_balanced_design(blocks, v, K=None, lambd=1, verbose=False): r""" Check that input is a Pairwise Balanced Design (PBD) on `\{0, \ldots, v-1\}`. @@ -663,7 +663,7 @@ def is_projective_plane(blocks, verbose=False): verbose=verbose) -def is_difference_matrix(M,G,k,lmbda=1,verbose=False): +def is_difference_matrix(M, G, k, lmbda=1, verbose=False): r""" Test if `M` is a `(G,k,\lambda)`-difference matrix. @@ -728,7 +728,7 @@ def is_difference_matrix(M,G,k,lmbda=1,verbose=False): return is_quasi_difference_matrix(M,G,k,lmbda=lmbda,mu=lmbda,u=0,verbose=verbose) -def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False): +def is_quasi_difference_matrix(M, G, int k, int lmbda, int mu, int u, verbose=False): r""" Test if the matrix is a `(G,k;\lambda,\mu;u)`-quasi-difference matrix. @@ -987,7 +987,7 @@ cpdef _OA_cache_set(int k, int n, truth_value): else: _OA_cache[n].min_false = k if k<_OA_cache[n].min_false else _OA_cache[n].min_false -cpdef _OA_cache_get(int k,int n): +cpdef _OA_cache_get(int k, int n): r""" Get a value from the OA cache of existence results. @@ -1006,7 +1006,7 @@ cpdef _OA_cache_get(int k,int n): return None -cpdef _OA_cache_construction_available(int k,int n): +cpdef _OA_cache_construction_available(int k, int n): r""" Test if a construction is implemented using the cache's information. diff --git a/src/sage/combinat/designs/difference_family.py b/src/sage/combinat/designs/difference_family.py index 49b25c12dd0..a74634d32cf 100644 --- a/src/sage/combinat/designs/difference_family.py +++ b/src/sage/combinat/designs/difference_family.py @@ -330,7 +330,7 @@ def is_difference_family(G, D, v=None, k=None, l=None, verbose=False): return True -def singer_difference_set(q,d): +def singer_difference_set(q, d): r""" Return a difference set associated to the set of hyperplanes in a projective space of dimension `d` over `GF(q)`. @@ -641,7 +641,7 @@ def radical_difference_set(K, k, l=1, existence=False, check=True): return D -def one_cyclic_tiling(A,n): +def one_cyclic_tiling(A, n): r""" Given a subset ``A`` of the cyclic additive group `G = Z / nZ` return another subset `B` so that `A + B = G` and `|A| |B| = n` (i.e. any element @@ -3532,7 +3532,7 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch For `k=6,7` we look at the set of small prime powers for which a construction is available:: - sage: def prime_power_mod(r,m): + sage: def prime_power_mod(r, m): ....: k = m+r ....: while True: ....: if is_prime_power(k): diff --git a/src/sage/combinat/designs/difference_matrices.py b/src/sage/combinat/designs/difference_matrices.py index 11fe16bb8d5..0e90358c234 100644 --- a/src/sage/combinat/designs/difference_matrices.py +++ b/src/sage/combinat/designs/difference_matrices.py @@ -124,7 +124,7 @@ def difference_matrix_product(k, M1, G1, lmbda1, M2, G2, lmbda2, check=True): return G,M -def difference_matrix(g,k,lmbda=1,existence=False,check=True): +def difference_matrix(g, k, lmbda=1, existence=False, check=True): r""" Return a `(g,k,\lambda)`-difference matrix. diff --git a/src/sage/combinat/designs/evenly_distributed_sets.pyx b/src/sage/combinat/designs/evenly_distributed_sets.pyx index 1d1a7acb8ec..8fdf10c0bf1 100644 --- a/src/sage/combinat/designs/evenly_distributed_sets.pyx +++ b/src/sage/combinat/designs/evenly_distributed_sets.pyx @@ -433,7 +433,7 @@ cdef class EvenlyDistributedSetsBacktracker: will be called only once. """ cdef unsigned int i,j,k,tmp1,tmp2,verify - cdef list B = [self.B[i] for i in range(1,self.k)] + cdef list B = [self.B[i] for i in range(1, self.k)] B.append(self.q-1) cdef list BB = [None]*self.k cdef set relabs = set([tuple(B)]) diff --git a/src/sage/combinat/designs/latin_squares.py b/src/sage/combinat/designs/latin_squares.py index c8b61827e90..b117f76b8e0 100644 --- a/src/sage/combinat/designs/latin_squares.py +++ b/src/sage/combinat/designs/latin_squares.py @@ -449,12 +449,12 @@ def latin_square_product(M, N, *others): P = Matrix(D) if others: - return latin_square_product(P, others[0],*others[1:]) + return latin_square_product(P, others[0], *others[1:]) else: return P -def MOLS_table(start,stop=None,compare=False,width=None): +def MOLS_table(start, stop=None, compare=False, width=None): r""" Print the MOLS table that Sage can produce. diff --git a/src/sage/combinat/designs/orthogonal_arrays.py b/src/sage/combinat/designs/orthogonal_arrays.py index daac0f322cf..5d4498cc5a3 100644 --- a/src/sage/combinat/designs/orthogonal_arrays.py +++ b/src/sage/combinat/designs/orthogonal_arrays.py @@ -392,7 +392,7 @@ class TransversalDesign(GroupDivisibleDesign): sage: designs.transversal_design(None,36) Transversal Design TD(10,36) """ - def __init__(self, blocks, k=None,n=None,check=True,**kwds): + def __init__(self, blocks, k=None, n=None, check=True, **kwds): r""" Constructor of the class. @@ -473,7 +473,7 @@ def is_transversal_design(B, k, n, verbose=False): return is_orthogonal_array([[x % n for x in R] for R in B],k,n,verbose=verbose) -def wilson_construction(OA,k,r,m,u,check=True,explain_construction=False): +def wilson_construction(OA, k, r, m, u, check=True, explain_construction=False): r""" Return a `OA(k,rm+\sum_i u_i)` from a truncated `OA(k+s,r)` by Wilson's construction. @@ -678,7 +678,7 @@ def wilson_construction(OA,k,r,m,u,check=True,explain_construction=False): return OA -def TD_product(k,TD1,n1,TD2,n2, check=True): +def TD_product(k, TD1, n1, TD2, n2, check=True): r""" Return the product of two transversal designs. @@ -726,7 +726,7 @@ def TD_product(k,TD1,n1,TD2,n2, check=True): return TD -def orthogonal_array(k,n,t=2,resolvable=False, check=True,existence=False,explain_construction=False): +def orthogonal_array(k, n, t=2, resolvable=False, check=True, existence=False, explain_construction=False): r""" Return an orthogonal array of parameters `k,n,t`. @@ -1055,7 +1055,7 @@ def largest_available_k(n, t=2): return k -def incomplete_orthogonal_array(k,n,holes,resolvable=False, existence=False): +def incomplete_orthogonal_array(k, n, holes, resolvable=False, existence=False): r""" Return an `OA(k,n)-\sum_{1\leq i\leq x} OA(k,s_i)`. @@ -1582,7 +1582,7 @@ def OA_standard_label(OA): return [[mapping[element] for element in row] for row in OA] -def OA_n_times_2_pow_c_from_matrix(k,c,G,A,Y,check=True): +def OA_n_times_2_pow_c_from_matrix(k, c, G, A, Y, check=True): r""" Return an `OA(k, |G| \cdot 2^c)` from a constrained `(G,k-1,2)`-difference matrix. @@ -1740,7 +1740,7 @@ def OA_n_times_2_pow_c_from_matrix(k,c,G,A,Y,check=True): return OA_from_quasi_difference_matrix(list(zip(*Mb)),GG,add_col=True) -def OA_from_quasi_difference_matrix(M,G,add_col=True,fill_hole=True): +def OA_from_quasi_difference_matrix(M, G, add_col=True, fill_hole=True): r""" Return an Orthogonal Array from a Quasi-Difference matrix. @@ -1860,7 +1860,7 @@ def OA_from_quasi_difference_matrix(M,G,add_col=True,fill_hole=True): return new_M -def OA_from_Vmt(m,t,V): +def OA_from_Vmt(m, t, V): r""" Return an Orthogonal Array from a `V(m,t)`. @@ -1884,7 +1884,7 @@ def OA_from_Vmt(m,t,V): return OA_from_quasi_difference_matrix(M,Fq,add_col=False) -def QDM_from_Vmt(m,t,V): +def QDM_from_Vmt(m, t, V): r""" Return a QDM from a `V(m,t)`. @@ -1948,7 +1948,7 @@ def QDM_from_Vmt(m,t,V): return Fq, M -def OA_from_PBD(k,n,PBD, check=True): +def OA_from_PBD(k, n, PBD, check=True): r""" Return an `OA(k,n)` from a PBD. @@ -2031,7 +2031,7 @@ def OA_from_PBD(k,n,PBD, check=True): return OA -def OA_from_wider_OA(OA,k): +def OA_from_wider_OA(OA, k): r""" Return the first `k` columns of `OA`. @@ -2116,7 +2116,7 @@ class OAMainFunctions: ... NotImplementedError: I don't know how to build an OA(12,20)! """ - def __init__(self,*args,**kwds): + def __init__(self, *args, **kwds): r""" There is nothing here. @@ -2132,7 +2132,7 @@ def __init__(self,*args,**kwds): largest_available_k = staticmethod(largest_available_k) @staticmethod - def explain_construction(k,n,t=2): + def explain_construction(k, n, t=2): r""" Return a string describing how to builds an `OA(k,n)`. @@ -2150,7 +2150,7 @@ def explain_construction(k,n,t=2): return orthogonal_array(k,n,t,explain_construction=True) @staticmethod - def build(k,n,t=2,resolvable=False): + def build(k, n, t=2, resolvable=False): r""" Return an `OA(k,n)` of strength `t`. @@ -2191,7 +2191,7 @@ def build(k,n,t=2,resolvable=False): return orthogonal_array(k,n,t,resolvable=resolvable) @staticmethod - def exists(k,n,t=2): + def exists(k, n, t=2): r""" Return the existence status of an `OA(k,n)`. @@ -2220,7 +2220,7 @@ def exists(k,n,t=2): return orthogonal_array(k,n,t,existence=True) @staticmethod - def is_available(k,n,t=2): + def is_available(k, n, t=2): r""" Return whether Sage can build an `OA(k,n)`. diff --git a/src/sage/combinat/designs/orthogonal_arrays_build_recursive.py b/src/sage/combinat/designs/orthogonal_arrays_build_recursive.py index 937076ebb07..2bfd385492c 100644 --- a/src/sage/combinat/designs/orthogonal_arrays_build_recursive.py +++ b/src/sage/combinat/designs/orthogonal_arrays_build_recursive.py @@ -35,7 +35,7 @@ from .orthogonal_arrays import orthogonal_array, wilson_construction, is_orthogonal_array -def construction_3_3(k,n,m,i,explain_construction=False): +def construction_3_3(k, n, m, i, explain_construction=False): r""" Return an `OA(k,nm+i)`. @@ -97,7 +97,7 @@ def construction_3_3(k,n,m,i,explain_construction=False): return OA -def construction_3_4(k,n,m,r,s,explain_construction=False): +def construction_3_4(k, n, m, r, s, explain_construction=False): r""" Return a `OA(k,nm+rs)`. @@ -180,7 +180,7 @@ def construction_3_4(k,n,m,r,s,explain_construction=False): return OA -def construction_3_5(k,n,m,r,s,t,explain_construction=False): +def construction_3_5(k, n, m, r, s, t, explain_construction=False): r""" Return an `OA(k,nm+r+s+t)`. @@ -275,7 +275,7 @@ def construction_3_5(k,n,m,r,s,t,explain_construction=False): return OA -def construction_3_6(k,n,m,i,explain_construction=False): +def construction_3_6(k, n, m, i, explain_construction=False): r""" Return a `OA(k,nm+i)`. @@ -578,7 +578,7 @@ def construction_q_x(k, q, x, check=True, explain_construction=False): return OA -def thwart_lemma_3_5(k,n,m,a,b,c,d=0,complement=False,explain_construction=False): +def thwart_lemma_3_5(k, n, m, a, b, c, d=0, complement=False, explain_construction=False): r""" Return an `OA(k,nm+a+b+c+d)`. @@ -757,7 +757,7 @@ def thwart_lemma_3_5(k,n,m,a,b,c,d=0,complement=False,explain_construction=False return wilson_construction(OA,k,n,m,sizes, check=False) -def thwart_lemma_4_1(k,n,m,explain_construction=False): +def thwart_lemma_4_1(k, n, m, explain_construction=False): r""" Return an `OA(k,nm+4(n-2))`. @@ -886,7 +886,7 @@ def thwart_lemma_4_1(k,n,m,explain_construction=False): return wilson_construction(OA,k,n,m,[n-2,]*4,check=False) -def three_factor_product(k,n1,n2,n3,check=False,explain_construction=False): +def three_factor_product(k, n1, n2, n3, check=False, explain_construction=False): r""" Return an `OA(k+1,n_1n_2n_3)`. @@ -1010,7 +1010,7 @@ def three_factor_product(k,n1,n2,n3,check=False,explain_construction=False): " A three-factor product construction for mutually orthogonal latin squares,\n" + " https://arxiv.org/abs/1401.1466").format(n1, n2, n3) - def assert_c_partition(classs,k,n,c): + def assert_c_partition(classs, k, n, c): r""" Makes sure that ``classs`` contains blocks `B` of size `k` such that the list of ``B[i]`` covers `[n]` exactly `c` times for every index `i`. @@ -1021,7 +1021,7 @@ def assert_c_partition(classs,k,n,c): for p in zip(*classs): assert all(x == i//c for i,x in enumerate(sorted(p))), "A class is not c(={})-parallel".format(c) - def product_with_parallel_classes(OA1,k,g1,g2,g1_parall,parall,check=True): + def product_with_parallel_classes(OA1, k, g1, g2, g1_parall, parall, check=True): r""" Return the product of two OA while keeping track of parallel classes. @@ -1203,7 +1203,7 @@ def _reorder_matrix(matrix): return list(zip(*matrix)) -def brouwer_separable_design(k,t,q,x,check=False,verbose=False,explain_construction=False): +def brouwer_separable_design(k, t, q, x, check=False, verbose=False, explain_construction=False): r""" Return a `OA(k,t(q^2+q+1)+x)` using Brouwer's result on separable designs. diff --git a/src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx b/src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx index f7f3502548b..dc9c278cd72 100644 --- a/src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx +++ b/src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx @@ -116,7 +116,7 @@ def find_recursive_construction(k, n): return False -cpdef find_product_decomposition(int k,int n): +cpdef find_product_decomposition(int k, int n): r""" Find `n_1n_2=n` to obtain an `OA(k,n)` by the product construction. @@ -157,7 +157,7 @@ cpdef find_product_decomposition(int k,int n): return wilson_construction, (None,k,n1,n2,(),False) return False -cpdef find_wilson_decomposition_with_one_truncated_group(int k,int n): +cpdef find_wilson_decomposition_with_one_truncated_group(int k, int n): r""" Find `rm+u=n` to obtain an `OA(k,n)` by Wilson's construction with one truncated column. @@ -206,7 +206,7 @@ cpdef find_wilson_decomposition_with_one_truncated_group(int k,int n): return False -cpdef find_wilson_decomposition_with_two_truncated_groups(int k,int n): +cpdef find_wilson_decomposition_with_two_truncated_groups(int k, int n): r""" Find `rm+r_1+r_2=n` to obtain an `OA(k,n)` by Wilson's construction with two truncated columns. @@ -268,7 +268,7 @@ cpdef find_wilson_decomposition_with_two_truncated_groups(int k,int n): return wilson_construction, (None,k,r,m,(r1,r2),False) return False -cpdef find_construction_3_3(int k,int n): +cpdef find_construction_3_3(int k, int n): r""" Find a decomposition for construction 3.3 from [AC07]_. @@ -398,7 +398,7 @@ cpdef find_construction_3_5(int k, int n): from sage.combinat.designs.orthogonal_arrays_build_recursive import construction_3_5 return construction_3_5, (k,nn,mm,r,s,t) -cpdef find_construction_3_6(int k,int n): +cpdef find_construction_3_6(int k, int n): r""" Find a decomposition for construction 3.6 from [AC07]_. @@ -439,7 +439,7 @@ cpdef find_construction_3_6(int k,int n): from sage.combinat.designs.orthogonal_arrays_build_recursive import construction_3_6 return construction_3_6, (k,nn,mm,i) -cpdef find_q_x(int k,int n): +cpdef find_q_x(int k, int n): r""" Find integers `q,x` such that the `q-x` construction yields an `OA(k,n)`. @@ -492,7 +492,7 @@ cpdef find_q_x(int k,int n): return construction_q_x, (k,q,x) return False -cpdef find_thwart_lemma_3_5(int k,int N): +cpdef find_thwart_lemma_3_5(int k, int N): r""" Find the values on which Lemma 3.5 from [Thwarts]_ applies. @@ -613,7 +613,7 @@ cpdef find_thwart_lemma_3_5(int k,int N): return False -cpdef find_thwart_lemma_4_1(int k,int n): +cpdef find_thwart_lemma_4_1(int k, int n): r""" Find a decomposition for Lemma 4.1 from [Thwarts]_. @@ -662,7 +662,7 @@ cpdef find_thwart_lemma_4_1(int k,int n): return False -cpdef find_three_factor_product(int k,int n): +cpdef find_three_factor_product(int k, int n): r""" Find `n_1n_2n_3=n` to obtain an `OA(k,n)` by the three-factor product from [DukesLing14]_. @@ -707,7 +707,7 @@ cpdef find_three_factor_product(int k,int n): return False -cpdef find_brouwer_separable_design(int k,int n): +cpdef find_brouwer_separable_design(int k, int n): r""" Find `t(q^2+q+1)+x=n` to obtain an `OA(k,n)` by Brouwer's separable design construction. @@ -878,7 +878,7 @@ def int_as_sum(int value, list S, int k_max): return None -cpdef find_brouwer_van_rees_with_one_truncated_column(int k,int n): +cpdef find_brouwer_van_rees_with_one_truncated_column(int k, int n): r""" Find `rm+x_1+...+x_c=n` such that the Brouwer-van Rees constructions yields a `OA(k,n)`. @@ -947,7 +947,7 @@ cpdef find_brouwer_van_rees_with_one_truncated_column(int k,int n): return False from sage.combinat.designs.designs_pyx cimport _OA_cache, _OA_cache_size -cdef int is_available(int k,int n) except -1: +cdef int is_available(int k, int n) except -1: r""" Return whether Sage can build an OA(k,n) diff --git a/src/sage/combinat/designs/resolvable_bibd.py b/src/sage/combinat/designs/resolvable_bibd.py index ccc11176d54..c6e0bbee33b 100644 --- a/src/sage/combinat/designs/resolvable_bibd.py +++ b/src/sage/combinat/designs/resolvable_bibd.py @@ -56,7 +56,7 @@ from sage.misc.unknown import Unknown -def resolvable_balanced_incomplete_block_design(v,k,existence=False): +def resolvable_balanced_incomplete_block_design(v, k, existence=False): r""" Return a resolvable BIBD of parameters `v,k`. @@ -141,7 +141,7 @@ def resolvable_balanced_incomplete_block_design(v,k,existence=False): raise NotImplementedError("I don't know how to build a ({},{},1)-RBIBD!".format(v,3)) -def kirkman_triple_system(v,existence=False): +def kirkman_triple_system(v, existence=False): r""" Return a Kirkman Triple System on `v` points. @@ -368,7 +368,7 @@ def kirkman_triple_system(v,existence=False): return KTS -def v_4_1_rbibd(v,existence=False): +def v_4_1_rbibd(v, existence=False): r""" Return a `(v,4,1)`-RBIBD. @@ -439,7 +439,7 @@ def v_4_1_rbibd(v,existence=False): return BIBD -def PBD_4_7(v,check=True, existence=False): +def PBD_4_7(v, check=True, existence=False): r""" Return a `(v,\{4,7\})`-PBD. @@ -686,7 +686,7 @@ def PBD_4_7(v,check=True, existence=False): copy=False) -def PBD_4_7_from_Y(gdd,check=True): +def PBD_4_7_from_Y(gdd, check=True): r""" Return a `(3v+1,\{4,7\})`-PBD from a `(v,\{4,5,7\},\NN-\{3,6,10\})`-GDD. diff --git a/src/sage/combinat/designs/steiner_quadruple_systems.py b/src/sage/combinat/designs/steiner_quadruple_systems.py index 9576ae5f5aa..af60e00b63e 100644 --- a/src/sage/combinat/designs/steiner_quadruple_systems.py +++ b/src/sage/combinat/designs/steiner_quadruple_systems.py @@ -540,7 +540,7 @@ def P(alpha, m): return pairs -def _missing_pair(n,l): +def _missing_pair(n, l): r""" Return the smallest `(x,x+1)` that is not contained in `l`. diff --git a/src/sage/combinat/designs/subhypergraph_search.pyx b/src/sage/combinat/designs/subhypergraph_search.pyx index 8de300efe2a..82be44dcd13 100644 --- a/src/sage/combinat/designs/subhypergraph_search.pyx +++ b/src/sage/combinat/designs/subhypergraph_search.pyx @@ -172,7 +172,7 @@ cdef void h_free(hypergraph h) noexcept: h.set_space = NULL h.sets = NULL -cdef hypergraph h_init(int n,list H) noexcept: +cdef hypergraph h_init(int n, list H) noexcept: r""" Build a C hypergraph from a list `H` of sets on `\{0,...,n-1\}`. """ @@ -210,7 +210,7 @@ cdef hypergraph h_init(int n,list H) noexcept: return h -cdef inline void permute(hypergraph * h,int n1,int n2) noexcept: +cdef inline void permute(hypergraph * h, int n1, int n2) noexcept: r""" Permutes two points of h inplace. @@ -265,7 +265,7 @@ cdef void trace_hypergraph64(hypergraph * h, int n, hypergraph * tmp) noexcept: tmp.limbs = 1 -cdef int is_subhypergraph_admissible(hypergraph h1,hypergraph * h2_trace,int n,hypergraph tmp1) noexcept: +cdef int is_subhypergraph_admissible(hypergraph h1, hypergraph * h2_trace, int n, hypergraph tmp1) noexcept: r""" If there are `c` sets of size `k` containing `S\subseteq \{0,...,n-1\}` in `h2`, then there must be `>=c` sets of size `k` containing `S` in h1. This @@ -308,7 +308,7 @@ cdef int cmp_128_bits(const void * a, const void * b) noexcept nogil: else: return -1 -cdef int is_induced_admissible64(hypergraph h1,hypergraph * h2_induced,int n,hypergraph tmp1) noexcept: +cdef int is_induced_admissible64(hypergraph h1, hypergraph * h2_induced, int n, hypergraph tmp1) noexcept: r""" Test if the hypergraph induced in h1 by 0,...,n-1 is equal to the hypergraph induced in h2 by 0,...,n-1. @@ -344,7 +344,7 @@ cdef class SubHypergraphSearch: cdef hypergraph * h2_traces cdef hypergraph * h2_induced - def __cinit__(self,H1,H2,induced): + def __cinit__(self, H1, H2, induced): r""" See the documentation's class. diff --git a/src/sage/combinat/enumeration_mod_permgroup.pyx b/src/sage/combinat/enumeration_mod_permgroup.pyx index b2f713228ed..bcc3236205b 100644 --- a/src/sage/combinat/enumeration_mod_permgroup.pyx +++ b/src/sage/combinat/enumeration_mod_permgroup.pyx @@ -121,7 +121,7 @@ cpdef int lex_cmp(ClonableIntArray v1, ClonableIntArray v2) noexcept: 1 """ cdef int i - cdef int step = min(v1._len,v2._len) + cdef int step = min(v1._len, v2._len) for i in range(step): if v1._list[i] != v2._list[i]: break diff --git a/src/sage/combinat/gray_codes.py b/src/sage/combinat/gray_codes.py index 63e366c2cb5..db1539d2376 100644 --- a/src/sage/combinat/gray_codes.py +++ b/src/sage/combinat/gray_codes.py @@ -103,7 +103,7 @@ def product(m): j = f[0] -def combinations(n,t): +def combinations(n, t): r""" Iterator through the switches of the revolving door algorithm. @@ -177,7 +177,7 @@ def combinations(n,t): TESTS:: - sage: def check_sets_from_iter(n,k): + sage: def check_sets_from_iter(n, k): ....: l = [] ....: s = set(range(k)) ....: l.append(frozenset(s)) @@ -209,7 +209,7 @@ def combinations(n,t): return _revolving_door_even(n,t) -def _revolving_door_odd(n,t): +def _revolving_door_odd(n, t): r""" Revolving door switch for odd `t`. @@ -255,7 +255,7 @@ def _revolving_door_odd(n,t): break -def _revolving_door_even(n,t): +def _revolving_door_even(n, t): r""" Revolving door algorithm for even `t`. diff --git a/src/sage/combinat/k_tableau.py b/src/sage/combinat/k_tableau.py index 2c048fe38fc..de6b783f15b 100644 --- a/src/sage/combinat/k_tableau.py +++ b/src/sage/combinat/k_tableau.py @@ -4179,7 +4179,7 @@ def add_marking( cls, unmarkedT, marking, k, weight ): sage: StrongTableaux.add_marking([], [], 2, []) [] """ - def msgn(c,v): + def msgn(c, v): if c in marking: return -v else: diff --git a/src/sage/combinat/knutson_tao_puzzles.py b/src/sage/combinat/knutson_tao_puzzles.py index f7a7c513c52..7e226bffee3 100644 --- a/src/sage/combinat/knutson_tao_puzzles.py +++ b/src/sage/combinat/knutson_tao_puzzles.py @@ -2092,7 +2092,7 @@ def _fill_strip(self, nw_labels, ne_label, pieces, final_pieces=None): [[0/\0 0\/0, 0/0\0]] sage: sorted(ps._fill_strip(('0',), '0', ps._rhombus_pieces), key=str) [[0/\0 0\/0], [0/\0 1\/10]] - sage: sorted(ps._fill_strip(('0','1'), '0', ps._rhombus_pieces), key =str) + sage: sorted(ps._fill_strip(('0','1'), '0', ps._rhombus_pieces), key=str) [[1/\0 0\/1, 0/\0 0\/0], [1/\0 0\/1, 0/\0 1\/10]] TESTS:: diff --git a/src/sage/combinat/misc.py b/src/sage/combinat/misc.py index d04b615be80..55a4b891bd2 100644 --- a/src/sage/combinat/misc.py +++ b/src/sage/combinat/misc.py @@ -127,7 +127,7 @@ def hide(self, i): self.next_value[self.prev_value[i]] = self.next_value[i] self.prev_value[self.next_value[i]] = self.prev_value[i] - def unhide(self,i): + def unhide(self, i): """ TESTS:: diff --git a/src/sage/combinat/multiset_partition_into_sets_ordered.py b/src/sage/combinat/multiset_partition_into_sets_ordered.py index 211837f0b05..67fbcb4e70a 100755 --- a/src/sage/combinat/multiset_partition_into_sets_ordered.py +++ b/src/sage/combinat/multiset_partition_into_sets_ordered.py @@ -3520,7 +3520,7 @@ def e(self, i): w = w.e(i) return P.element_class(P, (w, breaks)) - def f(self,i): + def f(self, i): r""" Return `f_i` on ``self``. diff --git a/src/sage/combinat/ncsf_qsym/combinatorics.py b/src/sage/combinat/ncsf_qsym/combinatorics.py index ef930596ab8..605ad56aa12 100644 --- a/src/sage/combinat/ncsf_qsym/combinatorics.py +++ b/src/sage/combinat/ncsf_qsym/combinatorics.py @@ -51,7 +51,7 @@ def coeff_pi(J, I): return prod(prod(K.partial_sums()) for K in J.refinement_splitting(I)) -def coeff_lp(J,I): +def coeff_lp(J, I): r""" Return the coefficient `lp_{J,I}` as defined in [NCSF]_. @@ -73,7 +73,7 @@ def coeff_lp(J,I): return prod(K[-1] for K in J.refinement_splitting(I)) -def coeff_ell(J,I): +def coeff_ell(J, I): r""" Return the coefficient `\ell_{J,I}` as defined in [NCSF]_. diff --git a/src/sage/combinat/partition_tuple.py b/src/sage/combinat/partition_tuple.py index 0e0e8e4aae9..527df5a2728 100644 --- a/src/sage/combinat/partition_tuple.py +++ b/src/sage/combinat/partition_tuple.py @@ -944,7 +944,7 @@ def cells(self): """ return [(c,a,b) for c in range(len(self)) for (a,b) in self[c].cells()] - def content(self, k,r,c, multicharge): + def content(self, k, r, c, multicharge): r""" Return the content of the cell. @@ -977,7 +977,7 @@ def content(self, k,r,c, multicharge): """ return multicharge[k]-r+c - def content_tableau(self,multicharge): + def content_tableau(self, multicharge): """ Return the tableau which has (k,r,c)th entry equal to the content ``multicharge[k]-r+c`` of this cell. @@ -1191,7 +1191,7 @@ def garnir_tableau(self, *cell): g._garnir_cell = (comp,row,col) return g - def top_garnir_tableau(self,e,cell): + def top_garnir_tableau(self, e, cell): r""" Return the most dominant *standard* tableau which dominates the corresponding Garnir tableau and has the same residue that has shape @@ -1268,7 +1268,7 @@ def top_garnir_tableau(self,e,cell): from .tableau_tuple import StandardTableauTuple return StandardTableauTuple(t) - def arm_length(self, k,r,c): + def arm_length(self, k, r, c): """ Return the length of the arm of cell ``(k, r, c)`` in ``self``. @@ -1298,7 +1298,7 @@ def arm_length(self, k,r,c): except IndexError: raise ValueError("The cell %s is not in the diagram" % ((k,r,c),)) - def leg_length(self, k,r,c): + def leg_length(self, k, r, c): """ Return the length of the leg of cell ``(k, r, c)`` in ``self``. @@ -1343,7 +1343,7 @@ def contains(self, mu): """ return mu.level() <= self.level() and all(self[c].contains(mu[c]) for c in range(len(mu))) - def hook_length(self, k,r,c): + def hook_length(self, k, r, c): r""" Return the length of the hook of cell ``(k, r, c)`` in the partition. @@ -1509,7 +1509,7 @@ def young_subgroup_generators(self): return gens @cached_method - def _initial_degree(self,e,multicharge): + def _initial_degree(self, e, multicharge): r""" Return the Brundan-Kleshchev-Wang degree of the initial tableau of shape ``self``. diff --git a/src/sage/combinat/path_tableaux/path_tableau.py b/src/sage/combinat/path_tableaux/path_tableau.py index 9d9177ee355..8d25be4a128 100644 --- a/src/sage/combinat/path_tableaux/path_tableau.py +++ b/src/sage/combinat/path_tableaux/path_tableau.py @@ -52,7 +52,7 @@ class PathTableau(ClonableArray, metaclass=InheritComparisonClasscallMetaclass): This is the abstract base class for a path tableau. """ @abstract_method - def local_rule(self,i): + def local_rule(self, i): r""" This is the abstract local rule defined in any coboundary category. @@ -216,7 +216,7 @@ def commutor(self, other, verbose=False): return (P(path[:m]), P(path[m-1:])) - def cactus(self,i,j): + def cactus(self, i, j): r""" Return the action of the generator `s_{i,j}` of the cactus group on ``self``. diff --git a/src/sage/combinat/path_tableaux/semistandard.py b/src/sage/combinat/path_tableaux/semistandard.py index 368caf54145..51ac4e4cbf8 100644 --- a/src/sage/combinat/path_tableaux/semistandard.py +++ b/src/sage/combinat/path_tableaux/semistandard.py @@ -173,7 +173,7 @@ def __init__(self, parent, st, check=True): elif isinstance(st, GelfandTsetlinPattern): w = list(st) w.reverse() - w = [(),*w] + w = [(), *w] elif isinstance(st, (Tableau,SkewTableau)): w = st.to_chain() diff --git a/src/sage/combinat/root_system/ambient_space.py b/src/sage/combinat/root_system/ambient_space.py index 0d00c45273f..d9afa05c169 100644 --- a/src/sage/combinat/root_system/ambient_space.py +++ b/src/sage/combinat/root_system/ambient_space.py @@ -197,7 +197,7 @@ def __call__(self, v): else: return CombinatorialFreeModule.__call__(self, v) - def __getitem__(self,i): + def __getitem__(self, i): """ Note that indexing starts at 1. diff --git a/src/sage/combinat/root_system/branching_rules.py b/src/sage/combinat/root_system/branching_rules.py index 91876ee8dd3..cf6b0012c85 100644 --- a/src/sage/combinat/root_system/branching_rules.py +++ b/src/sage/combinat/root_system/branching_rules.py @@ -136,7 +136,7 @@ def branch_weyl_character(chi, R, S, rule='default'): sage: B4 = WeylCharacterRing("B4", style='coroots') sage: A6 = WeylCharacterRing("A6", style='coroots') sage: A7 = WeylCharacterRing("A7", style='coroots') - sage: def try_default_rule(R,S): return [R(f).branch(S) for f in R.fundamental_weights()] + sage: def try_default_rule(R, S): return [R(f).branch(S) for f in R.fundamental_weights()] sage: try_default_rule(A2,A1) [A1(0) + A1(1), A1(0) + A1(1)] sage: try_default_rule(D4,B3) diff --git a/src/sage/combinat/root_system/extended_affine_weyl_group.py b/src/sage/combinat/root_system/extended_affine_weyl_group.py index b1d35c86f7a..9e72863e5bf 100644 --- a/src/sage/combinat/root_system/extended_affine_weyl_group.py +++ b/src/sage/combinat/root_system/extended_affine_weyl_group.py @@ -2035,7 +2035,7 @@ def __init__(self, E): """ # note that we have to use the multiplicative version of the translation lattice # and change the twist to deal with this - def twist(w,l): + def twist(w, l): return E.exp_lattice()(w.action(l.value)) GroupSemidirectProduct.__init__(self, E.exp_lattice(), E.classical_weyl(), twist=twist, act_to_right=False, prefix0=E._prefixt, print_tuple=E._print_tuple, category=E.Realizations()) @@ -2220,7 +2220,7 @@ def __init__(self, E): sage: W0P = ExtendedAffineWeylGroup(['D',3,2]).W0P() sage: TestSuite(W0P).run() """ - def twist(w,l): + def twist(w, l): return E.exp_lattice()(w.action(l.value)) GroupSemidirectProduct.__init__(self, E.classical_weyl(), E.exp_lattice(), twist=twist, act_to_right=True, prefix1=E._prefixt, print_tuple=E._print_tuple, category=E.Realizations()) @@ -2418,7 +2418,7 @@ def __init__(self, E): sage: WF = ExtendedAffineWeylGroup(['D',3,2]).WF() sage: TestSuite(WF).run() """ - def twist(g,w): + def twist(g, w): return g.act_on_affine_weyl(w) GroupSemidirectProduct.__init__(self, E.affine_weyl(), E.fundamental_group(), twist=twist, act_to_right=False, print_tuple=E._print_tuple, category=E.Realizations()) @@ -2579,7 +2579,7 @@ def __init__(self, E): sage: FW = ExtendedAffineWeylGroup(['D',3,2]).FW() sage: TestSuite(FW).run() """ - def twist(g,w): + def twist(g, w): return g.act_on_affine_weyl(w) GroupSemidirectProduct.__init__(self, E.fundamental_group(), E.affine_weyl(), twist=twist, act_to_right=True, print_tuple=E._print_tuple, category=E.Realizations()) @@ -2753,7 +2753,7 @@ def __init__(self, E): """ # note that we have to use the multiplicative version of the translation lattice # and change the twist to deal with this - def twist(w,l): + def twist(w, l): return E.exp_dual_lattice()(w.action(l.value)) GroupSemidirectProduct.__init__(self, E.exp_dual_lattice(), E.dual_classical_weyl(), twist=twist, act_to_right=False, prefix0=E._prefixt, print_tuple=E._print_tuple, category=E.Realizations()) @@ -2924,7 +2924,7 @@ def __init__(self, E): """ # note that we have to use the multiplicative version of the translation lattice # and change the twist to deal with this - def twist(w,l): + def twist(w, l): return E.exp_dual_lattice()(w.action(l.value)) GroupSemidirectProduct.__init__(self, E.dual_classical_weyl(), E.exp_dual_lattice(), twist=twist, act_to_right=True, prefix1=E._prefixt, print_tuple=E._print_tuple, category=E.Realizations()) diff --git a/src/sage/combinat/root_system/hecke_algebra_representation.py b/src/sage/combinat/root_system/hecke_algebra_representation.py index fd40907d33e..a2a5d4421dc 100644 --- a/src/sage/combinat/root_system/hecke_algebra_representation.py +++ b/src/sage/combinat/root_system/hecke_algebra_representation.py @@ -464,7 +464,7 @@ def _test_relations(self, **options): q2 = self._q2 T = self - def Ti(x,i,c): + def Ti(x, i, c): return T[i](x)+c*x try: diff --git a/src/sage/combinat/root_system/pieri_factors.py b/src/sage/combinat/root_system/pieri_factors.py index 36dc4a332f2..fa97defb73e 100644 --- a/src/sage/combinat/root_system/pieri_factors.py +++ b/src/sage/combinat/root_system/pieri_factors.py @@ -427,7 +427,7 @@ def maximal_elements_combinatorial(self): """ return [self.W.from_reduced_word(range(self.W.cartan_type().n, 0, -1))] - def stanley_symm_poly_weight(self,w): + def stanley_symm_poly_weight(self, w): r""" EXAMPLES:: diff --git a/src/sage/combinat/root_system/reflection_group_complex.py b/src/sage/combinat/root_system/reflection_group_complex.py index 32f57d5da95..1d2641d0c65 100644 --- a/src/sage/combinat/root_system/reflection_group_complex.py +++ b/src/sage/combinat/root_system/reflection_group_complex.py @@ -323,7 +323,7 @@ def __init__(self, W_types, index_set=None, hyperplane_index_set=None, reflectio raise ValueError("the given reflection index set (= %s) does not have the right size" % self._index_set.values()) self._reflection_index_set_inverse = {i: ii for ii,i in enumerate(self._reflection_index_set)} - def _irrcomp_repr_(self,W_type): + def _irrcomp_repr_(self, W_type): r""" Return the string representation of an irreducible component of ``self``. @@ -703,7 +703,7 @@ def reflections(self): return Family(self._reflection_index_set, lambda i: T[self._reflection_index_set_inverse[i]]) - def reflection(self,i): + def reflection(self, i): r""" Return the ``i``-th reflection of ``self``. @@ -1725,7 +1725,7 @@ def action_on_root(w, beta): return beta * w.to_matrix() @cached_function - def invariant_value(i,j): + def invariant_value(i, j): if i > j: return invariant_value(j,i).conjugate() val = sum(action_on_root(w, Delta[i]) * action_on_root(w, Delta[j]).conjugate() @@ -1782,7 +1782,7 @@ def invariant_form_standardization(self): """ return self.invariant_form().principal_square_root() - def set_reflection_representation(self,refl_repr=None): + def set_reflection_representation(self, refl_repr=None): r""" Set the reflection representation of ``self``. diff --git a/src/sage/combinat/root_system/weyl_characters.py b/src/sage/combinat/root_system/weyl_characters.py index d7f87d6f494..c8c44224741 100644 --- a/src/sage/combinat/root_system/weyl_characters.py +++ b/src/sage/combinat/root_system/weyl_characters.py @@ -2205,8 +2205,8 @@ def demazure_lusztig(self, i, v): sage: P. = PolynomialRing(QQ) sage: B2 = WeylCharacterRing("B2",style='coroots',base_ring=P); b2 = B2.ambient() - sage: def T1(f): return f.demazure_lusztig(1,v) - sage: def T2(f): return f.demazure_lusztig(2,v) + sage: def T1(f): return f.demazure_lusztig(1, v) + sage: def T2(f): return f.demazure_lusztig(2, v) sage: T1(T2(T1(T2(b2(1,-1))))) (v^2-v)*b2(0,-1) + v^2*b2(-1,1) sage: [T1(T1(f))==(v-1)*T1(f)+v*f for f in [b2(0,0), b2(1,0), b2(2,3)]] diff --git a/src/sage/combinat/sf/k_dual.py b/src/sage/combinat/sf/k_dual.py index ad7471ec001..6d8151c00ac 100644 --- a/src/sage/combinat/sf/k_dual.py +++ b/src/sage/combinat/sf/k_dual.py @@ -378,7 +378,7 @@ def one(self): """ return self.a_realization().one() - def retract(self,la): + def retract(self, la): r""" Give the retract map from the symmetric functions to the quotient ring of `k`-bounded symmetric functions. This method is here to make the TestSuite run @@ -492,7 +492,7 @@ def super_categories(self): class ParentMethods: - def retract(self,la): + def retract(self, la): r""" Give the retract map from the symmetric functions to the quotient ring of `k`-bounded symmetric functions. This method is here to make the TestSuite run diff --git a/src/sage/combinat/sf/sf.py b/src/sage/combinat/sf/sf.py index 9f15dd18fea..546a3d22367 100644 --- a/src/sage/combinat/sf/sf.py +++ b/src/sage/combinat/sf/sf.py @@ -1604,7 +1604,7 @@ def __init__(self, t, domain, codomain): sage: Sym = SymmetricFunctions(QQ['x']) sage: p = Sym.p(); s = Sym.s() - sage: def t(x) : [(p,c)] = x; return [ (p,2*c), (p.conjugate(), c) ] + sage: def t(x) : [(p, c)] = x; return [ (p, 2*c), (p.conjugate(), c) ] sage: f = sage.combinat.sf.sf.SymmetricaConversionOnBasis(t, p, s) sage: f(Partition([3,1])) s[2, 1, 1] + 2*s[3, 1] diff --git a/src/sage/combinat/sf/sfa.py b/src/sage/combinat/sf/sfa.py index 794f7a0cb42..8d911087b24 100644 --- a/src/sage/combinat/sf/sfa.py +++ b/src/sage/combinat/sf/sfa.py @@ -3783,7 +3783,7 @@ def omega(self): omega_involution = omega - def theta(self,a): + def theta(self, a): r""" Return the image of ``self`` under the theta endomorphism which sends `p_k` to `a \cdot p_k` for every positive integer `k`. diff --git a/src/sage/combinat/similarity_class_type.py b/src/sage/combinat/similarity_class_type.py index caa691ac559..de3ce6f7989 100644 --- a/src/sage/combinat/similarity_class_type.py +++ b/src/sage/combinat/similarity_class_type.py @@ -101,7 +101,7 @@ class type, it is also possible to compute the number of classes of that type sage: from sage.combinat.similarity_class_type import order_of_general_linear_group, centralizer_algebra_dim sage: q = ZZ['q'].gen() - sage: def simultaneous_similarity_classes(n,k): + sage: def simultaneous_similarity_classes(n, k): ....: return SimilarityClassTypes(n).sum(lambda la: q**(k*centralizer_algebra_dim(la)), invertible = True)/order_of_general_linear_group(n) sage: simultaneous_similarity_classes(3, 2) q^10 + q^8 + 2*q^7 + 2*q^6 + 2*q^5 + q^4 diff --git a/src/sage/combinat/sloane_functions.py b/src/sage/combinat/sloane_functions.py index 08897c8b6da..b9651829109 100644 --- a/src/sage/combinat/sloane_functions.py +++ b/src/sage/combinat/sloane_functions.py @@ -6366,7 +6366,7 @@ def _repr_(self): """ return "Linear second order recurrence. A051959." - def g(self,k): + def g(self, k): """ EXAMPLES:: diff --git a/src/sage/combinat/subset.py b/src/sage/combinat/subset.py index 6c8d923ce9f..d6cc38c5cd4 100644 --- a/src/sage/combinat/subset.py +++ b/src/sage/combinat/subset.py @@ -506,7 +506,7 @@ def __call__(self, el): else: return Parent.__call__(self, el) - def _element_constructor_(self,X): + def _element_constructor_(self, X): """ TESTS:: @@ -1148,7 +1148,7 @@ def __call__(self, el): else: return Parent.__call__(self, el) - def _element_constructor_(self,X): + def _element_constructor_(self, X): """ TESTS:: diff --git a/src/sage/combinat/subsets_pairwise.py b/src/sage/combinat/subsets_pairwise.py index d8fec5c1a0c..18f6e13a5a9 100644 --- a/src/sage/combinat/subsets_pairwise.py +++ b/src/sage/combinat/subsets_pairwise.py @@ -39,7 +39,7 @@ class PairwiseCompatibleSubsets(RecursivelyEnumeratedSet_forest): elements are pairwise relatively prime:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [4,5,6,8,9], predicate); P An enumerated set with a forest structure sage: P.list() @@ -91,7 +91,7 @@ def __init__(self, ambient, predicate, maximal=False, element_class=Set_object_e TESTS:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [4,5,6,8,9], predicate); P An enumerated set with a forest structure sage: import __main__; __main__.predicate = predicate @@ -113,7 +113,7 @@ def __eq__(self, other): TESTS:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [4,5,6,8,9], predicate); P An enumerated set with a forest structure sage: P == P @@ -131,7 +131,7 @@ def __contains__(self, subset): EXAMPLES:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [4,5,6,8,9], predicate); P An enumerated set with a forest structure sage: Set([5,8,9]) in P @@ -150,7 +150,7 @@ def post_process(self, subset_rest): TESTS:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [4,5,6,8,9], predicate); P An enumerated set with a forest structure sage: P.post_process( ((4,5), (9)) ) @@ -167,7 +167,7 @@ def children(self, subset_rest): TESTS:: sage: from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets - sage: def predicate(x,y): return gcd(x,y) == 1 + sage: def predicate(x, y): return gcd(x, y) == 1 sage: P = PairwiseCompatibleSubsets( [3,5,7,11,14], predicate); P An enumerated set with a forest structure sage: list(P.children( ((3,5), [14,11,7]) )) diff --git a/src/sage/combinat/tutorial.py b/src/sage/combinat/tutorial.py index ef77bf66d4e..c8d18942181 100644 --- a/src/sage/combinat/tutorial.py +++ b/src/sage/combinat/tutorial.py @@ -1314,7 +1314,7 @@ combinatorics, especially when combined with recursion. Here is how to generate all words of a given length on a given alphabet:: - sage: def words(alphabet,l): + sage: def words(alphabet, l): ....: if l == 0: ....: yield [] ....: else: diff --git a/src/sage/combinat/words/word_generators.py b/src/sage/combinat/words/word_generators.py index 5803709ba5b..05ccb242508 100644 --- a/src/sage/combinat/words/word_generators.py +++ b/src/sage/combinat/words/word_generators.py @@ -589,7 +589,7 @@ def FibonacciWord(self, alphabet=(0, 1), construction_method='recursive'): else: raise NotImplementedError - def _FibonacciWord_RecursiveConstructionIterator(self,alphabet=(0,1)): + def _FibonacciWord_RecursiveConstructionIterator(self, alphabet=(0, 1)): r""" Iterate over the symbols of the Fibonacci word, as defined by the following recursive construction: the Fibonacci word is the @@ -659,7 +659,7 @@ def FixedPointOfMorphism(self, morphism, first_letter): """ return WordMorphism(morphism).fixed_point(letter=first_letter) - def CodingOfRotationWord(self, alpha, beta, x=0, alphabet=(0,1)): + def CodingOfRotationWord(self, alpha, beta, x=0, alphabet=(0, 1)): r""" Return the infinite word obtained from the coding of rotation of parameters `(\alpha,\beta, x)` over the given two-letter alphabet. @@ -695,7 +695,7 @@ def CodingOfRotationWord(self, alpha, beta, x=0, alphabet=(0,1)): w = InfiniteWords(alphabet)(f, datatype='callable') return w - def _CodingOfRotationWord_function(self, n, alpha, beta, x=0, alphabet=(0,1)): + def _CodingOfRotationWord_function(self, n, alpha, beta, x=0, alphabet=(0, 1)): r""" Internal function that returns the symbol in position `n` of the coding of rotation word corresponding to the parameters `\alpha`, @@ -901,7 +901,7 @@ def CharacteristicSturmianWord(self, slope, alphabet=(0, 1), bits=None): datatype='iter') return w - def _CharacteristicSturmianWord_LetterIterator(self, cf, alphabet=(0,1)): + def _CharacteristicSturmianWord_LetterIterator(self, cf, alphabet=(0, 1)): r""" Return an iterator over the symbols of the characteristic Sturmian word of slope ``cf``. @@ -967,7 +967,7 @@ def _CharacteristicSturmianWord_LetterIterator(self, cf, alphabet=(0,1)): except StopIteration: return - def KolakoskiWord(self, alphabet=(1,2)): + def KolakoskiWord(self, alphabet=(1, 2)): r""" Return the Kolakoski word over the given alphabet and starting with the first letter of the alphabet. @@ -1392,7 +1392,7 @@ def RandomWord(self, n, m=2, alphabet=None): ChristoffelWord = LowerChristoffelWord - def UpperChristoffelWord(self, p, q, alphabet=(0,1)): + def UpperChristoffelWord(self, p, q, alphabet=(0, 1)): r""" Return the upper Christoffel word of slope `p/q`, where `p` and `q` are relatively prime nonnegative diff --git a/src/sage/crypto/boolean_function.pyx b/src/sage/crypto/boolean_function.pyx index 7f8f4b4fba0..1716c78f2d9 100644 --- a/src/sage/crypto/boolean_function.pyx +++ b/src/sage/crypto/boolean_function.pyx @@ -983,7 +983,7 @@ cdef class BooleanFunction(SageObject): self._sum_of_square_indicator = sum(a**2 for a in D) return self._sum_of_square_indicator - def annihilator(self,d, dim = False): + def annihilator(self, d, dim=False): r""" Return (if it exists) an annihilator of the boolean function of degree at most `d`, that is a Boolean polynomial `g` such that @@ -1054,7 +1054,7 @@ cdef class BooleanFunction(SageObject): else: return res - def algebraic_immunity(self, annihilator = False): + def algebraic_immunity(self, annihilator=False): """ Return the algebraic immunity of the Boolean function. diff --git a/src/sage/crypto/stream.py b/src/sage/crypto/stream.py index a9e94d63b24..1462295774e 100644 --- a/src/sage/crypto/stream.py +++ b/src/sage/crypto/stream.py @@ -95,7 +95,7 @@ def _repr_(self): """ return "LFSR cryptosystem over %s" % self._field - def encoding(self,M): + def encoding(self, M): S = self.cipher_domain() try: return S.encoding(M) @@ -160,7 +160,7 @@ def _repr_(self): """ return "Shrinking generator cryptosystem over %s" % self._field - def encoding(self,M): + def encoding(self, M): S = self.cipher_domain() try: return S.encoding(M) diff --git a/src/sage/data_structures/bitset.pxd b/src/sage/data_structures/bitset.pxd index 35343fa28ae..db627b294cd 100644 --- a/src/sage/data_structures/bitset.pxd +++ b/src/sage/data_structures/bitset.pxd @@ -12,7 +12,7 @@ from sage.data_structures.bitset_base cimport bitset_t # Python layer over bitset_t cdef class FrozenBitset: cdef bitset_t _bitset - cdef FrozenBitset _new(self,long int capacity) + cdef FrozenBitset _new(self, long int capacity) cpdef FrozenBitset _larger_capacity_(self, long size) cpdef long capacity(self) noexcept cpdef bint isempty(self) noexcept diff --git a/src/sage/data_structures/bounded_integer_sequences.pyx b/src/sage/data_structures/bounded_integer_sequences.pyx index 44635ad2364..96dd83b4f8e 100644 --- a/src/sage/data_structures/bounded_integer_sequences.pyx +++ b/src/sage/data_structures/bounded_integer_sequences.pyx @@ -1380,7 +1380,7 @@ def _biseq_stresstest(): cdef int branch cdef Py_ssize_t x, y, z from sage.misc.prandom import randint - cdef list L = [BoundedIntegerSequence(6, [randint(0,5) for z in range(randint(4,10))]) for y in range(100)] + cdef list L = [BoundedIntegerSequence(6, [randint(0, 5) for z in range(randint(4, 10))]) for y in range(100)] cdef BoundedIntegerSequence S, T while True: branch = randint(0,4) diff --git a/src/sage/databases/cremona.py b/src/sage/databases/cremona.py index 44c8fbcdc7f..ca859214155 100644 --- a/src/sage/databases/cremona.py +++ b/src/sage/databases/cremona.py @@ -1651,7 +1651,7 @@ def _init_allgens(self, ftpdata, largest_conductor=0): _db = None -def CremonaDatabase(name=None,mini=None,set_global=None): +def CremonaDatabase(name=None, mini=None, set_global=None): """ Initialize the Cremona database with name ``name``. If ``name`` is ``None`` it instead initializes large Cremona database (named 'cremona'), diff --git a/src/sage/databases/findstat.py b/src/sage/databases/findstat.py index 811a190db8f..1285569805e 100644 --- a/src/sage/databases/findstat.py +++ b/src/sage/databases/findstat.py @@ -1784,7 +1784,7 @@ def set_sage_code(self, value): EXAMPLES:: sage: q = findstat([(d, randint(1,1000)) for d in DyckWords(4)]) # optional -- internet - sage: q.set_sage_code("def statistic(x):\n return randint(1,1000)") # optional -- internet + sage: q.set_sage_code("def statistic(x):\n return randint(1, 1000)") # optional -- internet sage: print(q.sage_code()) # optional -- internet def statistic(x): return randint(1,1000) diff --git a/src/sage/databases/sql_db.py b/src/sage/databases/sql_db.py index fad05a0add9..3ee328c6cf9 100644 --- a/src/sage/databases/sql_db.py +++ b/src/sage/databases/sql_db.py @@ -296,7 +296,7 @@ def _create_print_table(cur, col_titles, **kwds): plot should be drawn by the object generated by a data slice. Note that plot kwds are permitted. The dictionary format is:: - {'column_name':((lambda x: plot_function(x)),**kwds)} + {'column_name':((lambda x: plot_function(x)), **kwds)} - ``relabel_cols`` -- dictionary to specify a relabeling of column headers. The dictionary format is:: @@ -629,7 +629,7 @@ def show(self, **kwds): plot should be drawn by the object generated by a data slice. Note that plot kwds are permitted. The dictionary format is:: - {'column_name':((lambda x: plot_function(x)),**kwds)} + {'column_name':((lambda x: plot_function(x)), **kwds)} - ``relabel_cols`` -- dictionary to specify a relabeling of column headers. The dictionary format is:: diff --git a/src/sage/doctest/sources.py b/src/sage/doctest/sources.py index 78c45195970..7589f62922b 100644 --- a/src/sage/doctest/sources.py +++ b/src/sage/doctest/sources.py @@ -1013,7 +1013,7 @@ def _update_quotetype(self, line): sage: print(FDS.quotetype) None """ - def _update_parens(start,end=None): + def _update_parens(start, end=None): self.paren_count += line.count("(",start,end) - line.count(")",start,end) self.bracket_count += line.count("[",start,end) - line.count("]",start,end) self.curly_count += line.count("{",start,end) - line.count("}",start,end) diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py index 8cd24f6611d..633f033b7f5 100644 --- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py @@ -2811,7 +2811,7 @@ def nth_preimage_tree(self, Q, n, **kwds): display_complex = True kwds["embed"] = embed else: - field_def = self.field_of_definition_preimage(Q,n) + field_def = self.field_of_definition_preimage(Q, n) fbar = self.change_ring(field_def) if display_complex: embed = field_def.embeddings(ComplexField())[0] @@ -2819,7 +2819,7 @@ def nth_preimage_tree(self, Q, n, **kwds): elif base_ring in FiniteFields(): if numerical: raise ValueError("can't solve numerically over a finite field, no embedding into CC") - field_def = self.field_of_definition_preimage(Q,n) + field_def = self.field_of_definition_preimage(Q, n) fbar = self.change_ring(field_def) # No embedding from finite field into C kwds["display_complex"] = False diff --git a/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py b/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py index 3ef9877e782..766dff990e0 100644 --- a/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py +++ b/src/sage/dynamics/arithmetic_dynamics/wehlerK3.py @@ -1299,7 +1299,7 @@ def sigmaX(self, P, **kwds): return Point return self.point(Point, False) - def sigmaY(self,P, **kwds): + def sigmaY(self, P, **kwds): r""" Return the involution on the Wehler K3 surfaces induced by the double covers. @@ -1579,7 +1579,7 @@ def phi(self, a, **kwds): kwds.update({"check":False}) return self.sigmaY(A, **kwds) - def psi(self,a, **kwds): + def psi(self, a, **kwds): r""" Evaluates the function `\psi = \sigma_x \circ \sigma_y`. @@ -2448,7 +2448,7 @@ def is_isomorphic(self, right): """ return self.defining_ideal() == right.defining_ideal() - def is_symmetric_orbit(self,orbit): + def is_symmetric_orbit(self, orbit): r""" Check to see if the orbit is symmetric (i.e. if one of the points on the orbit is fixed by '\sigma_x' or '\sigma_y'). diff --git a/src/sage/games/quantumino.py b/src/sage/games/quantumino.py index e40dc47f407..555f6901f4a 100644 --- a/src/sage/games/quantumino.py +++ b/src/sage/games/quantumino.py @@ -205,7 +205,7 @@ pentaminos.append(Polyomino([(0,0,0), (0,1,0), (1,1,0), (1,2,0), (1,2,1)], color='purple')) pentaminos.append(Polyomino([(0,1,0), (1,0,0), (1,1,0), (1,1,1), (1,2,0)], color='gray')) -def show_pentaminos(box=(5,8,2)): +def show_pentaminos(box=(5, 8, 2)): r""" Show the 17 3-D pentaminos included in the game and the `5 \times 8 \times 2` box where 16 of them must fit. @@ -278,7 +278,7 @@ class QuantuminoState(SageObject): Quantumino state where the following pentamino is put aside : Polyomino: [(0, 0, 0), (0, 1, 0), (0, 2, 0), (1, 0, 0), (1, 0, 1)], Color: green """ - def __init__(self, pentos, aside, box=(5,8,2)): + def __init__(self, pentos, aside, box=(5, 8, 2)): r""" EXAMPLES:: diff --git a/src/sage/geometry/cone.py b/src/sage/geometry/cone.py index c4b308adbfa..edb5aa3a3af 100644 --- a/src/sage/geometry/cone.py +++ b/src/sage/geometry/cone.py @@ -6796,7 +6796,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None, # Same thing, except when we're given a lattice. max_rays = 2*(lattice.dimension() - 1) - def random_min_max(l,u): + def random_min_max(l, u): r""" We need to handle two cases for the upper bounds, and we need to do the same thing for max_ambient_dim/max_rays. So we consolidate diff --git a/src/sage/geometry/cone_catalog.py b/src/sage/geometry/cone_catalog.py index d58302d5915..27a308193cf 100644 --- a/src/sage/geometry/cone_catalog.py +++ b/src/sage/geometry/cone_catalog.py @@ -530,7 +530,7 @@ def rearrangement(p, ambient_dim=None, lattice=None): cone should sum to a nonnegative number. In other words, the generators really are what we think they are:: - sage: def _has_rearrangement_property(v,p): + sage: def _has_rearrangement_property(v, p): ....: return sum( sorted(v)[0:p] ) >= 0 sage: all( ....: _has_rearrangement_property( @@ -713,7 +713,7 @@ def schur(ambient_dim=None, lattice=None): sage: ambient_dim = ZZ.random_element(10) sage: V = VectorSpace(QQ, ambient_dim) sage: rearrange = lambda z: V(sorted(z.list(),reverse=True)) - sage: def majorized_by(x,y): + sage: def majorized_by(x, y): ....: x = rearrange(x) ....: y = rearrange(y) ....: return (all(sum(x[0:i]) <= sum(y[0:i]) @@ -755,7 +755,7 @@ def schur(ambient_dim=None, lattice=None): ambient_dim, lattice = _preprocess_args(ambient_dim, lattice) - def _f(i,j): + def _f(i, j): if i == j: return 1 elif j - i == 1: diff --git a/src/sage/geometry/cone_critical_angles.py b/src/sage/geometry/cone_critical_angles.py index 9e5252a4bf9..964280e6205 100644 --- a/src/sage/geometry/cone_critical_angles.py +++ b/src/sage/geometry/cone_critical_angles.py @@ -676,7 +676,7 @@ def compute_gevp_M(gs, hs): True sage: G = matrix.column(gs) sage: H = matrix.column(hs) - sage: def _test_indexing(I,J): + sage: def _test_indexing(I, J): ....: G_I = G.matrix_from_columns(I) ....: H_J = H.matrix_from_columns(J) ....: return (G_I.transpose()*H_J == M[I,J] diff --git a/src/sage/geometry/polyhedron/double_description_inhomogeneous.py b/src/sage/geometry/polyhedron/double_description_inhomogeneous.py index 873b3b431ea..bc7d3b76539 100644 --- a/src/sage/geometry/polyhedron/double_description_inhomogeneous.py +++ b/src/sage/geometry/polyhedron/double_description_inhomogeneous.py @@ -7,7 +7,7 @@ H/V-representations of polyhedra. The latter works with cones only. This is sufficient to treat general polyhedra by the following construction: Any polyhedron can be embedded in one dimension higher -in the hyperplane `(1,*,\dots,*)`. The cone over the embedded +in the hyperplane `(1, *, \dots, *)`. The cone over the embedded polyhedron will be called the *homogenized cone* in the following. Conversely, intersecting the homogenized cone with the hyperplane `x_0=1` gives you back the original polyhedron. @@ -268,13 +268,13 @@ def _split_linear_subspace(self): return l1, L0 + [l - l[0] * l1 for l in L1] def _extract_Vrep(self, DD): - """ + r""" Extract the V-representation from the extremal rays of the homogeneous cone. The V-representation is the intersection of the cone generated by the rays `R` and ``self._linear_subspace`` with the - hyperplane `(1,*,*,...,*)`. + hyperplane `(1, *, *, \ldots, *)`. INPUT: diff --git a/src/sage/geometry/polyhedron/modules/formal_polyhedra_module.py b/src/sage/geometry/polyhedron/modules/formal_polyhedra_module.py index b17c2a1ce71..d7ef932a4cf 100644 --- a/src/sage/geometry/polyhedron/modules/formal_polyhedra_module.py +++ b/src/sage/geometry/polyhedron/modules/formal_polyhedra_module.py @@ -26,7 +26,7 @@ class FormalPolyhedraModule(CombinatorialFreeModule): EXAMPLES:: sage: from sage.geometry.polyhedron.modules.formal_polyhedra_module import FormalPolyhedraModule - sage: def closed_interval(a,b): return Polyhedron(vertices=[[a], [b]]) + sage: def closed_interval(a, b): return Polyhedron(vertices=[[a], [b]]) A three-dimensional vector space of polyhedra:: @@ -104,7 +104,7 @@ def __init__(self, base_ring, dimension, basis, category): TESTS:: sage: from sage.geometry.polyhedron.modules.formal_polyhedra_module import FormalPolyhedraModule - sage: def closed_interval(a,b): return Polyhedron(vertices=[[a], [b]]) + sage: def closed_interval(a, b): return Polyhedron(vertices=[[a], [b]]) sage: I01 = closed_interval(0, 1); I01.rename('conv([0], [1])') sage: I11 = closed_interval(1, 1); I11.rename('{[1]}') sage: I12 = closed_interval(1, 2); I12.rename('conv([1], [2])') @@ -125,7 +125,7 @@ def degree_on_basis(self, m): EXAMPLES:: sage: from sage.geometry.polyhedron.modules.formal_polyhedra_module import FormalPolyhedraModule - sage: def closed_interval(a,b): return Polyhedron(vertices=[[a], [b]]) + sage: def closed_interval(a, b): return Polyhedron(vertices=[[a], [b]]) sage: I01 = closed_interval(0, 1); I01.rename('conv([0], [1])') sage: I11 = closed_interval(1, 1); I11.rename('{[1]}') sage: I12 = closed_interval(1, 2); I12.rename('conv([1], [2])') diff --git a/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py b/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py index 27940e9a723..17fb5028df1 100644 --- a/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py +++ b/src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py @@ -789,7 +789,7 @@ def first_fundamental_form_inverse_coefficient(self, index): raise ValueError("Index %s out of bounds." % str(index)) @cached_method - def rotation(self,theta): + def rotation(self, theta): r""" Give the matrix of the rotation operator over a given angle `\theta` with respect to the natural frame. @@ -1185,7 +1185,7 @@ def second_fundamental_form_coefficients(self): self._compute_second_fundamental_form_coefficient(index) return coefficients - def second_fundamental_form(self,vector1,vector2): + def second_fundamental_form(self, vector1, vector2): r""" Evaluates the second fundamental form on two vectors on the surface. If the vectors are given by `v=(v^1,v^2)` and `w=(w^1,w^2)`, the @@ -1569,7 +1569,7 @@ def _create_pt_ode_system(self, curve, t): pt_ode.function = lambda t, v1_v2: [fun1(t, v1_v2[0], v1_v2[1]), fun2(t, v1_v2[0], v1_v2[1])] return pt_ode - def parallel_translation_numerical(self,curve,t,v0,tinterval): + def parallel_translation_numerical(self, curve, t, v0, tinterval): r""" Numerically solve the equations for parallel translation of a vector along a curve on the surface. Explicitly, the equations for parallel diff --git a/src/sage/geometry/triangulation/triangulations.cc b/src/sage/geometry/triangulation/triangulations.cc index 8ea306d8f7c..fa8805c9e9d 100644 --- a/src/sage/geometry/triangulation/triangulations.cc +++ b/src/sage/geometry/triangulation/triangulations.cc @@ -68,9 +68,9 @@ void triangulations::add_neighbours(const simplices & s) { for (flips::const_iterator f=bistellar_flips.begin(); f!=bistellar_flips.end(); ++f) { - goodcircuit goody(s,*f); + goodcircuit goody(s, *f); if (goody.is_good()) { - goody.do_flip(s,*f); + goody.do_flip(s, *f); compact_simplices new_triang=goody.get_neighbor(); add_triang_if_new(new_triang); } diff --git a/src/sage/graphs/base/static_dense_graph.pxd b/src/sage/graphs/base/static_dense_graph.pxd index 0e580a02b57..af3c4db74eb 100644 --- a/src/sage/graphs/base/static_dense_graph.pxd +++ b/src/sage/graphs/base/static_dense_graph.pxd @@ -1,4 +1,4 @@ from sage.data_structures.binary_matrix cimport binary_matrix_t from libc.stdint cimport uint32_t, uint64_t -cdef dict dense_graph_init(binary_matrix_t m, g, translation = ?, force_undirected = ?) +cdef dict dense_graph_init(binary_matrix_t m, g, translation=?, force_undirected=?) diff --git a/src/sage/graphs/convexity_properties.pxd b/src/sage/graphs/convexity_properties.pxd index f6c1b68b6b8..f435ae0aba0 100644 --- a/src/sage/graphs/convexity_properties.pxd +++ b/src/sage/graphs/convexity_properties.pxd @@ -12,4 +12,4 @@ cdef class ConvexityProperties: cdef _bitset_convex_hull(self, bitset_t hull) cpdef hull(self, list vertices) cdef _greedy_increase(self, bitset_t bs) - cpdef hull_number(self, value_only = *, verbose = *) + cpdef hull_number(self, value_only=*, verbose=*) diff --git a/src/sage/graphs/generic_graph_pyx.pyx b/src/sage/graphs/generic_graph_pyx.pyx index a350ceeba86..9f8b90d79ab 100644 --- a/src/sage/graphs/generic_graph_pyx.pyx +++ b/src/sage/graphs/generic_graph_pyx.pyx @@ -390,7 +390,7 @@ cdef inline double sqrt_approx(double x, double y, double xx, double yy) noexcep Assuming that `x > y > 0`, it is a taylor expansion at `x^2`. To see how 'bad' the approximation is:: - sage: def dist(x,y): + sage: def dist(x, y): ....: x = abs(x) ....: y = abs(y) ....: return max(x,y) + min(x,y)**2/(2*max(x,y)) diff --git a/src/sage/graphs/strongly_regular_db.pyx b/src/sage/graphs/strongly_regular_db.pyx index 0fa241ba218..72db0131c59 100644 --- a/src/sage/graphs/strongly_regular_db.pyx +++ b/src/sage/graphs/strongly_regular_db.pyx @@ -1840,7 +1840,7 @@ def eigenmatrix(int v, int k, int l, int mu): return Matrix(ZZ, [[1, k, v-k-1], [1, r, -r-1], [1, s, -s-1]]) -cpdef latin_squares_graph_parameters(int v, int k, int l,int mu): +cpdef latin_squares_graph_parameters(int v, int k, int l, int mu): r""" Check whether (v,k,l,mu)-strongly regular graph has parameters of an `L_g(n)` s.r.g. diff --git a/src/sage/groups/group_semidirect_product.py b/src/sage/groups/group_semidirect_product.py index 7287a79f614..5e06d203172 100644 --- a/src/sage/groups/group_semidirect_product.py +++ b/src/sage/groups/group_semidirect_product.py @@ -31,7 +31,7 @@ def _repr_(self): EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: GroupSemidirectProduct(WeylGroup(['A',2],prefix='s'), # indirect doctest ....: WeylGroup(['A',3],prefix='t'), twist) @@ -73,7 +73,7 @@ def __invert__(self): sage: from sage.groups.group_exp import GroupExp sage: EL = GroupExp()(L) sage: W = L.weyl_group(prefix='s') - sage: def twist(w,v): + sage: def twist(w, v): ....: return EL(w.action(v.value)) sage: G = GroupSemidirectProduct(W, EL, twist, prefix1='t') sage: g = G.an_element(); g @@ -105,7 +105,7 @@ def to_opposite(self): sage: W = L.weyl_group(prefix='s'); W Weyl Group of type ['A', 2] (as a matrix group acting on the root lattice) - sage: def twist(w,v): + sage: def twist(w, v): ....: return EL(w.action(v.value)) sage: G = GroupSemidirectProduct(W, EL, twist, prefix1='t'); G Semidirect product of Weyl Group of type ['A', 2] (as a matrix @@ -215,7 +215,7 @@ class GroupSemidirectProduct(CartesianProduct): sage: G = GL(2,QQ) sage: V = QQ^2 sage: EV = GroupExp()(V) # make a multiplicative version of V - sage: def twist(g,v): + sage: def twist(g, v): ....: return EV(g*v.value) sage: H = GroupSemidirectProduct(G, EV, twist=twist, prefix1='t'); H Semidirect product of General Linear Group of degree 2 @@ -229,7 +229,7 @@ class GroupSemidirectProduct(CartesianProduct): sage: # needs sage.rings.number_field sage: cartan_type = CartanType(['A',2]) sage: W = WeylGroup(cartan_type, prefix='s') - sage: def twist(w,v): + sage: def twist(w, v): ....: return w*v*(~w) sage: WW = GroupSemidirectProduct(W, W, twist=twist, print_tuple=True) sage: s = Family(cartan_type.index_set(), lambda i: W.simple_reflection(i)) @@ -252,7 +252,7 @@ def __init__(self, G, H, twist=None, act_to_right=True, prefix0=None, EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: import __main__ sage: __main__.twist = twist @@ -297,7 +297,7 @@ def act_to_right(self): EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: GroupSemidirectProduct(WeylGroup(['A',2],prefix='s'), ....: WeylGroup(['A',3],prefix='t'), twist).act_to_right() @@ -311,7 +311,7 @@ def _repr_(self): EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: GroupSemidirectProduct(WeylGroup(['A',2],prefix='s'), # indirect doctest ....: WeylGroup(['A',3],prefix='t'), twist) @@ -332,7 +332,7 @@ def _element_constructor_(self, x): r""" EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: import __main__ sage: __main__.twist = twist @@ -368,7 +368,7 @@ def one(self): sage: G = GL(2,QQ) sage: V = QQ^2 sage: EV = GroupExp()(V) # make a multiplicative version of V - sage: def twist(g,v): + sage: def twist(g, v): ....: return EV(g*v.value) sage: one = GroupSemidirectProduct(G, EV, twist=twist, prefix1='t').one(); one 1 @@ -418,7 +418,7 @@ def product(self, x, y): sage: G = GL(2,QQ) sage: V = QQ^2 sage: EV = GroupExp()(V) # make a multiplicative version of V - sage: def twist(g,v): + sage: def twist(g, v): ....: return EV(g*v.value) sage: S = GroupSemidirectProduct(G, EV, twist=twist, prefix1='t') sage: g = G([[2,1],[3,1]]); g @@ -491,7 +491,7 @@ def construction(self): EXAMPLES:: - sage: def twist(x,y): + sage: def twist(x, y): ....: return y sage: H = GroupSemidirectProduct(WeylGroup(['A',2],prefix='s'), ....: WeylGroup(['A',3],prefix='t'), twist) diff --git a/src/sage/groups/matrix_gps/isometries.py b/src/sage/groups/matrix_gps/isometries.py index 8e0df5f154b..a377066913b 100644 --- a/src/sage/groups/matrix_gps/isometries.py +++ b/src/sage/groups/matrix_gps/isometries.py @@ -288,7 +288,7 @@ class GroupActionOnSubmodule(Action): Echelon basis matrix: [0 1] """ - def __init__(self, MatrixGroup,submodule, is_left=False): + def __init__(self, MatrixGroup, submodule, is_left=False): r""" Initialize the action. diff --git a/src/sage/groups/perm_gps/partn_ref/data_structures.pyx b/src/sage/groups/perm_gps/partn_ref/data_structures.pyx index 919deebd0de..a3ef7193d3d 100644 --- a/src/sage/groups/perm_gps/partn_ref/data_structures.pyx +++ b/src/sage/groups/perm_gps/partn_ref/data_structures.pyx @@ -1311,7 +1311,7 @@ def SC_test_list_perms(list L, int n, int limit, bint gap, bint limit_complain, sage: def random_perm(x): ....: shuffle(x) ....: return x - sage: def test_stab_chain_fns_6(m,n,k, gap, contains): + sage: def test_stab_chain_fns_6(m, n, k, gap, contains): ....: perms = [] ....: for i in range(k): ....: perm = sum([random_perm(list(range(i*(n//m),min(n,(i+1)*(n//m))))) for i in range(m)], []) diff --git a/src/sage/groups/perm_gps/partn_ref/refinement_python.pyx b/src/sage/groups/perm_gps/partn_ref/refinement_python.pyx index 3a58fc0b9f6..c210c4c0521 100644 --- a/src/sage/groups/perm_gps/partn_ref/refinement_python.pyx +++ b/src/sage/groups/perm_gps/partn_ref/refinement_python.pyx @@ -345,11 +345,11 @@ class PythonObjectWrapper: EXAMPLES:: sage: from sage.groups.perm_gps.partn_ref.refinement_python import PythonObjectWrapper - sage: def acae(a,b): + sage: def acae(a, b): ....: return 0 - sage: def rari(a,b,c): + sage: def rari(a, b, c): ....: return 0 - sage: def cs(a,b,c,d,e): + sage: def cs(a, b, c, d, e): ....: return 0 sage: from sage.groups.perm_gps.partn_ref.refinement_python import PythonObjectWrapper sage: P = PythonObjectWrapper(None, acae, rari, cs, 7) # implicit doctest @@ -434,11 +434,11 @@ def aut_gp_and_can_lab_python(S, partition, n, EXAMPLES:: sage: from sage.groups.perm_gps.partn_ref.refinement_python import aut_gp_and_can_lab_python - sage: def acae(a,b): + sage: def acae(a, b): ....: return 0 - sage: def rari(a,b,c): + sage: def rari(a, b, c): ....: return 0 - sage: def cs(a,b,c,d,e): + sage: def cs(a, b, c, d, e): ....: return 0 sage: aut_gp_and_can_lab_python(None, [[0,1,2,3],[4,5]], 6, acae, rari, cs, True, True, True) ([[0, 1, 3, 2, 4, 5], @@ -513,16 +513,16 @@ def double_coset_python(S1, S2, partition1, ordering2, n, EXAMPLES:: sage: from sage.groups.perm_gps.partn_ref.refinement_python import double_coset_python - sage: def acae(a,b): + sage: def acae(a, b): ....: return 0 - sage: def rari(a,b,c): + sage: def rari(a, b, c): ....: return 0 - sage: def cs(a,b,c,d,e): + sage: def cs(a, b, c, d, e): ....: return 0 sage: double_coset_python(None, None, [[0,1,2,3],[4,5]], [2,3,1,5,0,4], 6, acae, rari, cs) [1, 2, 3, 5, 0, 4] - sage: def compare_lists(p1,p2,l1,l2,deg): + sage: def compare_lists(p1, p2, l1, l2, deg): ....: for i in range(len(l1)): ....: a1 = l1[p1[i]] ....: a2 = l2[p2[i]] diff --git a/src/sage/interfaces/mathematica.py b/src/sage/interfaces/mathematica.py index 71f233746e7..39c3aff9dc2 100644 --- a/src/sage/interfaces/mathematica.py +++ b/src/sage/interfaces/mathematica.py @@ -315,7 +315,7 @@ OTHER Examples:: - sage: def math_bessel_K(nu,x): + sage: def math_bessel_K(nu, x): ....: return mathematica(nu).BesselK(x).N(20) sage: math_bessel_K(2,I) # optional - mathematica -2.59288617549119697817 + 0.18048997206696202663*I diff --git a/src/sage/interfaces/mathics.py b/src/sage/interfaces/mathics.py index 3104fefe665..a6d39ad3c14 100644 --- a/src/sage/interfaces/mathics.py +++ b/src/sage/interfaces/mathics.py @@ -319,7 +319,7 @@ OTHER Examples:: - sage: def math_bessel_K(nu,x): + sage: def math_bessel_K(nu, x): ....: return mathics(nu).BesselK(x).N(20) sage: math_bessel_K(2,I) # optional - mathics -2.5928861754911969782 + 0.18048997206696202663 I diff --git a/src/sage/interfaces/maxima.py b/src/sage/interfaces/maxima.py index 96158d73039..08a8f37f751 100644 --- a/src/sage/interfaces/maxima.py +++ b/src/sage/interfaces/maxima.py @@ -1099,19 +1099,19 @@ def _object_function_class(self): # living in the symbolic ring and return something # that is hopefully coercible into the symbolic ring again. -# def sr_integral(self,*args): +# def sr_integral(self, *args): # return args[0]._maxima_().integrate(*args[1:]) -# def sr_sum(self,expression,v,a,b): +# def sr_sum(self, expression, v, a, b): # sum = "'sum(%s, %s, %s, %s)" % tuple([repr(expr._maxima_()) for expr in (expression, v, a, b)]) # result = self.simplify_sum(sum) # result = result.ratsimp() # return expression.parent()(result) -# def sr_limit(self,ex,*args): +# def sr_limit(self, ex, *args): # return ex._maxima_().limit(*args) -# def sr_tlimit(self,ex,*args): +# def sr_tlimit(self, ex, *args): # return ex._maxima_().tlimit(*args) diff --git a/src/sage/interfaces/tides.py b/src/sage/interfaces/tides.py index c1076496cea..42877ede9ee 100644 --- a/src/sage/interfaces/tides.py +++ b/src/sage/interfaces/tides.py @@ -340,7 +340,7 @@ def remove_repeated(l1, l2): j += 1 -def remove_constants(l1,l2): +def remove_constants(l1, l2): """ Given two lists, remove the entries in the first that are real constants, and also the corresponding elements in the second one. diff --git a/src/sage/libs/gap/element.pyx b/src/sage/libs/gap/element.pyx index c24408f401a..b35626b29e1 100644 --- a/src/sage/libs/gap/element.pyx +++ b/src/sage/libs/gap/element.pyx @@ -3251,7 +3251,7 @@ cdef class GapElement_RecordIterator(): # note the abs: negative values mean the rec keys are not sorted key_index = abs(GET_RNAM_PREC(self.rec.value, i)) key = char_to_str(GAP_CSTR_STRING(NAME_RNAM(key_index))) - cdef Obj result = GET_ELM_PREC(self.rec.value,i) + cdef Obj result = GET_ELM_PREC(self.rec.value, i) val = make_any_gap_element(self.rec.parent(), result) self.i += 1 return (key, val) diff --git a/src/sage/libs/giac/__init__.py b/src/sage/libs/giac/__init__.py index ef2267c4378..ba0be068152 100644 --- a/src/sage/libs/giac/__init__.py +++ b/src/sage/libs/giac/__init__.py @@ -88,7 +88,7 @@ def local_giacsettings(func): EXAMPLES:: - sage: def testf(a,b): + sage: def testf(a, b): ....: giacsettings.proba_epsilon = a/100 ....: giacsettings.threads = b+2 ....: return (giacsettings.proba_epsilon, giacsettings.threads) diff --git a/src/sage/libs/giac/auto-methods.pxi b/src/sage/libs/giac/auto-methods.pxi index 478c9c21bed..a7c214acab9 100644 --- a/src/sage/libs/giac/auto-methods.pxi +++ b/src/sage/libs/giac/auto-methods.pxi @@ -9,7 +9,7 @@ cdef class GiacMethods_base: :class:`Pygen` instead. """ - def Airy_Ai(self,*args): + def Airy_Ai(self, *args): r'''From Giac's documentation: Help for Airy_Ai: Airy_Ai(Real) @@ -18,9 +18,9 @@ cdef class GiacMethods_base: Ex1:Airy_Ai(0) Ex2:Airy_Ai(1.5) ''' - return GiacMethods['Airy_Ai'](self,*args) + return GiacMethods['Airy_Ai'](self, *args) - def Airy_Bi(self,*args): + def Airy_Bi(self, *args): r'''From Giac's documentation: Help for Airy_Bi: Airy_Bi(Real) @@ -29,9 +29,9 @@ cdef class GiacMethods_base: Ex1:Airy_Bi(1.5) Ex2:Airy_Bi(0) ''' - return GiacMethods['Airy_Bi'](self,*args) + return GiacMethods['Airy_Bi'](self, *args) - def Archive(self,*args): + def Archive(self, *args): r'''From Giac's documentation: Help for Archive: Archive(SeqVar) @@ -39,9 +39,9 @@ cdef class GiacMethods_base: See also: 1/ Unarchiv 2/ archive 3/ unarchive Ex1:Archive(a,b) ''' - return GiacMethods['Archive'](self,*args) + return GiacMethods['Archive'](self, *args) - def BesselJ(self,*args): + def BesselJ(self, *args): r'''From Giac's documentation: Help for BesselJ: BesselJ(Int(p),Real(x)) @@ -50,9 +50,9 @@ cdef class GiacMethods_base: Ex1:BesselJ(2,sqrt(2)) Ex2:BesselJ(-2,sqrt(2)) ''' - return GiacMethods['BesselJ'](self,*args) + return GiacMethods['BesselJ'](self, *args) - def BesselY(self,*args): + def BesselY(self, *args): r'''From Giac's documentation: Help for BesselY: BesselY(Int(p),Real(x)) @@ -61,9 +61,9 @@ cdef class GiacMethods_base: Ex1:BesselY(BesselJ(2,sqrt(2))) Ex2:BesselY(BesselJ(-2,sqrt(2))) ''' - return GiacMethods['BesselY'](self,*args) + return GiacMethods['BesselY'](self, *args) - def Beta(self,*args): + def Beta(self, *args): r'''From Giac's documentation: Help for Beta: Beta(Expr,Expr,[Expr],[1]) @@ -74,9 +74,9 @@ cdef class GiacMethods_base: Ex3:Beta(3,2,0.5) Ex4:Beta(3,2,0.5,1) ''' - return GiacMethods['Beta'](self,*args) + return GiacMethods['Beta'](self, *args) - def BlockDiagonal(self,*args): + def BlockDiagonal(self, *args): r'''From Giac's documentation: Help for BlockDiagonal: BlockDiagonal(Lst(l)||Mtrx(A)) @@ -85,9 +85,9 @@ cdef class GiacMethods_base: Ex1:BlockDiagonal([[1,2],[3,4]]) Ex2:BlockDiagonal([1,2,3]) ''' - return GiacMethods['BlockDiagonal'](self,*args) + return GiacMethods['BlockDiagonal'](self, *args) - def Ci(self,*args): + def Ci(self, *args): r'''From Giac's documentation: Help for Ci: Ci(Expr) @@ -95,9 +95,9 @@ cdef class GiacMethods_base: See also: 1/ Ei 2/ Si 3/ Li Ex1:Ci(1.0) ''' - return GiacMethods['Ci'](self,*args) + return GiacMethods['Ci'](self, *args) - def Circle(self,*args): + def Circle(self, *args): r'''From Giac's documentation: Help for Circle: Circle(Real(xc),Real(yc),Real(r),[Intg(option)]) @@ -107,9 +107,9 @@ cdef class GiacMethods_base: Ex2:Circle(0,1,1,0) Ex3:Circle(0,1,1,1) ''' - return GiacMethods['Circle'](self,*args) + return GiacMethods['Circle'](self, *args) - def Col(self,*args): + def Col(self, *args): r'''From Giac's documentation: Help for Col: Col(NULL) @@ -117,9 +117,9 @@ cdef class GiacMethods_base: See also: 1/ Row Ex1:Col() ''' - return GiacMethods['Col'](self,*args) + return GiacMethods['Col'](self, *args) - def CopyVar(self,*args): + def CopyVar(self, *args): r'''From Giac's documentation: Help for CopyVar: CopyVar(Var(var1),Var(var2)) @@ -127,9 +127,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:CopyVar(A,B) ''' - return GiacMethods['CopyVar'](self,*args) + return GiacMethods['CopyVar'](self, *args) - def Dirac(self,*args): + def Dirac(self, *args): r'''From Giac's documentation: Help for Dirac: Dirac(Real) @@ -139,9 +139,9 @@ cdef class GiacMethods_base: Ex2:Dirac(-1) Ex3: int(Dirac(x)*(x-1)^2,x,-1,2) ''' - return GiacMethods['Dirac'](self,*args) + return GiacMethods['Dirac'](self, *args) - def Ei(self,*args): + def Ei(self, *args): r'''From Giac's documentation: Help for Ei: Ei(Expr) @@ -149,9 +149,9 @@ cdef class GiacMethods_base: See also: 1/ Si 2/ Ci 3/ Li Ex1:Ei(1.0) ''' - return GiacMethods['Ei'](self,*args) + return GiacMethods['Ei'](self, *args) - def Factor(self,*args): + def Factor(self, *args): r'''From Giac's documentation: Help for Factor: Factor(Expr) @@ -160,9 +160,9 @@ cdef class GiacMethods_base: Ex1:Factor(x^4-1) Ex2:Factor(x^4+12*x^3+54*x^2+108*x+81) ''' - return GiacMethods['Factor'](self,*args) + return GiacMethods['Factor'](self, *args) - def GF(self,*args): + def GF(self, *args): r'''From Giac's documentation: Help for GF: GF(Intg(p), Intg(n)|Minpoly,[Variable],[0|undef|Poly]) @@ -174,9 +174,9 @@ cdef class GiacMethods_base: Ex5:GF(2,8,['a','G']) Ex6: G:=GF(2,a^8+a^6+a^3+a^2+1,['a','G'],undef) ''' - return GiacMethods['GF'](self,*args) + return GiacMethods['GF'](self, *args) - def Gamma(self,*args): + def Gamma(self, *args): r'''From Giac's documentation: Help for Gamma: Gamma(Real(a),[Real(b)]) @@ -187,9 +187,9 @@ cdef class GiacMethods_base: Ex3:Gamma(gamma(-5.1)) Ex4:Gamma(-5.1,2.1) ''' - return GiacMethods['Gamma'](self,*args) + return GiacMethods['Gamma'](self, *args) - def Heaviside(self,*args): + def Heaviside(self, *args): r'''From Giac's documentation: Help for Heaviside: Heaviside(Real) @@ -199,9 +199,9 @@ cdef class GiacMethods_base: Ex2:Heaviside(-1) Ex3:Heaviside(0) ''' - return GiacMethods['Heaviside'](self,*args) + return GiacMethods['Heaviside'](self, *args) - def JordanBlock(self,*args): + def JordanBlock(self, *args): r'''From Giac's documentation: Help for JordanBlock: JordanBlock(Expr(a),Intg(n)) @@ -209,9 +209,9 @@ cdef class GiacMethods_base: See also: 1/ jordan Ex1:JordanBlock(7,3) ''' - return GiacMethods['JordanBlock'](self,*args) + return GiacMethods['JordanBlock'](self, *args) - def LU(self,*args): + def LU(self, *args): r'''From Giac's documentation: Help for LU: LU(Mtrx(A),Var(L),Var(U),Var(P)) @@ -220,9 +220,9 @@ cdef class GiacMethods_base: Ex1:LU([[1,2],[3,4]],L,U,P) Ex2:LU([[6,12,18],[5,14,31],[3,8,18]],L,U,P) ''' - return GiacMethods['LU'](self,*args) + return GiacMethods['LU'](self, *args) - def LambertW(self,*args): + def LambertW(self, *args): r'''From Giac's documentation: Help for LambertW: LambertW(Real(x),[Intg(n)]) @@ -231,9 +231,9 @@ cdef class GiacMethods_base: Ex2:LambertW(ln(4)) Ex3:LambertW(-0.1,-1) ''' - return GiacMethods['LambertW'](self,*args) + return GiacMethods['LambertW'](self, *args) - def Li(self,*args): + def Li(self, *args): r'''From Giac's documentation: Help for Li: Li(Expr) @@ -241,9 +241,9 @@ cdef class GiacMethods_base: See also: 1/ Si 2/ Ci 3/ Ei Ex1:Li(2.0) ''' - return GiacMethods['Li'](self,*args) + return GiacMethods['Li'](self, *args) - def Line(self,*args): + def Line(self, *args): r'''From Giac's documentation: Help for Line: Line(Expr(a),Expr(b),Expr(c),Expr(d)) @@ -251,9 +251,9 @@ cdef class GiacMethods_base: See also: 1/ segment Ex1:Line(-1,-2,1,2) ''' - return GiacMethods['Line'](self,*args) + return GiacMethods['Line'](self, *args) - def LineHorz(self,*args): + def LineHorz(self, *args): r'''From Giac's documentation: Help for LineHorz: LineHorz(Expr(a)) @@ -261,9 +261,9 @@ cdef class GiacMethods_base: See also: 1/ Line 2/ LineVert Ex1:LineHorz(-1) ''' - return GiacMethods['LineHorz'](self,*args) + return GiacMethods['LineHorz'](self, *args) - def LineTan(self,*args): + def LineTan(self, *args): r'''From Giac's documentation: Help for LineTan: LineTan(Expr(f(x)),[Var],Expr(a)) @@ -275,9 +275,9 @@ cdef class GiacMethods_base: Ex4: LineTan x^2-x,1 Ex5: (LineTan sin(t),t,pi/4) ''' - return GiacMethods['LineTan'](self,*args) + return GiacMethods['LineTan'](self, *args) - def LineVert(self,*args): + def LineVert(self, *args): r'''From Giac's documentation: Help for LineVert: LineVert(Expr(a)) @@ -285,9 +285,9 @@ cdef class GiacMethods_base: See also: 1/ Line 2/ LineHorz Ex1:LineVert(2) ''' - return GiacMethods['LineVert'](self,*args) + return GiacMethods['LineVert'](self, *args) - def Phi(self,*args): + def Phi(self, *args): r'''From Giac's documentation: Help for Phi: Phi(Intg(n)) @@ -296,9 +296,9 @@ cdef class GiacMethods_base: Ex1:Phi(11) Ex2:Phi(6) ''' - return GiacMethods['Phi'](self,*args) + return GiacMethods['Phi'](self, *args) - def Pi(self,*args): + def Pi(self, *args): r'''From Giac's documentation: Help for Pi: Pi() @@ -309,9 +309,9 @@ cdef class GiacMethods_base: Ex3: evalf(pi) Ex4: evalf(Pi) ''' - return GiacMethods['Pi'](self,*args) + return GiacMethods['Pi'](self, *args) - def Psi(self,*args): + def Psi(self, *args): r'''From Giac's documentation: Help for Psi: Psi(Real(a),Intg(n)) @@ -319,9 +319,9 @@ cdef class GiacMethods_base: See also: 1/ Gamma Ex1:Psi(3,1) ''' - return GiacMethods['Psi'](self,*args) + return GiacMethods['Psi'](self, *args) - def QR(self,*args): + def QR(self, *args): r'''From Giac's documentation: Help for QR: QR(Mtrx,Var(Q),Var(R),[Real(eps)]) @@ -329,9 +329,9 @@ cdef class GiacMethods_base: See also: 1/ qr 2/ LU Ex1:QR([[1,2],[3,4]],Q,R) ''' - return GiacMethods['QR'](self,*args) + return GiacMethods['QR'](self, *args) - def RandSeed(self,*args): + def RandSeed(self, *args): r'''From Giac's documentation: Help for RandSeed: RandSeed(Intg) @@ -339,9 +339,9 @@ cdef class GiacMethods_base: See also: 1/ srand Ex1:RandSeed(321) ''' - return GiacMethods['RandSeed'](self,*args) + return GiacMethods['RandSeed'](self, *args) - def Row(self,*args): + def Row(self, *args): r'''From Giac's documentation: Help for Row: Row(NULL) @@ -349,9 +349,9 @@ cdef class GiacMethods_base: See also: 1/ Col Ex1:Row() ''' - return GiacMethods['Row'](self,*args) + return GiacMethods['Row'](self, *args) - def SortA(self,*args): + def SortA(self, *args): r'''From Giac's documentation: Help for SortA: SortA(LstReal||Seq||Mtrx) @@ -362,9 +362,9 @@ cdef class GiacMethods_base: Ex3: SortA [3,4,2],[6,4,5] Ex4: SortA [[3,4,2],[6,4,5]] ''' - return GiacMethods['SortA'](self,*args) + return GiacMethods['SortA'](self, *args) - def SortD(self,*args): + def SortD(self, *args): r'''From Giac's documentation: Help for SortD: SortD(LstReal||Seq||Mtrx) @@ -375,9 +375,9 @@ cdef class GiacMethods_base: Ex3: SortD [[3,4,2],[6,4,5]] Ex4: SortD [3,4,2],[6,4,5] ''' - return GiacMethods['SortD'](self,*args) + return GiacMethods['SortD'](self, *args) - def UTPC(self,*args): + def UTPC(self, *args): r'''From Giac's documentation: Help for UTPC: UTPC(Intg(n),Real(x0)) @@ -386,9 +386,9 @@ cdef class GiacMethods_base: Ex1:UTPC(2,6.1) Ex2:UTPC(4,6.1) ''' - return GiacMethods['UTPC'](self,*args) + return GiacMethods['UTPC'](self, *args) - def UTPF(self,*args): + def UTPF(self, *args): r'''From Giac's documentation: Help for UTPF: UTPF(Intg(n),Intg(d),Real(x0)) @@ -397,9 +397,9 @@ cdef class GiacMethods_base: Ex1:UTPF(4,10,3.5) Ex2:UTPF(4,4,2.1) ''' - return GiacMethods['UTPF'](self,*args) + return GiacMethods['UTPF'](self, *args) - def UTPN(self,*args): + def UTPN(self, *args): r'''From Giac's documentation: Help for UTPN: UTPN(Real(mu),Real(v),Real(x0)) @@ -408,9 +408,9 @@ cdef class GiacMethods_base: Ex1:UTPN(1.96) Ex2:UTPN(1,4,2.96)+normal_cdf(1,2,2.96) ''' - return GiacMethods['UTPN'](self,*args) + return GiacMethods['UTPN'](self, *args) - def UTPT(self,*args): + def UTPT(self, *args): r'''From Giac's documentation: Help for UTPT: UTPT(Intg(n),Real(x0)) @@ -419,9 +419,9 @@ cdef class GiacMethods_base: Ex1:UTPT(3,2.35) Ex2:UTPT(3,-2.35) ''' - return GiacMethods['UTPT'](self,*args) + return GiacMethods['UTPT'](self, *args) - def VARS(self,*args): + def VARS(self, *args): r'''From Giac's documentation: Help for VARS: VARS(NULL) @@ -429,9 +429,9 @@ cdef class GiacMethods_base: See also: 1/ lvar Ex1:VARS() ''' - return GiacMethods['VARS'](self,*args) + return GiacMethods['VARS'](self, *args) - def VAS(self,*args): + def VAS(self, *args): r'''From Giac's documentation: Help for VAS: VAS(Poly(P)) @@ -439,9 +439,9 @@ cdef class GiacMethods_base: See also: 1/ VAS_positive 2/ sturmab 3/ realroot Ex1:VAS(x^3-7*x+7) ''' - return GiacMethods['VAS'](self,*args) + return GiacMethods['VAS'](self, *args) - def VAS_positive(self,*args): + def VAS_positive(self, *args): r'''From Giac's documentation: Help for VAS_positive: VAS_positive(Poly(P)) @@ -449,9 +449,9 @@ cdef class GiacMethods_base: See also: 1/ poslbdLMQ 2/ posubLMQ 3/ VAS 4/ realroot Ex1:VAS_positive(x^3-7*x+7) ''' - return GiacMethods['VAS_positive'](self,*args) + return GiacMethods['VAS_positive'](self, *args) - def Zeta(self,*args): + def Zeta(self, *args): r'''From Giac's documentation: Help for Zeta: Zeta(Real(a)) @@ -459,9 +459,9 @@ cdef class GiacMethods_base: See also: 1/ sum Ex1:Zeta(2) ''' - return GiacMethods['Zeta'](self,*args) + return GiacMethods['Zeta'](self, *args) - def a2q(self,*args): + def a2q(self, *args): r'''From Giac's documentation: Help for a2q: a2q(Mtrx,VectVar) @@ -470,9 +470,9 @@ cdef class GiacMethods_base: Ex1:a2q([[1,2],[4,4]],[x,y]) Ex2:a2q([[1,3],[3,4]],[x,y]) ''' - return GiacMethods['a2q'](self,*args) + return GiacMethods['a2q'](self, *args) - def abcuv(self,*args): + def abcuv(self, *args): r'''From Giac's documentation: Help for abcuv: abcuv(Poly(a),Poly(b),Poly(c),[Var]) @@ -484,9 +484,9 @@ cdef class GiacMethods_base: Ex4:abcuv(X^2+2*X+1,X^2-1,X^3+1,X) Ex5:abcuv([1,2,1],[1,0,-1],[1,0,0,1]) ''' - return GiacMethods['abcuv'](self,*args) + return GiacMethods['abcuv'](self, *args) - def about(self,*args): + def about(self, *args): r'''From Giac's documentation: Help for about: about(Var(a)) @@ -495,9 +495,9 @@ cdef class GiacMethods_base: Ex1:about(a) Ex2:about(n) ''' - return GiacMethods['about'](self,*args) + return GiacMethods['about'](self, *args) - def abs(self,*args): + def abs(self, *args): r'''From Giac's documentation: Help for abs: abs(Cplx||LstCplx) @@ -508,9 +508,9 @@ cdef class GiacMethods_base: Ex3:abs((1+2*i)^2) Ex4:abs([-2,1+i,-4]) ''' - return GiacMethods['abs'](self,*args) + return GiacMethods['abs'](self, *args) - def abscissa(self,*args): + def abscissa(self, *args): r'''From Giac's documentation: Help for abscissa: abscissa(Pnt or Vect) @@ -521,9 +521,9 @@ cdef class GiacMethods_base: Ex3:abscissa(-1-i) Ex4:abscissa(point(1,2,3)) ''' - return GiacMethods['abscissa'](self,*args) + return GiacMethods['abscissa'](self, *args) - def accumulate_head_tail(self,*args): + def accumulate_head_tail(self, *args): r'''From Giac's documentation: Help for accumulate_head_tail: accumulate_head_tail(Lst(l),Intg(p),Intg(q)) @@ -531,9 +531,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:accumulate_head_tail([0,1,2,3,4,5,6,7,8,9],3,2) ''' - return GiacMethods['accumulate_head_tail'](self,*args) + return GiacMethods['accumulate_head_tail'](self, *args) - def acos(self,*args): + def acos(self, *args): r'''From Giac's documentation: Help for acos: acos(Expr) @@ -541,9 +541,9 @@ cdef class GiacMethods_base: See also: 1/ cos 2/ acosh Ex1:acos(0) ''' - return GiacMethods['acos'](self,*args) + return GiacMethods['acos'](self, *args) - def acos2asin(self,*args): + def acos2asin(self, *args): r'''From Giac's documentation: Help for acos2asin: acos2asin(Expr) @@ -552,9 +552,9 @@ cdef class GiacMethods_base: Ex1:acos2asin(acos(x)+asin(x)) Ex2:acos2asin(2*acos(x)) ''' - return GiacMethods['acos2asin'](self,*args) + return GiacMethods['acos2asin'](self, *args) - def acos2atan(self,*args): + def acos2atan(self, *args): r'''From Giac's documentation: Help for acos2atan: acos2atan(Expr) @@ -563,9 +563,9 @@ cdef class GiacMethods_base: Ex1:acos2atan(2*acos(x)) Ex2:acos2atan(acos(sqrt(1-x^2))+acos(x)) ''' - return GiacMethods['acos2atan'](self,*args) + return GiacMethods['acos2atan'](self, *args) - def acosh(self,*args): + def acosh(self, *args): r'''From Giac's documentation: Help for acosh: acosh(Expr) @@ -573,9 +573,9 @@ cdef class GiacMethods_base: See also: 1/ cosh 2/ acos Ex1:acosh(1) ''' - return GiacMethods['acosh'](self,*args) + return GiacMethods['acosh'](self, *args) - def acot(self,*args): + def acot(self, *args): r'''From Giac's documentation: Help for acot: acot(Expr) @@ -583,9 +583,9 @@ cdef class GiacMethods_base: See also: 1/ atan 2/ arccos Ex1:acot(0) ''' - return GiacMethods['acot'](self,*args) + return GiacMethods['acot'](self, *args) - def acsc(self,*args): + def acsc(self, *args): r'''From Giac's documentation: Help for acsc: acsc(Expr) @@ -594,18 +594,18 @@ cdef class GiacMethods_base: Ex1:acsc(1) Ex2:acsc(2) ''' - return GiacMethods['acsc'](self,*args) + return GiacMethods['acsc'](self, *args) - def acyclic(self,*args): + def acyclic(self, *args): r'''From Giac's documentation: Help for acyclic: acyclic(Opt) Option for the random_network command. See also: 1/ random_network ''' - return GiacMethods['acyclic'](self,*args) + return GiacMethods['acyclic'](self, *args) - def add(self,*args): + def add(self, *args): r'''From Giac's documentation: Help for add: add(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) @@ -622,9 +622,9 @@ cdef class GiacMethods_base: Ex9:add(1/(x*(x+1)),x) Ex10:add(cos(n*x),n) ''' - return GiacMethods['add'](self,*args) + return GiacMethods['add'](self, *args) - def add_arc(self,*args): + def add_arc(self, *args): r'''From Giac's documentation: Help for add_arc: add_arc(Graph(G),Edge(e)||Trail(T)||Lst(E)) @@ -632,9 +632,9 @@ cdef class GiacMethods_base: See also: 1/ add_edge 2/ delete_arc 3/ digraph 4/ edges 5/ has_arc 6/ trail Ex1:add_arc(digraph(trail(1,2,3,4,5,1)),[[1,3],[2,4]]) ''' - return GiacMethods['add_arc'](self,*args) + return GiacMethods['add_arc'](self, *args) - def add_edge(self,*args): + def add_edge(self, *args): r'''From Giac's documentation: Help for add_edge: add_edge(Graph(G),Edge(e)||Trail(T)||Lst(E)) @@ -642,9 +642,9 @@ cdef class GiacMethods_base: See also: 1/ add_arc 2/ delete_edge 3/ edges 4/ graph 5/ has_edge 6/ trail Ex1:add_edge(graph(trail(1,2,3,4)),[4,1]) ''' - return GiacMethods['add_edge'](self,*args) + return GiacMethods['add_edge'](self, *args) - def add_vertex(self,*args): + def add_vertex(self, *args): r'''From Giac's documentation: Help for add_vertex: add_vertex(Graph(G),Vrtx(v)||Lst(V)) @@ -652,9 +652,9 @@ cdef class GiacMethods_base: See also: 1/ add_arc 2/ add_edge 3/ delete_vertex Ex1:add_vertex(cycle_graph(5),["a","b"]) ''' - return GiacMethods['add_vertex'](self,*args) + return GiacMethods['add_vertex'](self, *args) - def additionally(self,*args): + def additionally(self, *args): r'''From Giac's documentation: Help for additionally: additionally(Expr) @@ -663,9 +663,9 @@ cdef class GiacMethods_base: Ex1: assume(n,integer);additionally(n>5) Ex2: assume(n,integer);assume(n>=2,additionally) ''' - return GiacMethods['additionally'](self,*args) + return GiacMethods['additionally'](self, *args) - def addtable(self,*args): + def addtable(self, *args): r'''From Giac's documentation: Help for addtable: addtable(fourier||laplace,f(x),F(s),Var(x),Var(s)) @@ -673,9 +673,9 @@ cdef class GiacMethods_base: See also: 1/ fourier 2/ laplace Ex1:addtable(fourier,y(x),Y(s),x,s) ''' - return GiacMethods['addtable'](self,*args) + return GiacMethods['addtable'](self, *args) - def adjacency_matrix(self,*args): + def adjacency_matrix(self, *args): r'''From Giac's documentation: Help for adjacency_matrix: adjacency_matrix(Graph(G)) @@ -683,9 +683,9 @@ cdef class GiacMethods_base: See also: 1/ neighbors Ex1:adjacency_matrix(graph(trail(1,2,3,4,2,5,1,3))) ''' - return GiacMethods['adjacency_matrix'](self,*args) + return GiacMethods['adjacency_matrix'](self, *args) - def adjoint_matrix(self,*args): + def adjoint_matrix(self, *args): r'''From Giac's documentation: Help for adjoint_matrix: adjoint_matrix(Mtrx) @@ -693,9 +693,9 @@ cdef class GiacMethods_base: See also: 1/ pcar Ex1:adjoint_matrix([[1,i],[2,3]]) ''' - return GiacMethods['adjoint_matrix'](self,*args) + return GiacMethods['adjoint_matrix'](self, *args) - def affix(self,*args): + def affix(self, *args): r'''From Giac's documentation: Help for affix: affix(Pnt||Vect) @@ -705,9 +705,9 @@ cdef class GiacMethods_base: Ex2:affix(point(i)-point(1+2*i)) Ex3:affix([1,2]) ''' - return GiacMethods['affix'](self,*args) + return GiacMethods['affix'](self, *args) - def algsubs(self,*args): + def algsubs(self, *args): r'''From Giac's documentation: Help for algsubs: algsubs(Equal(Xpr1=Xpr2),Expr(Xpr)) @@ -717,9 +717,9 @@ cdef class GiacMethods_base: Ex2:algsubs(a*b/c=d, 2*a*b^2/c) Ex3:algsubs(2a=p^2-q^2,algsubs(2c=p^2+q^2,c^2-a^2)) ''' - return GiacMethods['algsubs'](self,*args) + return GiacMethods['algsubs'](self, *args) - def algvar(self,*args): + def algvar(self, *args): r'''From Giac's documentation: Help for algvar: algvar(Expr) @@ -727,9 +727,9 @@ cdef class GiacMethods_base: See also: 1/ lvar 2/ lname Ex1:algvar(sqrt(x)+y) ''' - return GiacMethods['algvar'](self,*args) + return GiacMethods['algvar'](self, *args) - def all_trig_solutions(self,*args): + def all_trig_solutions(self, *args): r'''From Giac's documentation: Help for all_trig_solutions: all_trig_solutions(:=Intg(0 or 1)) @@ -738,9 +738,9 @@ cdef class GiacMethods_base: Ex1: all_trig_solutions:=1 Ex2: all_trig_solutions:=0 ''' - return GiacMethods['all_trig_solutions'](self,*args) + return GiacMethods['all_trig_solutions'](self, *args) - def allpairs_distance(self,*args): + def allpairs_distance(self, *args): r'''From Giac's documentation: Help for allpairs_distance: allpairs_distance(Graph(G)) @@ -748,9 +748,9 @@ cdef class GiacMethods_base: See also: 1/ dijkstra 2/ graph_diameter 3/ vertex_distance Ex1:allpairs_distance(graph(%{[1,2],[1,3],[1,4],[1,5],[2,3],[3,4],[4,5],[5,2]%})) ''' - return GiacMethods['allpairs_distance'](self,*args) + return GiacMethods['allpairs_distance'](self, *args) - def alog10(self,*args): + def alog10(self, *args): r'''From Giac's documentation: Help for alog10: alog10(Expr) @@ -758,9 +758,9 @@ cdef class GiacMethods_base: See also: 1/ log10 Ex1:alog10(3) ''' - return GiacMethods['alog10'](self,*args) + return GiacMethods['alog10'](self, *args) - def altitude(self,*args): + def altitude(self, *args): r'''From Giac's documentation: Help for altitude: altitude((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -768,9 +768,9 @@ cdef class GiacMethods_base: See also: 1/ perpendicular 2/ orthogonal 3/ orthocenter 4/ common_perpendicular Ex1:altitude(-1,1-i,i) ''' - return GiacMethods['altitude'](self,*args) + return GiacMethods['altitude'](self, *args) - def angle(self,*args): + def angle(self, *args): r'''From Giac's documentation: Help for angle: angle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -782,9 +782,9 @@ cdef class GiacMethods_base: Ex4:angle(0,1,i,"a") Ex5:angle(i,1,1+i,"b") ''' - return GiacMethods['angle'](self,*args) + return GiacMethods['angle'](self, *args) - def angle_radian(self,*args): + def angle_radian(self, *args): r'''From Giac's documentation: Help for angle_radian: angle_radian(:=Intg(0 or 1)) @@ -793,9 +793,9 @@ cdef class GiacMethods_base: Ex1: angle_radian:=1 Ex2: angle_radian:=0 ''' - return GiacMethods['angle_radian'](self,*args) + return GiacMethods['angle_radian'](self, *args) - def angleat(self,*args): + def angleat(self, *args): r'''From Giac's documentation: Help for angleat: angleat(Pnt(A),Pnt(B),Pnt(C),(Pnt or Cplx(z0))) @@ -803,9 +803,9 @@ cdef class GiacMethods_base: See also: 1/ angle 2/ angleatraw 3/ legend Ex1: A:=point(0);B:=point(1);C:=point(i);angleat(A,B,C,-2-i) ''' - return GiacMethods['angleat'](self,*args) + return GiacMethods['angleat'](self, *args) - def angleatraw(self,*args): + def angleatraw(self, *args): r'''From Giac's documentation: Help for angleatraw: angleatraw(Pnt(A)),Pnt(B),Pnt(C),(Pnt or Cplx(z0))) @@ -813,9 +813,9 @@ cdef class GiacMethods_base: See also: 1/ angle 2/ angleat Ex1: A:=point(0);B:=point(1);C:=point(i);angleatraw(A,B,C,-2-i) ''' - return GiacMethods['angleatraw'](self,*args) + return GiacMethods['angleatraw'](self, *args) - def ans(self,*args): + def ans(self, *args): r'''From Giac's documentation: Help for ans: ans(Intg(n)) @@ -825,9 +825,9 @@ cdef class GiacMethods_base: Ex2:ans(2) Ex3:ans(-2) ''' - return GiacMethods['ans'](self,*args) + return GiacMethods['ans'](self, *args) - def antiprism_graph(self,*args): + def antiprism_graph(self, *args): r'''From Giac's documentation: Help for antiprism_graph: antiprism_graph(Intg(n)) @@ -835,9 +835,9 @@ cdef class GiacMethods_base: See also: 1/ prism_graph Ex1:antiprism_graph(5) ''' - return GiacMethods['antiprism_graph'](self,*args) + return GiacMethods['antiprism_graph'](self, *args) - def append(self,*args): + def append(self, *args): r'''From Giac's documentation: Help for append: append((Lst||Set||Str(L),Elem)) @@ -850,9 +850,9 @@ cdef class GiacMethods_base: Ex5: S:=set[1,2,4];S:=append(S,6) Ex6: S:=set[1,2,4];S.append(6) ''' - return GiacMethods['append'](self,*args) + return GiacMethods['append'](self, *args) - def apply(self,*args): + def apply(self, *args): r'''From Giac's documentation: Help for apply: apply(Fnc(f),Lst(l)) @@ -861,9 +861,9 @@ cdef class GiacMethods_base: Ex1:apply(x->x^3,[1,2,3]) Ex2:apply(x->x+1,[[1,2,3],[1,2,3]],matrix) ''' - return GiacMethods['apply'](self,*args) + return GiacMethods['apply'](self, *args) - def approx(self,*args): + def approx(self, *args): r'''From Giac's documentation: Help for approx: approx(Expr,[Int]) @@ -876,9 +876,9 @@ cdef class GiacMethods_base: Ex5:approx(sqrt(2)+pi) Ex6:approx(sqrt(2)+pi,30) ''' - return GiacMethods['approx'](self,*args) + return GiacMethods['approx'](self, *args) - def arc(self,*args): + def arc(self, *args): r'''From Giac's documentation: Help for arc: arc(Pnt, Pnt, Real,[Var(C)],[Var(r)],[Opt(segment)]) @@ -889,9 +889,9 @@ cdef class GiacMethods_base: Ex3:arc(i,1,pi/4,segment) Ex4:arc(i,1,pi/4,segment,affichage=1+rempli) ''' - return GiacMethods['arc'](self,*args) + return GiacMethods['arc'](self, *args) - def arcLen(self,*args): + def arcLen(self, *args): r'''From Giac's documentation: Help for arcLen: arcLen(Expr(Xpr) or Lst([Xpr1,Xpr2]),Var,Real(a),Real(b)) @@ -901,9 +901,9 @@ cdef class GiacMethods_base: Ex2:arcLen([t,t^2],t,1,2) Ex3:arcLen([cos(t),sin(t)],t,1,2) ''' - return GiacMethods['arcLen'](self,*args) + return GiacMethods['arcLen'](self, *args) - def arccos(self,*args): + def arccos(self, *args): r'''From Giac's documentation: Help for arccos: arccos(Expr) @@ -911,9 +911,9 @@ cdef class GiacMethods_base: See also: 1/ cos 2/ acosh Ex1:arccos(0) ''' - return GiacMethods['arccos'](self,*args) + return GiacMethods['arccos'](self, *args) - def arccosh(self,*args): + def arccosh(self, *args): r'''From Giac's documentation: Help for arccosh: arccosh(Expr) @@ -921,9 +921,9 @@ cdef class GiacMethods_base: See also: 1/ cosh 2/ acos Ex1:arccosh(1) ''' - return GiacMethods['arccosh'](self,*args) + return GiacMethods['arccosh'](self, *args) - def arclen(self,*args): + def arclen(self, *args): r'''From Giac's documentation: Help for arclen: arclen(Expr(Xpr) or Lst([Xpr1,Xpr2]),Var,Real(a),Real(b)) @@ -933,9 +933,9 @@ cdef class GiacMethods_base: Ex2:arclen([t,t^2],t,1,2) Ex3:arclen([cos(t),sin(t)],t,1,2) ''' - return GiacMethods['arclen'](self,*args) + return GiacMethods['arclen'](self, *args) - def arcsin(self,*args): + def arcsin(self, *args): r'''From Giac's documentation: Help for arcsin: arcsin(Expr) @@ -943,9 +943,9 @@ cdef class GiacMethods_base: See also: 1/ sin Ex1:arcsin(0) ''' - return GiacMethods['arcsin'](self,*args) + return GiacMethods['arcsin'](self, *args) - def arcsinh(self,*args): + def arcsinh(self, *args): r'''From Giac's documentation: Help for arcsinh: arcsinh(Expr) @@ -953,9 +953,9 @@ cdef class GiacMethods_base: See also: 1/ sinh 2/ asin Ex1:arcsinh(0) ''' - return GiacMethods['arcsinh'](self,*args) + return GiacMethods['arcsinh'](self, *args) - def arctan(self,*args): + def arctan(self, *args): r'''From Giac's documentation: Help for arctan: arctan(Expr) @@ -963,9 +963,9 @@ cdef class GiacMethods_base: See also: 1/ tan 2/ atanh Ex1:arctan(0) ''' - return GiacMethods['arctan'](self,*args) + return GiacMethods['arctan'](self, *args) - def arctanh(self,*args): + def arctanh(self, *args): r'''From Giac's documentation: Help for arctanh: arctanh(Expr) @@ -973,9 +973,9 @@ cdef class GiacMethods_base: See also: 1/ atan 2/ tanh Ex1:arctanh(0) ''' - return GiacMethods['arctanh'](self,*args) + return GiacMethods['arctanh'](self, *args) - def area(self,*args): + def area(self, *args): r'''From Giac's documentation: Help for area: area(Polygone || Expr,x=a..b,[n],[Method]) @@ -989,9 +989,9 @@ cdef class GiacMethods_base: Ex6:area(x^2,x=0..1,5,simpson) Ex7:area(x^2,x=0..1,5,rombergm) ''' - return GiacMethods['area'](self,*args) + return GiacMethods['area'](self, *args) - def areaat(self,*args): + def areaat(self, *args): r'''From Giac's documentation: Help for areaat: areaat(Polygone, Pnt||Cplx(z0)) @@ -1003,9 +1003,9 @@ cdef class GiacMethods_base: Ex4: p:=polygon(0,1,i);areaat(p,1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);areaat(c,i) ''' - return GiacMethods['areaat'](self,*args) + return GiacMethods['areaat'](self, *args) - def areaatraw(self,*args): + def areaatraw(self, *args): r'''From Giac's documentation: Help for areaatraw: areaatraw(Polygone, Pnt||Cplx(z0)) @@ -1017,9 +1017,9 @@ cdef class GiacMethods_base: Ex4:areaatraw(polygon(0,1,i),1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);areaatraw(c,i) ''' - return GiacMethods['areaatraw'](self,*args) + return GiacMethods['areaatraw'](self, *args) - def areaplot(self,*args): + def areaplot(self, *args): r'''From Giac's documentation: Help for areaplot: areaplot(Expr,x=a..b,[n],[Method]) @@ -1029,9 +1029,9 @@ cdef class GiacMethods_base: Ex2:areaplot(x^2,x=0..1,5,trapezoid) Ex3:areaplot(x^2,x=0..1,5,middle_point) ''' - return GiacMethods['areaplot'](self,*args) + return GiacMethods['areaplot'](self, *args) - def arg(self,*args): + def arg(self, *args): r'''From Giac's documentation: Help for arg: arg(Expr) @@ -1041,9 +1041,9 @@ cdef class GiacMethods_base: Ex2:arg(1+2*i) Ex3:arg((1+2*i)^2) ''' - return GiacMethods['arg'](self,*args) + return GiacMethods['arg'](self, *args) - def array(self,*args): + def array(self, *args): r'''From Giac's documentation: Help for array: array(Opt) @@ -1052,9 +1052,9 @@ cdef class GiacMethods_base: Ex1: A[0..2,0..2]:=1;A[0..1,1..2]:=2;convert(A,array) Ex2: B[0..1,1..2]:=1;B[2,2]:=2;convert(B,array) ''' - return GiacMethods['array'](self,*args) + return GiacMethods['array'](self, *args) - def arrivals(self,*args): + def arrivals(self, *args): r'''From Giac's documentation: Help for arrivals: arrivals(Graph(G),[Vrtx(v)]) @@ -1062,9 +1062,9 @@ cdef class GiacMethods_base: See also: 1/ in_degree Ex1:arrivals(digraph(%{[1,2],[1,3],[2,3]%}),1) ''' - return GiacMethods['arrivals'](self,*args) + return GiacMethods['arrivals'](self, *args) - def articulation_points(self,*args): + def articulation_points(self, *args): r'''From Giac's documentation: Help for articulation_points: articulation_points(Graph(G)) @@ -1073,9 +1073,9 @@ cdef class GiacMethods_base: Ex1:articulation_points(path_graph(5)) Ex2:articulation_points(cycle_graph(5)) ''' - return GiacMethods['articulation_points'](self,*args) + return GiacMethods['articulation_points'](self, *args) - def asin(self,*args): + def asin(self, *args): r'''From Giac's documentation: Help for asin: asin(Expr) @@ -1083,9 +1083,9 @@ cdef class GiacMethods_base: See also: 1/ sin Ex1:asin(0) ''' - return GiacMethods['asin'](self,*args) + return GiacMethods['asin'](self, *args) - def asin2acos(self,*args): + def asin2acos(self, *args): r'''From Giac's documentation: Help for asin2acos: asin2acos(Expr) @@ -1094,9 +1094,9 @@ cdef class GiacMethods_base: Ex1:asin2acos(acos(x)+asin(x)) Ex2:asin2acos(2*asin(x)) ''' - return GiacMethods['asin2acos'](self,*args) + return GiacMethods['asin2acos'](self, *args) - def asin2atan(self,*args): + def asin2atan(self, *args): r'''From Giac's documentation: Help for asin2atan: asin2atan(Expr) @@ -1105,9 +1105,9 @@ cdef class GiacMethods_base: Ex1:asin2atan(2*asin(x)) Ex2:asin2atan(asin(sqrt(1-x^2))+asin(x)) ''' - return GiacMethods['asin2atan'](self,*args) + return GiacMethods['asin2atan'](self, *args) - def asinh(self,*args): + def asinh(self, *args): r'''From Giac's documentation: Help for asinh: asinh(Expr) @@ -1115,9 +1115,9 @@ cdef class GiacMethods_base: See also: 1/ sinh 2/ asin Ex1:asinh(0) ''' - return GiacMethods['asinh'](self,*args) + return GiacMethods['asinh'](self, *args) - def assign_edge_weights(self,*args): + def assign_edge_weights(self, *args): r'''From Giac's documentation: Help for assign_edge_weights: assign_edge_weights(Graph(G),Seq(m,n)||Intrv(a..b)) @@ -1126,9 +1126,9 @@ cdef class GiacMethods_base: Ex1:assign_edge_weights(digraph(trail(1,2,3,4,1)),1,9) Ex2:assign_edge_weights(digraph(trail(1,2,3,4,1)),0..1) ''' - return GiacMethods['assign_edge_weights'](self,*args) + return GiacMethods['assign_edge_weights'](self, *args) - def assume(self,*args): + def assume(self, *args): r'''From Giac's documentation: Help for assume: assume(Expr) @@ -1145,9 +1145,9 @@ cdef class GiacMethods_base: Ex9:assume(a>=2);additionally(a<6) Ex10:assume(a) ''' - return GiacMethods['assume'](self,*args) + return GiacMethods['assume'](self, *args) - def at(self,*args): + def at(self, *args): r'''From Giac's documentation: Help for at: at(Lst(l)||Mtrx(m),Index(j)||Lst([j,k])) @@ -1156,9 +1156,9 @@ cdef class GiacMethods_base: Ex1:at([10,11,12],1) Ex2:at([[1,2],[3,4]],[1,0]) ''' - return GiacMethods['at'](self,*args) + return GiacMethods['at'](self, *args) - def atan(self,*args): + def atan(self, *args): r'''From Giac's documentation: Help for atan: atan(Expr) @@ -1166,27 +1166,27 @@ cdef class GiacMethods_base: See also: 1/ tan 2/ atanh Ex1:atan(0) ''' - return GiacMethods['atan'](self,*args) + return GiacMethods['atan'](self, *args) - def atan2acos(self,*args): + def atan2acos(self, *args): r'''From Giac's documentation: Help for atan2acos: atan2acos(Expr) Replaces arctan(x) by pi/2-arccos(x/sqrt(1+x^2)) in the argument. See also: 1/ atan2acos(atan(x)) ''' - return GiacMethods['atan2acos'](self,*args) + return GiacMethods['atan2acos'](self, *args) - def atan2asin(self,*args): + def atan2asin(self, *args): r'''From Giac's documentation: Help for atan2asin: atan2asin(Expr) Replaces arctan(x) by arcsin(x/sqrt(1+x^2)) in the argument. See also: 1/ atan2asin(atan(x)) ''' - return GiacMethods['atan2asin'](self,*args) + return GiacMethods['atan2asin'](self, *args) - def atanh(self,*args): + def atanh(self, *args): r'''From Giac's documentation: Help for atanh: atanh(Expr) @@ -1194,9 +1194,9 @@ cdef class GiacMethods_base: See also: 1/ atan 2/ tanh Ex1:atanh(0) ''' - return GiacMethods['atanh'](self,*args) + return GiacMethods['atanh'](self, *args) - def atrig2ln(self,*args): + def atrig2ln(self, *args): r'''From Giac's documentation: Help for atrig2ln: atrig2ln(Expr) @@ -1206,9 +1206,9 @@ cdef class GiacMethods_base: Ex2:atrig2ln(asin(x)) Ex3:atrig2ln(acos(x)) ''' - return GiacMethods['atrig2ln'](self,*args) + return GiacMethods['atrig2ln'](self, *args) - def augment(self,*args): + def augment(self, *args): r'''From Giac's documentation: Help for augment: augment(Lst,Lst||Seq,Seq||Str,Str||Mtrx,Mtrx) @@ -1220,9 +1220,9 @@ cdef class GiacMethods_base: Ex4: L:=[1,2];L.concat([3,4,5]) Ex5: S:="abcd";S.concat("efghi") ''' - return GiacMethods['augment'](self,*args) + return GiacMethods['augment'](self, *args) - def auto_correlation(self,*args): + def auto_correlation(self, *args): r'''From Giac's documentation: Help for auto_correlation: auto_correlation(Lst) @@ -1230,9 +1230,9 @@ cdef class GiacMethods_base: See also: 1/ cross_correlation 2/ correlation Ex1:auto_correlation([1,-1,0,2,1]) ''' - return GiacMethods['auto_correlation'](self,*args) + return GiacMethods['auto_correlation'](self, *args) - def autosimplify(self,*args): + def autosimplify(self, *args): r'''From Giac's documentation: Help for autosimplify: autosimplify(Cmds) @@ -1245,9 +1245,9 @@ cdef class GiacMethods_base: Ex5:autosimplify(factor) Ex6:autosimplify(simplify) ''' - return GiacMethods['autosimplify'](self,*args) + return GiacMethods['autosimplify'](self, *args) - def avance(self,*args): + def avance(self, *args): r'''From Giac's documentation: Help for avance: avance(NULL or Real(n)) @@ -1256,9 +1256,9 @@ cdef class GiacMethods_base: Ex1: avance 30 Ex2:avance(30) ''' - return GiacMethods['avance'](self,*args) + return GiacMethods['avance'](self, *args) - def avgRC(self,*args): + def avgRC(self, *args): r'''From Giac's documentation: Help for avgRC: avgRC(Expr(Xpr),Var(Var),[Real(h)]) @@ -1268,9 +1268,9 @@ cdef class GiacMethods_base: Ex2:avgRC(x^2,x,0.1) Ex3:avgRC(x^2,x) ''' - return GiacMethods['avgRC'](self,*args) + return GiacMethods['avgRC'](self, *args) - def axes(self,*args): + def axes(self, *args): r'''From Giac's documentation: Help for axes: axes(Opt) @@ -1279,18 +1279,18 @@ cdef class GiacMethods_base: Ex1: axes=0;segment(0,point(1,1)) Ex2: axes=1;segment(0,point(1,1),epaisseur=5) ''' - return GiacMethods['axes'](self,*args) + return GiacMethods['axes'](self, *args) - def axis(self,*args): + def axis(self, *args): r'''From Giac's documentation: Help for axis: axis(xmin,xmax,ymin,ymax,[zmin,zmaz]) Defines the graphic display Ex1:axis(-2,4,-1,6) ''' - return GiacMethods['axis'](self,*args) + return GiacMethods['axis'](self, *args) - def back(self,*args): + def back(self, *args): r'''From Giac's documentation: Help for back: back(Vect or Seq or Str) @@ -1300,9 +1300,9 @@ cdef class GiacMethods_base: Ex2:back([1,2,3]) Ex3:back("bonjour") ''' - return GiacMethods['back'](self,*args) + return GiacMethods['back'](self, *args) - def backward(self,*args): + def backward(self, *args): r'''From Giac's documentation: Help for backward: backward(NULL or Real(n)) @@ -1311,9 +1311,9 @@ cdef class GiacMethods_base: Ex1: recule 30 Ex2:backward(30) ''' - return GiacMethods['backward'](self,*args) + return GiacMethods['backward'](self, *args) - def baisse_crayon(self,*args): + def baisse_crayon(self, *args): r'''From Giac's documentation: Help for baisse_crayon: baisse_crayon(NULL) @@ -1321,18 +1321,18 @@ cdef class GiacMethods_base: See also: 1/ leve_crayon 2/ crayon Ex1:baisse_crayon() ''' - return GiacMethods['baisse_crayon'](self,*args) + return GiacMethods['baisse_crayon'](self, *args) - def bandwidth(self,*args): + def bandwidth(self, *args): r'''From Giac's documentation: Help for bandwidth: bandwidth(Opt) Option for the kernel_density command. See also: 1/ kernel_density 2/ bins ''' - return GiacMethods['bandwidth'](self,*args) + return GiacMethods['bandwidth'](self, *args) - def bar_plot(self,*args): + def bar_plot(self, *args): r'''From Giac's documentation: Help for bar_plot: bar_plot(Mtrx) @@ -1342,9 +1342,9 @@ cdef class GiacMethods_base: Ex2:bar_plot([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:bar_plot([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) ''' - return GiacMethods['bar_plot'](self,*args) + return GiacMethods['bar_plot'](self, *args) - def barplot(self,*args): + def barplot(self, *args): r'''From Giac's documentation: Help for barplot: barplot(Mtrx) @@ -1354,9 +1354,9 @@ cdef class GiacMethods_base: Ex2:barplot([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:barplot([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) ''' - return GiacMethods['barplot'](self,*args) + return GiacMethods['barplot'](self, *args) - def bartlett_hann_window(self,*args): + def bartlett_hann_window(self, *args): r'''From Giac's documentation: Help for bartlett_hann_window: bartlett_hann_window(Lst,[Interval(n1..n2)]) @@ -1364,9 +1364,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(bartlett_hann_window(randvector(1000,0..1))) ''' - return GiacMethods['bartlett_hann_window'](self,*args) + return GiacMethods['bartlett_hann_window'](self, *args) - def barycenter(self,*args): + def barycenter(self, *args): r'''From Giac's documentation: Help for barycenter: barycenter([Pnt,Real],[Pnt,Real],[Pnt,Real]) @@ -1376,9 +1376,9 @@ cdef class GiacMethods_base: Ex2:barycenter([[point(-1),1],[point(1+i),2],[point(1-i),1]]) Ex3:barycenter([point(-1),point(1+i),point(1-i)],[1,2,1]) ''' - return GiacMethods['barycenter'](self,*args) + return GiacMethods['barycenter'](self, *args) - def base(self,*args): + def base(self, *args): r'''From Giac's documentation: Help for base: base(Opt) @@ -1388,9 +1388,9 @@ cdef class GiacMethods_base: Ex2: convert([3,7,1],base,8) Ex3: horner(revlist([3,7,1]),8) ''' - return GiacMethods['base'](self,*args) + return GiacMethods['base'](self, *args) - def basis(self,*args): + def basis(self, *args): r'''From Giac's documentation: Help for basis: basis(Lst(vector1,..,vectorn)) @@ -1398,9 +1398,9 @@ cdef class GiacMethods_base: See also: 1/ ker 2/ ibasis Ex1:basis([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]) ''' - return GiacMethods['basis'](self,*args) + return GiacMethods['basis'](self, *args) - def batons(self,*args): + def batons(self, *args): r'''From Giac's documentation: Help for batons: batons(Mtrx) @@ -1410,9 +1410,9 @@ cdef class GiacMethods_base: Ex2:batons([[1,3],[2,5],[3,2]]) Ex3:batons([1,2,3],[3,5,2]) ''' - return GiacMethods['batons'](self,*args) + return GiacMethods['batons'](self, *args) - def bellman_ford(self,*args): + def bellman_ford(self, *args): r'''From Giac's documentation: Help for bellman_ford: bellman_ford(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) @@ -1420,9 +1420,9 @@ cdef class GiacMethods_base: See also: 1/ dijkstra 2/ shortest_path Ex1:bellman_ford(graph(%{[[1,2],-1],[[2,3],-3],[[3,4],-7],[[4,5],-3],[[5,6],-3],[[1,6],-3]%}),1,4) ''' - return GiacMethods['bellman_ford'](self,*args) + return GiacMethods['bellman_ford'](self, *args) - def bernoulli(self,*args): + def bernoulli(self, *args): r'''From Giac's documentation: Help for bernoulli: bernoulli(Intg||(Intg,Var)) @@ -1431,9 +1431,9 @@ cdef class GiacMethods_base: Ex1:bernoulli(6) Ex2:bernoulli(6,x) ''' - return GiacMethods['bernoulli'](self,*args) + return GiacMethods['bernoulli'](self, *args) - def besselJ(self,*args): + def besselJ(self, *args): r'''From Giac's documentation: Help for besselJ: besselJ(Real(x),Int(p)) @@ -1442,9 +1442,9 @@ cdef class GiacMethods_base: Ex1:besselJ(sqrt(2),2) Ex2:besselJ(sqrt(2),-2) ''' - return GiacMethods['besselJ'](self,*args) + return GiacMethods['besselJ'](self, *args) - def besselY(self,*args): + def besselY(self, *args): r'''From Giac's documentation: Help for besselY: besselY(Real(x),Int(p)) @@ -1453,9 +1453,9 @@ cdef class GiacMethods_base: Ex1:besselY(sqrt(2),2) Ex2:besselY(sqrt(2),-2) ''' - return GiacMethods['besselY'](self,*args) + return GiacMethods['besselY'](self, *args) - def betad(self,*args): + def betad(self, *args): r'''From Giac's documentation: Help for betad: betad(Real(a>0),Real(b>0),Real(0<=x<=1)) @@ -1463,9 +1463,9 @@ cdef class GiacMethods_base: See also: 1/ betad_cdf 2/ betad_icdf Ex1:betad(2.2,1.5,0.8) ''' - return GiacMethods['betad'](self,*args) + return GiacMethods['betad'](self, *args) - def betad_cdf(self,*args): + def betad_cdf(self, *args): r'''From Giac's documentation: Help for betad_cdf: betad_cdf(Real(a>0),Real(b>0),Real(0<=x0<=1),[Real(0<=y0<=1)]) @@ -1474,9 +1474,9 @@ cdef class GiacMethods_base: Ex1:betad_cdf(2,1,0.2) Ex2:betad_cdf(2,1,0.1,0.3) ''' - return GiacMethods['betad_cdf'](self,*args) + return GiacMethods['betad_cdf'](self, *args) - def betad_icdf(self,*args): + def betad_icdf(self, *args): r'''From Giac's documentation: Help for betad_icdf: betad_icdf(Real(a>0),Real(b>0),Real(0<=p<=1)) @@ -1485,9 +1485,9 @@ cdef class GiacMethods_base: Ex1:betad_icdf(2,1,0.95) Ex2:betad_icdf(2,1,0.5) ''' - return GiacMethods['betad_icdf'](self,*args) + return GiacMethods['betad_icdf'](self, *args) - def betavariate(self,*args): + def betavariate(self, *args): r'''From Giac's documentation: Help for betavariate: betavariate(Real(a),Real(b)) @@ -1496,9 +1496,9 @@ cdef class GiacMethods_base: Ex1:betavariate(1,2) Ex2:betavariate(1.5,4) ''' - return GiacMethods['betavariate'](self,*args) + return GiacMethods['betavariate'](self, *args) - def bezier(self,*args): + def bezier(self, *args): r'''From Giac's documentation: Help for bezier: bezier(Lst,[plot]) @@ -1509,9 +1509,9 @@ cdef class GiacMethods_base: Ex3: parameq(bezier(1,1+i,2+i,3-i)) Ex4: parameq(bezier(point([0,0,0]),point([1,1,0]),point([0,1,1]))) ''' - return GiacMethods['bezier'](self,*args) + return GiacMethods['bezier'](self, *args) - def bezout_entiers(self,*args): + def bezout_entiers(self, *args): r'''From Giac's documentation: Help for bezout_entiers: bezout_entiers(Intg,Intg) @@ -1521,9 +1521,9 @@ cdef class GiacMethods_base: Ex2:bezout_entiers(21,28) Ex3:bezout_entiers(30,49) ''' - return GiacMethods['bezout_entiers'](self,*args) + return GiacMethods['bezout_entiers'](self, *args) - def biconnected_components(self,*args): + def biconnected_components(self, *args): r'''From Giac's documentation: Help for biconnected_components: biconnected_components(Graph(G)) @@ -1531,9 +1531,9 @@ cdef class GiacMethods_base: See also: 1/ articulation_points 2/ is_biconnected 3/ is_connected 4/ trail Ex1:biconnected_components(graph(trail(1,2,3,4,2),trail(4,5,6,7,5))) ''' - return GiacMethods['biconnected_components'](self,*args) + return GiacMethods['biconnected_components'](self, *args) - def binomial(self,*args): + def binomial(self, *args): r'''From Giac's documentation: Help for binomial: binomial(Intg(n),Intg(k),[Real(p in 0..1)]) @@ -1547,9 +1547,9 @@ cdef class GiacMethods_base: Ex6: randvector(6,binomial,4,0.2) Ex7: ranm(4,6,binomial,4,0.7) ''' - return GiacMethods['binomial'](self,*args) + return GiacMethods['binomial'](self, *args) - def binomial_cdf(self,*args): + def binomial_cdf(self, *args): r'''From Giac's documentation: Help for binomial_cdf: binomial_cdf(Intg(n),Real(p),Real(x),[Real(y)]) @@ -1559,9 +1559,9 @@ cdef class GiacMethods_base: Ex2:binomial_cdf(4,0.1,2) Ex3:binomial_cdf(4,0.5,2,3) ''' - return GiacMethods['binomial_cdf'](self,*args) + return GiacMethods['binomial_cdf'](self, *args) - def binomial_icdf(self,*args): + def binomial_icdf(self, *args): r'''From Giac's documentation: Help for binomial_icdf: binomial_icdf(Intg(n),Real(p),Real(t)) @@ -1570,27 +1570,27 @@ cdef class GiacMethods_base: Ex1:binomial_icdf(4,0.5,0.68) Ex2:binomial_icdf(4,0.1,0.95) ''' - return GiacMethods['binomial_icdf'](self,*args) + return GiacMethods['binomial_icdf'](self, *args) - def bins(self,*args): + def bins(self, *args): r'''From Giac's documentation: Help for bins: bins(Opt) Option for the kernel_density command. See also: 1/ kernel_density 2/ bandwidth ''' - return GiacMethods['bins'](self,*args) + return GiacMethods['bins'](self, *args) - def bipartite(self,*args): + def bipartite(self, *args): r'''From Giac's documentation: Help for bipartite: bipartite(Opt) Option for the draw_graph command See also: 1/ draw_graph ''' - return GiacMethods['bipartite'](self,*args) + return GiacMethods['bipartite'](self, *args) - def bipartite_matching(self,*args): + def bipartite_matching(self, *args): r'''From Giac's documentation: Help for bipartite_matching: bipartite_matching(Graph(G)) @@ -1598,9 +1598,9 @@ cdef class GiacMethods_base: See also: 1/ is_bipartite 2/ maximum_matching Ex1:bipartite_matching(graph("desargues")) ''' - return GiacMethods['bipartite_matching'](self,*args) + return GiacMethods['bipartite_matching'](self, *args) - def bisection_solver(self,*args): + def bisection_solver(self, *args): r'''From Giac's documentation: Help for bisection_solver: bisection_solver(Opt) @@ -1613,9 +1613,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['bisection_solver'](self,*args) + return GiacMethods['bisection_solver'](self, *args) - def bisector(self,*args): + def bisector(self, *args): r'''From Giac's documentation: Help for bisector: bisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx)) @@ -1623,9 +1623,9 @@ cdef class GiacMethods_base: See also: 1/ angle 2/ exbisector Ex1:bisector(0,1,i) ''' - return GiacMethods['bisector'](self,*args) + return GiacMethods['bisector'](self, *args) - def bit_depth(self,*args): + def bit_depth(self, *args): r'''From Giac's documentation: Help for bit_depth: bit_depth(Lst(clip)) @@ -1633,9 +1633,9 @@ cdef class GiacMethods_base: See also: 1/ channels 2/ channel_data 3/ duration 4/ samplerate Ex1:bit_depth(readwav("/some/file")) ''' - return GiacMethods['bit_depth'](self,*args) + return GiacMethods['bit_depth'](self, *args) - def bitand(self,*args): + def bitand(self, *args): r'''From Giac's documentation: Help for bitand: bitand(Intg,Intg) @@ -1643,9 +1643,9 @@ cdef class GiacMethods_base: See also: 1/ bitxor 2/ bitor Ex1:bitand(0x12,0x38) ''' - return GiacMethods['bitand'](self,*args) + return GiacMethods['bitand'](self, *args) - def bitor(self,*args): + def bitor(self, *args): r'''From Giac's documentation: Help for bitor: bitor(Intg,Intg) @@ -1653,9 +1653,9 @@ cdef class GiacMethods_base: See also: 1/ bitxor 2/ bitand Ex1:bitor(0x12,0x38) ''' - return GiacMethods['bitor'](self,*args) + return GiacMethods['bitor'](self, *args) - def bitxor(self,*args): + def bitxor(self, *args): r'''From Giac's documentation: Help for bitxor: bitxor(Intg,Intg) @@ -1663,9 +1663,9 @@ cdef class GiacMethods_base: See also: 1/ bitor 2/ bitand Ex1:bitxor(0x12,0x38) ''' - return GiacMethods['bitxor'](self,*args) + return GiacMethods['bitxor'](self, *args) - def blackman_harris_window(self,*args): + def blackman_harris_window(self, *args): r'''From Giac's documentation: Help for blackman_harris_window: blackman_harris_window(Lst,[Interval(n1..n2)]) @@ -1673,9 +1673,9 @@ cdef class GiacMethods_base: See also: 1/ bartlett_hann_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(blackman_harris_window(randvector(1000,0..1))) ''' - return GiacMethods['blackman_harris_window'](self,*args) + return GiacMethods['blackman_harris_window'](self, *args) - def blackman_window(self,*args): + def blackman_window(self, *args): r'''From Giac's documentation: Help for blackman_window: blackman_window(Lst,[Real(a)],[Interval(n1..n2)]) @@ -1683,9 +1683,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ bartlett_harris_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(blackman_window(randvector(1000,0..1))) ''' - return GiacMethods['blackman_window'](self,*args) + return GiacMethods['blackman_window'](self, *args) - def blockmatrix(self,*args): + def blockmatrix(self, *args): r'''From Giac's documentation: Help for blockmatrix: blockmatrix(Intg(n),Intg(m),Lst) @@ -1694,9 +1694,9 @@ cdef class GiacMethods_base: Ex1:blockmatrix(2,3,[idn(2),idn(2),idn(2),idn(2),idn(2),idn(2)]) Ex2:blockmatrix(2,2,[idn(2),newMat(2,3),newMat(3,2),idn(3)]) ''' - return GiacMethods['blockmatrix'](self,*args) + return GiacMethods['blockmatrix'](self, *args) - def bohman_window(self,*args): + def bohman_window(self, *args): r'''From Giac's documentation: Help for bohman_window: bohman_window(Lst,[Interval(n1..n2)]) @@ -1704,9 +1704,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bartlett_hann_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(bohman_window(randvector(1000,0..1))) ''' - return GiacMethods['bohman_window'](self,*args) + return GiacMethods['bohman_window'](self, *args) - def border(self,*args): + def border(self, *args): r'''From Giac's documentation: Help for border: border(Mtrx(A),Lst(b)) @@ -1715,9 +1715,9 @@ cdef class GiacMethods_base: Ex1:border([[1,2,3,4],[4,5,6,8],[7,8,9,10]],[1,3,5]) Ex2:border([[1,2,3],[4,5,6],[7,8,9]],[1,0,1]) ''' - return GiacMethods['border'](self,*args) + return GiacMethods['border'](self, *args) - def boxcar(self,*args): + def boxcar(self, *args): r'''From Giac's documentation: Help for boxcar: boxcar(Real(a),Real(b),Expr(x)) @@ -1725,9 +1725,9 @@ cdef class GiacMethods_base: See also: 1/ rect 2/ Heaviside Ex1:boxcar(1,2,x) ''' - return GiacMethods['boxcar'](self,*args) + return GiacMethods['boxcar'](self, *args) - def boxwhisker(self,*args): + def boxwhisker(self, *args): r'''From Giac's documentation: Help for boxwhisker: boxwhisker(Lst,[Lst],[x=a..b||y=a..b]) @@ -1738,9 +1738,9 @@ cdef class GiacMethods_base: Ex3:boxwhisker([1,2,3,5,10,4],[1,2,3,1,2,3]) Ex4:boxwhisker([[6,0,1,3,4,2,5],[0,1,3,4,2,5,6],[1,3,4,2,5,6,0],[3,4,2,5,6,0,1],[4,2,5,6,0,1,3],[2,5,6,0,1,3,4]]) ''' - return GiacMethods['boxwhisker'](self,*args) + return GiacMethods['boxwhisker'](self, *args) - def brent_solver(self,*args): + def brent_solver(self, *args): r'''From Giac's documentation: Help for brent_solver: brent_solver(Opt) @@ -1753,9 +1753,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['brent_solver'](self,*args) + return GiacMethods['brent_solver'](self, *args) - def bvpsolve(self,*args): + def bvpsolve(self, *args): r'''From Giac's documentation: Help for bvpsolve: bvpsolve(Expr(f(x,y,y')),Lst(x=a..b,y),Lst(y(a),y(b),[y'(1)]),[options]) @@ -1764,9 +1764,9 @@ cdef class GiacMethods_base: Ex1:bvpsolve((32+2x^3-y*diff(y(x),x))/8,[x=1..3,y],[17,43/3],20) Ex2:bvpsolve((x^2*diff(y(x),x)^2-9y^2+4x^6)/x^5,[x=1..2,y],[0,ln(256),1],10,output=spline) ''' - return GiacMethods['bvpsolve'](self,*args) + return GiacMethods['bvpsolve'](self, *args) - def cFactor(self,*args): + def cFactor(self, *args): r'''From Giac's documentation: Help for cFactor: cFactor(Expr) @@ -1776,9 +1776,9 @@ cdef class GiacMethods_base: Ex2:cFactor(x^2*y^2+y^2+4*x^2+4) Ex3:cFactor(x^2*y^2+y^2+2*x^2+2) ''' - return GiacMethods['cFactor'](self,*args) + return GiacMethods['cFactor'](self, *args) - def cSolve(self,*args): + def cSolve(self, *args): r'''From Giac's documentation: Help for cSolve: cSolve(LstEq,LstVar) @@ -1789,9 +1789,9 @@ cdef class GiacMethods_base: Ex3:cSolve(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:cSolve(u*v-u=v and v^2=u,[u,v]) ''' - return GiacMethods['cSolve'](self,*args) + return GiacMethods['cSolve'](self, *args) - def cZeros(self,*args): + def cZeros(self, *args): r'''From Giac's documentation: Help for cZeros: cZeros(Expr(Xpr)||LstExpr, [Var||LstVar]) @@ -1800,9 +1800,9 @@ cdef class GiacMethods_base: Ex1:cZeros(x^2-1) Ex2:cZeros([x^2-1,x^2-y^2],[x,y]) ''' - return GiacMethods['cZeros'](self,*args) + return GiacMethods['cZeros'](self, *args) - def camembert(self,*args): + def camembert(self, *args): r'''From Giac's documentation: Help for camembert: camembert(Mtrx) @@ -1812,9 +1812,9 @@ cdef class GiacMethods_base: Ex2:camembert([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:camembert([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) ''' - return GiacMethods['camembert'](self,*args) + return GiacMethods['camembert'](self, *args) - def canonical_form(self,*args): + def canonical_form(self, *args): r'''From Giac's documentation: Help for canonical_form: canonical_form(Trinom(a*x^2+b*x+c),[Var]) @@ -1823,9 +1823,9 @@ cdef class GiacMethods_base: Ex1:canonical_form(2*x^2-12*x+1) Ex2:canonical_form(2*a^2-12*a+1,a) ''' - return GiacMethods['canonical_form'](self,*args) + return GiacMethods['canonical_form'](self, *args) - def canonical_labeling(self,*args): + def canonical_labeling(self, *args): r'''From Giac's documentation: Help for canonical_labeling: canonical_labeling(Graph(G)) @@ -1833,9 +1833,9 @@ cdef class GiacMethods_base: See also: 1/ isomorphic_copy 2/ relabel_vertices Ex1:canonical_labeling(graph("petersen")) ''' - return GiacMethods['canonical_labeling'](self,*args) + return GiacMethods['canonical_labeling'](self, *args) - def cartesian_product(self,*args): + def cartesian_product(self, *args): r'''From Giac's documentation: Help for cartesian_product: cartesian_product(Seq(G1,G2,..)) @@ -1843,9 +1843,9 @@ cdef class GiacMethods_base: See also: 1/ tensor_product Ex1:cartesian_product(graph(trail(1,2,3,4,5,2)),star_graph(3)) ''' - return GiacMethods['cartesian_product'](self,*args) + return GiacMethods['cartesian_product'](self, *args) - def cauchy(self,*args): + def cauchy(self, *args): r'''From Giac's documentation: Help for cauchy: cauchy(Real(x0),Real(a),Real(x)) @@ -1853,9 +1853,9 @@ cdef class GiacMethods_base: See also: 1/ cauchy_cdf 2/ cauchy_icdf Ex1:cauchy(0.0,2.0,1.0) ''' - return GiacMethods['cauchy'](self,*args) + return GiacMethods['cauchy'](self, *args) - def cauchy_cdf(self,*args): + def cauchy_cdf(self, *args): r'''From Giac's documentation: Help for cauchy_cdf: cauchy_cdf(Real(x0),Real(a),Real(x),[Real(y)]) @@ -1864,9 +1864,9 @@ cdef class GiacMethods_base: Ex1:cauchy_cdf(0.0,2.0,2.1) Ex2:cauchy_cdf(2,3,-1.9,1.4) ''' - return GiacMethods['cauchy_cdf'](self,*args) + return GiacMethods['cauchy_cdf'](self, *args) - def cauchy_icdf(self,*args): + def cauchy_icdf(self, *args): r'''From Giac's documentation: Help for cauchy_icdf: cauchy_icdf(Real(x0),Real(a),Real(p)) @@ -1874,9 +1874,9 @@ cdef class GiacMethods_base: See also: 1/ cauchy_cdf 2/ cauchy Ex1:cauchy_icdf(0.0,2.0,0.95) ''' - return GiacMethods['cauchy_icdf'](self,*args) + return GiacMethods['cauchy_icdf'](self, *args) - def cauchyd(self,*args): + def cauchyd(self, *args): r'''From Giac's documentation: Help for cauchyd: cauchyd(Real(x0),Real(a),Real(x)) @@ -1884,9 +1884,9 @@ cdef class GiacMethods_base: See also: 1/ cauchy_cdf 2/ cauchy_icdf Ex1:cauchyd(0.0,2.0,1.0) ''' - return GiacMethods['cauchyd'](self,*args) + return GiacMethods['cauchyd'](self, *args) - def cauchyd_cdf(self,*args): + def cauchyd_cdf(self, *args): r'''From Giac's documentation: Help for cauchyd_cdf: cauchyd_cdf(Real(x0),Real(a),Real(x),[Real(y)]) @@ -1895,9 +1895,9 @@ cdef class GiacMethods_base: Ex1:cauchyd_cdf(0.0,2.0,2.1) Ex2:cauchyd_cdf(2,3,-1.9,1.4) ''' - return GiacMethods['cauchyd_cdf'](self,*args) + return GiacMethods['cauchyd_cdf'](self, *args) - def cauchyd_icdf(self,*args): + def cauchyd_icdf(self, *args): r'''From Giac's documentation: Help for cauchyd_icdf: cauchyd_icdf(Real(x0),Real(a),Real(p)) @@ -1905,9 +1905,9 @@ cdef class GiacMethods_base: See also: 1/ cauchy_cdf 2/ cauchy Ex1:cauchyd_icdf(0.0,2.0,0.95) ''' - return GiacMethods['cauchyd_icdf'](self,*args) + return GiacMethods['cauchyd_icdf'](self, *args) - def cdf(self,*args): + def cdf(self, *args): r'''From Giac's documentation: Help for cdf: cdf(Func,FuncParams) @@ -1918,9 +1918,9 @@ cdef class GiacMethods_base: Ex3:cdf([1,3,4,3,5,6],4) Ex4:cdf([1,3,4,3,5,6],plot) ''' - return GiacMethods['cdf'](self,*args) + return GiacMethods['cdf'](self, *args) - def ceil(self,*args): + def ceil(self, *args): r'''From Giac's documentation: Help for ceil: ceil(Real or Cplx) @@ -1929,9 +1929,9 @@ cdef class GiacMethods_base: Ex1:ceil(-4.2) Ex2:ceil(4.3+2.4*i) ''' - return GiacMethods['ceil'](self,*args) + return GiacMethods['ceil'](self, *args) - def ceiling(self,*args): + def ceiling(self, *args): r'''From Giac's documentation: Help for ceiling: ceiling(Real or Cplx) @@ -1940,9 +1940,9 @@ cdef class GiacMethods_base: Ex1:ceiling(-4.2) Ex2:ceiling(4.3+2.4*i) ''' - return GiacMethods['ceiling'](self,*args) + return GiacMethods['ceiling'](self, *args) - def center(self,*args): + def center(self, *args): r'''From Giac's documentation: Help for center: center(Crcle) @@ -1951,9 +1951,9 @@ cdef class GiacMethods_base: Ex1:center(circle(1+i,2)) Ex2:center(circumcircle(0,1,1+i)) ''' - return GiacMethods['center'](self,*args) + return GiacMethods['center'](self, *args) - def center2interval(self,*args): + def center2interval(self, *args): r'''From Giac's documentation: Help for center2interval: center2interval(LstVal(l),[Real(a0)]) @@ -1962,9 +1962,9 @@ cdef class GiacMethods_base: Ex1:center2interval([2,5,9],1) Ex2:center2interval([2,5,8]) ''' - return GiacMethods['center2interval'](self,*args) + return GiacMethods['center2interval'](self, *args) - def centered_cube(self,*args): + def centered_cube(self, *args): r'''From Giac's documentation: Help for centered_cube: centered_cube(Pnt(A),Pnt(B),Pnt(C)) @@ -1973,9 +1973,9 @@ cdef class GiacMethods_base: Ex1:centered_cube([0,0,0],[3,0,0],[0,0,1]) Ex2:centered_cube(evalf([0,0,0],[3,2,4],[1,1,0])) ''' - return GiacMethods['centered_cube'](self,*args) + return GiacMethods['centered_cube'](self, *args) - def centered_tetrahedron(self,*args): + def centered_tetrahedron(self, *args): r'''From Giac's documentation: Help for centered_tetrahedron: centered_tetrahedron(Pnt(A),Pnt(B),Pnt(C)) @@ -1984,9 +1984,9 @@ cdef class GiacMethods_base: Ex1:centered_tetrahedron([0,0,0],[3,0,0],[0,1,0]) Ex2:centered_tetrahedron(evalf([0,0,0],[3,2,4],[1,1,0])) ''' - return GiacMethods['centered_tetrahedron'](self,*args) + return GiacMethods['centered_tetrahedron'](self, *args) - def cfactor(self,*args): + def cfactor(self, *args): r'''From Giac's documentation: Help for cfactor: cfactor(Expr) @@ -1996,9 +1996,9 @@ cdef class GiacMethods_base: Ex2:cfactor(x^2*y^2+y^2+4*x^2+4) Ex3:cfactor(x^2*y^2+y^2+2*x^2+2) ''' - return GiacMethods['cfactor'](self,*args) + return GiacMethods['cfactor'](self, *args) - def cfsolve(self,*args): + def cfsolve(self, *args): r'''From Giac's documentation: Help for cfsolve: cfsolve(Expr,Var,[Guess or Interval],[Method]) @@ -2007,9 +2007,9 @@ cdef class GiacMethods_base: Ex1:cfsolve(cos(x)=2) Ex2:cfsolve([x^2+y+2,x+y^2+2],[x,y]) ''' - return GiacMethods['cfsolve'](self,*args) + return GiacMethods['cfsolve'](self, *args) - def changebase(self,*args): + def changebase(self, *args): r'''From Giac's documentation: Help for changebase: changebase(Mtrx(A),Mtrx(P)) @@ -2018,9 +2018,9 @@ cdef class GiacMethods_base: Ex1:changebase([[1,2],[1,3]],[[1,1],[0,1]]) Ex2:changebase([[1,2],[1,3]],[[1,0],[1,1]]) ''' - return GiacMethods['changebase'](self,*args) + return GiacMethods['changebase'](self, *args) - def channel_data(self,*args): + def channel_data(self, *args): r'''From Giac's documentation: Help for channel_data: channel_data(Lst(clip),[Intg(chn) or matrix],[range=a..b]) @@ -2031,9 +2031,9 @@ cdef class GiacMethods_base: Ex3:channel_data(readwav("/some/file"),2) Ex4:channel_data(readwav("/some/file"),matrix,range=1.0..2.5) ''' - return GiacMethods['channel_data'](self,*args) + return GiacMethods['channel_data'](self, *args) - def channels(self,*args): + def channels(self, *args): r'''From Giac's documentation: Help for channels: channels(Lst(clip)) @@ -2041,9 +2041,9 @@ cdef class GiacMethods_base: See also: 1/ bit_depth 2/ channel_data 3/ duration 4/ samplerate Ex1:channels(readwav("/some/file")) ''' - return GiacMethods['channels'](self,*args) + return GiacMethods['channels'](self, *args) - def char(self,*args): + def char(self, *args): r'''From Giac's documentation: Help for char: char(Intg or Lst(Intg)) @@ -2052,9 +2052,9 @@ cdef class GiacMethods_base: Ex1:char(65) Ex2:char([65,66,67]) ''' - return GiacMethods['char'](self,*args) + return GiacMethods['char'](self, *args) - def charpoly(self,*args): + def charpoly(self, *args): r'''From Giac's documentation: Help for charpoly: charpoly(Mtrx,[Var]) @@ -2065,9 +2065,9 @@ cdef class GiacMethods_base: Ex3:charpoly([[1,2,3],[1,3,6],[2,5,7]]) Ex4:charpoly([[1,2,3],[1,3,6],[2,5,7]],z) ''' - return GiacMethods['charpoly'](self,*args) + return GiacMethods['charpoly'](self, *args) - def chinrem(self,*args): + def chinrem(self, *args): r'''From Giac's documentation: Help for chinrem: chinrem([Lst||Expr,Lst||Expr],[Lst||Expr,Lst||Expr]) @@ -2076,9 +2076,9 @@ cdef class GiacMethods_base: Ex1:chinrem([x+2,x^2+1],[x+1,x^2+x+1]) Ex2:chinrem([[1,2],[1,0,1]],[[1,1],[1,1,1]]) ''' - return GiacMethods['chinrem'](self,*args) + return GiacMethods['chinrem'](self, *args) - def chisquare(self,*args): + def chisquare(self, *args): r'''From Giac's documentation: Help for chisquare: chisquare(Intg(n),Real(x0)) @@ -2089,9 +2089,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,chisquare,2) Ex4: ranm(4,3,chisquare,2) ''' - return GiacMethods['chisquare'](self,*args) + return GiacMethods['chisquare'](self, *args) - def chisquare_cdf(self,*args): + def chisquare_cdf(self, *args): r'''From Giac's documentation: Help for chisquare_cdf: chisquare_cdf(Intg(n),Real(x0)) @@ -2100,9 +2100,9 @@ cdef class GiacMethods_base: Ex1:chisquare_cdf(2,6.1) Ex2:chisquare_cdf(4,6.1) ''' - return GiacMethods['chisquare_cdf'](self,*args) + return GiacMethods['chisquare_cdf'](self, *args) - def chisquare_icdf(self,*args): + def chisquare_icdf(self, *args): r'''From Giac's documentation: Help for chisquare_icdf: chisquare_icdf(Intg(n),Real(p)) @@ -2111,9 +2111,9 @@ cdef class GiacMethods_base: Ex1:chisquare_icdf(2,0.95) Ex2:chisquare_icdf(4,0.05) ''' - return GiacMethods['chisquare_icdf'](self,*args) + return GiacMethods['chisquare_icdf'](self, *args) - def chisquared(self,*args): + def chisquared(self, *args): r'''From Giac's documentation: Help for chisquared: chisquared(Intg(n),Real(x0)) @@ -2124,9 +2124,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,chisquare,2) Ex4: ranm(4,3,chisquare,2) ''' - return GiacMethods['chisquared'](self,*args) + return GiacMethods['chisquared'](self, *args) - def chisquared_cdf(self,*args): + def chisquared_cdf(self, *args): r'''From Giac's documentation: Help for chisquared_cdf: chisquared_cdf(Intg(n),Real(x0)) @@ -2135,9 +2135,9 @@ cdef class GiacMethods_base: Ex1:chisquared_cdf(2,6.1) Ex2:chisquared_cdf(4,6.1) ''' - return GiacMethods['chisquared_cdf'](self,*args) + return GiacMethods['chisquared_cdf'](self, *args) - def chisquared_icdf(self,*args): + def chisquared_icdf(self, *args): r'''From Giac's documentation: Help for chisquared_icdf: chisquared_icdf(Intg(n),Real(p)) @@ -2146,9 +2146,9 @@ cdef class GiacMethods_base: Ex1:chisquared_icdf(2,0.95) Ex2:chisquared_icdf(4,0.05) ''' - return GiacMethods['chisquared_icdf'](self,*args) + return GiacMethods['chisquared_icdf'](self, *args) - def chisquaret(self,*args): + def chisquaret(self, *args): r'''From Giac's documentation: Help for chisquaret: chisquaret(Data,[Func],[FuncParams]) @@ -2164,9 +2164,9 @@ cdef class GiacMethods_base: Ex8:chisquaret([11,16,17,22,14,10],[1/6,1/6,1/6,1/6,1/6,1/6]) Ex9:chisquaret([11,16,17,22,14,10],[(1/6)$6]) ''' - return GiacMethods['chisquaret'](self,*args) + return GiacMethods['chisquaret'](self, *args) - def choice(self,*args): + def choice(self, *args): r'''From Giac's documentation: Help for choice: choice(Lst(L)) @@ -2177,9 +2177,9 @@ cdef class GiacMethods_base: Ex3: L:=[1,2,3,4,5,6];L:=choice(L) Ex4: L:=[1,2,3,4,5,6];L.choice() ''' - return GiacMethods['choice'](self,*args) + return GiacMethods['choice'](self, *args) - def cholesky(self,*args): + def cholesky(self, *args): r'''From Giac's documentation: Help for cholesky: cholesky(Mtrx) @@ -2187,9 +2187,9 @@ cdef class GiacMethods_base: See also: 1/ lu 2/ qr 3/ gauss Ex1:cholesky([[3,1],[1,4]]) ''' - return GiacMethods['cholesky'](self,*args) + return GiacMethods['cholesky'](self, *args) - def chr(self,*args): + def chr(self, *args): r'''From Giac's documentation: Help for chr: chr(Intg or Lst(Intg)) @@ -2198,9 +2198,9 @@ cdef class GiacMethods_base: Ex1:chr(65) Ex2:chr([65,66,67]) ''' - return GiacMethods['chr'](self,*args) + return GiacMethods['chr'](self, *args) - def chrem(self,*args): + def chrem(self, *args): r'''From Giac's documentation: Help for chrem: chrem(LstIntg(a,b,c....),LstIntg(p,q,r,....)) @@ -2212,9 +2212,9 @@ cdef class GiacMethods_base: Ex4:chrem([2,4,6,7],[3,5,7,11]) Ex5:chrem([2*x+1,4*x+2,6*x-1,x+1],[3,5,7,11]) ''' - return GiacMethods['chrem'](self,*args) + return GiacMethods['chrem'](self, *args) - def chromatic_index(self,*args): + def chromatic_index(self, *args): r'''From Giac's documentation: Help for chromatic_index: chromatic_index(Graph(G),[Lst(cols)]) @@ -2223,18 +2223,18 @@ cdef class GiacMethods_base: Ex1:chromatic_index(graph("petersen")) Ex2:chromatic_index(graph("dodecahedron"),colors) ''' - return GiacMethods['chromatic_index'](self,*args) + return GiacMethods['chromatic_index'](self, *args) - def chromatic_number(self,*args): + def chromatic_number(self, *args): r'''From Giac's documentation: Help for chromatic_number: chromatic_number(Graph(G)) Returns the chromatic number of G. Ex1:chromatic_number(graph("petersen")) ''' - return GiacMethods['chromatic_number'](self,*args) + return GiacMethods['chromatic_number'](self, *args) - def chromatic_polynomial(self,*args): + def chromatic_polynomial(self, *args): r'''From Giac's documentation: Help for chromatic_polynomial: chromatic_polynomial(Graph(G),[Var(t)]) @@ -2243,9 +2243,9 @@ cdef class GiacMethods_base: Ex1:chromatic_polynomial(graph("petersen")) Ex2:chromatic_polynomial(graph("petersen"),3) ''' - return GiacMethods['chromatic_polynomial'](self,*args) + return GiacMethods['chromatic_polynomial'](self, *args) - def circle(self,*args): + def circle(self, *args): r'''From Giac's documentation: Help for circle: circle((Pnt(M) or Cplx(M),(Pnt(N) or Cplx(zN)),[Real(a)],[Real(b)],[Var(A)],[Var(B)]) @@ -2260,9 +2260,9 @@ cdef class GiacMethods_base: Ex7:circle(cercle(point([-1,0,0]),point([1,0,0]),point([0,2,0]))) Ex8:circle(cercle([-1,0,0],point([1,0,0]),[0,2,0])) ''' - return GiacMethods['circle'](self,*args) + return GiacMethods['circle'](self, *args) - def circumcircle(self,*args): + def circumcircle(self, *args): r'''From Giac's documentation: Help for circumcircle: circumcircle((Pnt or Cplx),(Pnt or Cplx),((Pnt or Cplx)) @@ -2270,9 +2270,9 @@ cdef class GiacMethods_base: See also: 1/ circle 2/ incircle 3/ excircle Ex1:circumcircle(0,1,1+i) ''' - return GiacMethods['circumcircle'](self,*args) + return GiacMethods['circumcircle'](self, *args) - def classes(self,*args): + def classes(self, *args): r'''From Giac's documentation: Help for classes: classes(Lst(l),[ClassMin],[ClassSize||Lst(Center)]) @@ -2284,9 +2284,9 @@ cdef class GiacMethods_base: Ex4:classes([1,1.2,1.4,1.6,1.8,2,2.5],1,[1.2,1.6,2.2]) Ex5:classes([0,0.5,1,1.5,2,2.5,3,3.5,4],[0..2,2..4,4..6]) ''' - return GiacMethods['classes'](self,*args) + return GiacMethods['classes'](self, *args) - def clear(self,*args): + def clear(self, *args): r'''From Giac's documentation: Help for clear: clear(NULL) @@ -2294,9 +2294,9 @@ cdef class GiacMethods_base: See also: 1/ set_pixel 2/ show_pixels Ex1:clear() ''' - return GiacMethods['clear'](self,*args) + return GiacMethods['clear'](self, *args) - def clique_cover(self,*args): + def clique_cover(self, *args): r'''From Giac's documentation: Help for clique_cover: clique_cover(Graph(G),[Intg(k)]) @@ -2306,9 +2306,9 @@ cdef class GiacMethods_base: Ex2:clique_cover(cycle_graph(5)) Ex3:clique_cover(graph_complement(complete_graph(3,4))) ''' - return GiacMethods['clique_cover'](self,*args) + return GiacMethods['clique_cover'](self, *args) - def clique_cover_number(self,*args): + def clique_cover_number(self, *args): r'''From Giac's documentation: Help for clique_cover_number: clique_cover_number(Graph(G)) @@ -2318,9 +2318,9 @@ cdef class GiacMethods_base: Ex2:clique_cover_number(cycle_graph(5)) Ex3:clique_cover_number(graph_complement(complete_graph(3,4))) ''' - return GiacMethods['clique_cover_number'](self,*args) + return GiacMethods['clique_cover_number'](self, *args) - def clique_number(self,*args): + def clique_number(self, *args): r'''From Giac's documentation: Help for clique_number: clique_number(Graph(G)) @@ -2328,9 +2328,9 @@ cdef class GiacMethods_base: See also: 1/ maximum_clique Ex1:clique_number(graph_complement(complete_graph(3,4))) ''' - return GiacMethods['clique_number'](self,*args) + return GiacMethods['clique_number'](self, *args) - def clique_stats(self,*args): + def clique_stats(self, *args): r'''From Giac's documentation: Help for clique_stats: clique_stats(Graph(G),[Intg(k)||Intrv(m..n)]) @@ -2340,9 +2340,9 @@ cdef class GiacMethods_base: Ex2:clique_stats(random_graph(50,0.5),5) Ex3:clique_stats(random_graph(50,0.5),3..5) ''' - return GiacMethods['clique_stats'](self,*args) + return GiacMethods['clique_stats'](self, *args) - def clustering_coefficient(self,*args): + def clustering_coefficient(self, *args): r'''From Giac's documentation: Help for clustering_coefficient: clustering_coefficient(Graph(G),[Vrtx(v)]) @@ -2351,9 +2351,9 @@ cdef class GiacMethods_base: Ex1:clustering_coefficient(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%})) Ex2:clustering_coefficient(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%}),2) ''' - return GiacMethods['clustering_coefficient'](self,*args) + return GiacMethods['clustering_coefficient'](self, *args) - def coeff(self,*args): + def coeff(self, *args): r'''From Giac's documentation: Help for coeff: coeff(Expr(P),[Var]) @@ -2363,9 +2363,9 @@ cdef class GiacMethods_base: Ex2:coeff(5*y^2-3,y) Ex3:coeff(5*y^2-3,y,2) ''' - return GiacMethods['coeff'](self,*args) + return GiacMethods['coeff'](self, *args) - def coeffs(self,*args): + def coeffs(self, *args): r'''From Giac's documentation: Help for coeffs: coeffs(Expr(P),[Var]) @@ -2375,9 +2375,9 @@ cdef class GiacMethods_base: Ex2:coeffs(5*y^2-3,y) Ex3:coeffs(5*y^2-3,y,2) ''' - return GiacMethods['coeffs'](self,*args) + return GiacMethods['coeffs'](self, *args) - def col(self,*args): + def col(self, *args): r'''From Giac's documentation: Help for col: col(Mtrx(A),Intg(n)||Interval(n1..n2)) @@ -2387,9 +2387,9 @@ cdef class GiacMethods_base: Ex2:col([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3: count_eq(3,[[3,2,3],[4,3,2],[3,2,1]],col) ''' - return GiacMethods['col'](self,*args) + return GiacMethods['col'](self, *args) - def colDim(self,*args): + def colDim(self, *args): r'''From Giac's documentation: Help for colDim: colDim(Mtrx) @@ -2398,9 +2398,9 @@ cdef class GiacMethods_base: Ex1:colDim([[1,2,3],[4,5,6]]) Ex2:colDim([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['colDim'](self,*args) + return GiacMethods['colDim'](self, *args) - def colNorm(self,*args): + def colNorm(self, *args): r'''From Giac's documentation: Help for colNorm: colNorm(Vect or Mtrx) @@ -2409,9 +2409,9 @@ cdef class GiacMethods_base: Ex1:colNorm([[1,2],[3,-4]]) Ex2:colNorm([[1,2,3,-4],[-5,3,2,1]]) ''' - return GiacMethods['colNorm'](self,*args) + return GiacMethods['colNorm'](self, *args) - def colSwap(self,*args): + def colSwap(self, *args): r'''From Giac's documentation: Help for colSwap: colSwap(Mtrx(A),Intg(n1),Intg(n2)) @@ -2419,9 +2419,9 @@ cdef class GiacMethods_base: See also: 1/ rowSwap Ex1:colSwap([[1,2],[3,4],[5,6]],0,1) ''' - return GiacMethods['colSwap'](self,*args) + return GiacMethods['colSwap'](self, *args) - def coldim(self,*args): + def coldim(self, *args): r'''From Giac's documentation: Help for coldim: coldim(Mtrx) @@ -2430,9 +2430,9 @@ cdef class GiacMethods_base: Ex1:coldim([[1,2,3],[4,5,6]]) Ex2:coldim([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['coldim'](self,*args) + return GiacMethods['coldim'](self, *args) - def collect(self,*args): + def collect(self, *args): r'''From Giac's documentation: Help for collect: collect(Poly or LstPoly) @@ -2442,9 +2442,9 @@ cdef class GiacMethods_base: Ex2:collect(x^2-2) Ex3:collect([x^2-2,x^2-4]) ''' - return GiacMethods['collect'](self,*args) + return GiacMethods['collect'](self, *args) - def colnorm(self,*args): + def colnorm(self, *args): r'''From Giac's documentation: Help for colnorm: colnorm(Vect or Mtrx) @@ -2453,9 +2453,9 @@ cdef class GiacMethods_base: Ex1:colnorm([[1,2],[3,-4]]) Ex2:colnorm([[1,2,3,-4],[-5,3,2,1]]) ''' - return GiacMethods['colnorm'](self,*args) + return GiacMethods['colnorm'](self, *args) - def color(self,*args): + def color(self, *args): r'''From Giac's documentation: Help for color: color([GeoObj or legende],Intg) @@ -2472,9 +2472,9 @@ cdef class GiacMethods_base: Ex9:color(red);square(0,1); Ex10:color(red+filled);square(0,1); ''' - return GiacMethods['color'](self,*args) + return GiacMethods['color'](self, *args) - def colspace(self,*args): + def colspace(self, *args): r'''From Giac's documentation: Help for colspace: colspace(Mtrx(A), [Var(d)]) @@ -2483,9 +2483,9 @@ cdef class GiacMethods_base: Ex1:colspace([[1,2,3],[1,2,3],[1,2,4],[1,2,5]]) Ex2:colspace([[1,2,3],[1,3,6],[2,5,9]],d) ''' - return GiacMethods['colspace'](self,*args) + return GiacMethods['colspace'](self, *args) - def colswap(self,*args): + def colswap(self, *args): r'''From Giac's documentation: Help for colswap: colswap(Mtrx(A),Intg(n1),Intg(n2)) @@ -2493,9 +2493,9 @@ cdef class GiacMethods_base: See also: 1/ rowSwap Ex1:colswap([[1,2],[3,4],[5,6]],0,1) ''' - return GiacMethods['colswap'](self,*args) + return GiacMethods['colswap'](self, *args) - def comDenom(self,*args): + def comDenom(self, *args): r'''From Giac's documentation: Help for comDenom: comDenom(Expr,[Var(Var)]) @@ -2505,9 +2505,9 @@ cdef class GiacMethods_base: Ex2:comDenom(1/x+1/y^2+1,y) Ex3:comDenom(1/x+1/y^2+1,x) ''' - return GiacMethods['comDenom'](self,*args) + return GiacMethods['comDenom'](self, *args) - def comb(self,*args): + def comb(self, *args): r'''From Giac's documentation: Help for comb: comb(Intg(n),Intg(r)) @@ -2515,9 +2515,9 @@ cdef class GiacMethods_base: See also: 1/ factorial 2/ perm Ex1:comb(4,2) ''' - return GiacMethods['comb'](self,*args) + return GiacMethods['comb'](self, *args) - def combine(self,*args): + def combine(self, *args): r'''From Giac's documentation: Help for combine: combine(Expr(Xpr),Fnc(f).) @@ -2527,9 +2527,9 @@ cdef class GiacMethods_base: Ex2:combine(sin(x)*cos(x),trig) Ex3:combine(ln(x)+ln(y),ln) ''' - return GiacMethods['combine'](self,*args) + return GiacMethods['combine'](self, *args) - def comment(self,*args): + def comment(self, *args): r'''From Giac's documentation: Help for comment: comment(Expr) @@ -2537,9 +2537,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:comment("my_comment") ''' - return GiacMethods['comment'](self,*args) + return GiacMethods['comment'](self, *args) - def common_perpendicular(self,*args): + def common_perpendicular(self, *args): r'''From Giac's documentation: Help for common_perpendicular: common_perpendicular(Line(D1),Line(D2)) @@ -2547,9 +2547,9 @@ cdef class GiacMethods_base: See also: 1/ altitude 2/ perpendicular Ex1:common_perpendicular(line([0,0,0],[0,5,5]),line([5,0,0],[0,0,5])) ''' - return GiacMethods['common_perpendicular'](self,*args) + return GiacMethods['common_perpendicular'](self, *args) - def companion(self,*args): + def companion(self, *args): r'''From Giac's documentation: Help for companion: companion(Poly,Var) @@ -2558,9 +2558,9 @@ cdef class GiacMethods_base: Ex1:companion(x^2+5x-7,x) Ex2:companion(-pcar([[1,0,1],[0,2,-1],[1,-1,1]],x),x) ''' - return GiacMethods['companion'](self,*args) + return GiacMethods['companion'](self, *args) - def compare(self,*args): + def compare(self, *args): r'''From Giac's documentation: Help for compare: compare(Obj(arg1),Obj(arg2)) @@ -2570,9 +2570,9 @@ cdef class GiacMethods_base: Ex2:compare(1.0,2) Ex3:compare("ab","cd") ''' - return GiacMethods['compare'](self,*args) + return GiacMethods['compare'](self, *args) - def complete_binary_tree(self,*args): + def complete_binary_tree(self, *args): r'''From Giac's documentation: Help for complete_binary_tree: complete_binary_tree(Intg(n)) @@ -2580,9 +2580,9 @@ cdef class GiacMethods_base: See also: 1/ complete_kary_tree 2/ is_tree 3/ random_tree Ex1:complete_binary_tree(3) ''' - return GiacMethods['complete_binary_tree'](self,*args) + return GiacMethods['complete_binary_tree'](self, *args) - def complete_graph(self,*args): + def complete_graph(self, *args): r'''From Giac's documentation: Help for complete_graph: complete_graph(Intg(n)||Lst(V)||Seq(n1,n2,...,nk)) @@ -2592,9 +2592,9 @@ cdef class GiacMethods_base: Ex2:complete_graph(["one","two","three"]) Ex3:complete_graph(2,3,4) ''' - return GiacMethods['complete_graph'](self,*args) + return GiacMethods['complete_graph'](self, *args) - def complete_kary_tree(self,*args): + def complete_kary_tree(self, *args): r'''From Giac's documentation: Help for complete_kary_tree: complete_kary_tree(Intg(n)) @@ -2602,9 +2602,9 @@ cdef class GiacMethods_base: See also: 1/ complete_binary_tree 2/ is_tree 3/ random_tree Ex1:complete_kary_tree(3,3) ''' - return GiacMethods['complete_kary_tree'](self,*args) + return GiacMethods['complete_kary_tree'](self, *args) - def complex(self,*args): + def complex(self, *args): r'''From Giac's documentation: Help for complex: complex(Opt) @@ -2614,9 +2614,9 @@ cdef class GiacMethods_base: Ex2: assume(a,DOM_COMPLEX) Ex3: a:=1+i;type(a) ''' - return GiacMethods['complex'](self,*args) + return GiacMethods['complex'](self, *args) - def complex_variables(self,*args): + def complex_variables(self, *args): r'''From Giac's documentation: Help for complex_variables: complex_variables(:=Intg(0 or 1)) @@ -2625,9 +2625,9 @@ cdef class GiacMethods_base: Ex1: complex_variables:=1 Ex2: complex_variables:=0 ''' - return GiacMethods['complex_variables'](self,*args) + return GiacMethods['complex_variables'](self, *args) - def complexroot(self,*args): + def complexroot(self, *args): r'''From Giac's documentation: Help for complexroot: complexroot(Poly(P),Real(l),[Cplx(a)],[Cplx(b)]) @@ -2638,9 +2638,9 @@ cdef class GiacMethods_base: Ex3:complexroot(x^3+8,1e-5,0,2+2*i) Ex4:complexroot(x^5-2*x^4+x^3+i,0.1,1+0.5*i,1.1+0.7*i) ''' - return GiacMethods['complexroot'](self,*args) + return GiacMethods['complexroot'](self, *args) - def concat(self,*args): + def concat(self, *args): r'''From Giac's documentation: Help for concat: concat(Lst,Lst||Seq,Seq||Str,Str||Mtrx,Mtrx) @@ -2652,9 +2652,9 @@ cdef class GiacMethods_base: Ex4: L:=[1,2];L.concat([3,4,5]) Ex5: S:="abcd";S.concat("efghi") ''' - return GiacMethods['concat'](self,*args) + return GiacMethods['concat'](self, *args) - def cond(self,*args): + def cond(self, *args): r'''From Giac's documentation: Help for cond: cond(Mtrx,[2]||[inf]) @@ -2665,9 +2665,9 @@ cdef class GiacMethods_base: Ex3:cond([[1,2],[1,4]],2) Ex4:cond([[1,2],[1,4]],inf) ''' - return GiacMethods['cond'](self,*args) + return GiacMethods['cond'](self, *args) - def condensation(self,*args): + def condensation(self, *args): r'''From Giac's documentation: Help for condensation: condensation(Graph(G)) @@ -2675,9 +2675,9 @@ cdef class GiacMethods_base: See also: 1/ strongly_connected_components Ex1:condensation(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%})) ''' - return GiacMethods['condensation'](self,*args) + return GiacMethods['condensation'](self, *args) - def cone(self,*args): + def cone(self, *args): r'''From Giac's documentation: Help for cone: cone(Pnt(A),Vect(v),Real(t),[Real(h)]) @@ -2686,9 +2686,9 @@ cdef class GiacMethods_base: Ex1:cone([0,0,0],[0,0,1],pi/6) Ex2:cone([0,0,0],[0,1,1],pi/6,4) ''' - return GiacMethods['cone'](self,*args) + return GiacMethods['cone'](self, *args) - def confrac(self,*args): + def confrac(self, *args): r'''From Giac's documentation: Help for confrac: confrac(Opt) @@ -2696,9 +2696,9 @@ cdef class GiacMethods_base: See also: 1/ convert Ex1: convert(sqrt(2),confrac,'L'),L ''' - return GiacMethods['confrac'](self,*args) + return GiacMethods['confrac'](self, *args) - def conic(self,*args): + def conic(self, *args): r'''From Giac's documentation: Help for conic: conic(Expr,[LstVar]) @@ -2709,9 +2709,9 @@ cdef class GiacMethods_base: Ex3:conic(u^2-2*v^2-2*u*v-1,[u,v]) Ex4:conic(y^2-x*y+3,[x,y]) ''' - return GiacMethods['conic'](self,*args) + return GiacMethods['conic'](self, *args) - def conj(self,*args): + def conj(self, *args): r'''From Giac's documentation: Help for conj: conj(Cplx) @@ -2722,9 +2722,9 @@ cdef class GiacMethods_base: Ex3:conj((1+2*i)^2) Ex4:conj([[1+i,2,3],[1,3,6],[2,5,9-i]]) ''' - return GiacMethods['conj'](self,*args) + return GiacMethods['conj'](self, *args) - def conjugate_equation(self,*args): + def conjugate_equation(self, *args): r'''From Giac's documentation: Help for conjugate_equation: conjugate_equation(Expr(y0),Lst(P),Lst(V),Var(x),Real(a)) @@ -2732,9 +2732,9 @@ cdef class GiacMethods_base: See also: 1/ jacobi_equation 2/ euler_lagrange Ex1:conjugate_equation(A*sin(t)+B*cos(t),[A,B],[1,0],t,0) ''' - return GiacMethods['conjugate_equation'](self,*args) + return GiacMethods['conjugate_equation'](self, *args) - def conjugate_gradient(self,*args): + def conjugate_gradient(self, *args): r'''From Giac's documentation: Help for conjugate_gradient: conjugate_gradient(Mtrx(A),Vect(y),[Vect(x0),Real(eps)]) @@ -2745,18 +2745,18 @@ cdef class GiacMethods_base: Ex3:conjugate_gradient([[2,1],[1,5]],[1,0],[0.55,-0.11],1e-2) Ex4:conjugate_gradient([[2,1],[1,5]],[1,0],[0.55,-0.11],1e-10) ''' - return GiacMethods['conjugate_gradient'](self,*args) + return GiacMethods['conjugate_gradient'](self, *args) - def connected(self,*args): + def connected(self, *args): r'''From Giac's documentation: Help for connected: connected(Opt) Option for the random_regular_graph command. See also: 1/ directed 2/ weighted 3/ random_regular_graph ''' - return GiacMethods['connected'](self,*args) + return GiacMethods['connected'](self, *args) - def connected_components(self,*args): + def connected_components(self, *args): r'''From Giac's documentation: Help for connected_components: connected_components(Graph(G)) @@ -2764,9 +2764,9 @@ cdef class GiacMethods_base: See also: 1/ articulation_points 2/ is_biconnected 3/ is_strongly_connected 4/ strongly_connected_components 5/ underlying_graph Ex1:connected_components(graph_complement(cycle_graph(4))) ''' - return GiacMethods['connected_components'](self,*args) + return GiacMethods['connected_components'](self, *args) - def cont(self,*args): + def cont(self, *args): r'''From Giac's documentation: Help for cont: cont(NULL) @@ -2774,9 +2774,9 @@ cdef class GiacMethods_base: See also: 1/ continue Ex1:cont() ''' - return GiacMethods['cont'](self,*args) + return GiacMethods['cont'](self, *args) - def contains(self,*args): + def contains(self, *args): r'''From Giac's documentation: Help for contains: contains((Lst(l) or Set(l)),Elem(e)) @@ -2786,9 +2786,9 @@ cdef class GiacMethods_base: Ex2:contains([0,1,2,3],4) Ex3:contains([1..2],1.5) ''' - return GiacMethods['contains'](self,*args) + return GiacMethods['contains'](self, *args) - def content(self,*args): + def content(self, *args): r'''From Giac's documentation: Help for content: content(Poly(P),[Var]) @@ -2798,9 +2798,9 @@ cdef class GiacMethods_base: Ex2:content([2,10,6]) Ex3:content(2*t^2+10*t+6,t) ''' - return GiacMethods['content'](self,*args) + return GiacMethods['content'](self, *args) - def contourplot(self,*args): + def contourplot(self, *args): r'''From Giac's documentation: Help for contourplot: contourplot(Expr(Xpr),[LstVar],[LstVal]) @@ -2811,9 +2811,9 @@ cdef class GiacMethods_base: Ex3:contourplot(x^2+2*y^2-2,[x,y],[1.0,2.0,3.0]) Ex4:contourplot(x^2-y^2,[x=-4..4,y=-4..4],seq(k,k,-11,11,3),xstep=0.1,ystep=0.1) ''' - return GiacMethods['contourplot'](self,*args) + return GiacMethods['contourplot'](self, *args) - def contract_edge(self,*args): + def contract_edge(self, *args): r'''From Giac's documentation: Help for contract_edge: contract_edge(Graph(G),Edge(e)) @@ -2821,9 +2821,9 @@ cdef class GiacMethods_base: See also: 1/ delete_edge 2/ delete_vertex 3/ foldl Ex1:contract_edge(complete_graph(4),[1,3]) ''' - return GiacMethods['contract_edge'](self,*args) + return GiacMethods['contract_edge'](self, *args) - def convert(self,*args): + def convert(self, *args): r'''From Giac's documentation: Help for convert: convert(Expr(Xpr),Cmd(cmd)) @@ -2847,9 +2847,9 @@ cdef class GiacMethods_base: Ex16: A[2,1]:=1;convert(A,array) Ex17: B[0..1,1..2]:=1;B[2,2]:=2;convert(B,array) ''' - return GiacMethods['convert'](self,*args) + return GiacMethods['convert'](self, *args) - def convertir(self,*args): + def convertir(self, *args): r'''From Giac's documentation: Help for convertir: convertir(Expr(Xpr),Cmd(cmd)) @@ -2873,9 +2873,9 @@ cdef class GiacMethods_base: Ex16: A[2,1]:=1;convert(A,array) Ex17: B[0..1,1..2]:=1;B[2,2]:=2;convert(B,array) ''' - return GiacMethods['convertir'](self,*args) + return GiacMethods['convertir'](self, *args) - def convex(self,*args): + def convex(self, *args): r'''From Giac's documentation: Help for convex: convex(Expr(f),Lst(x,y,..)) @@ -2891,9 +2891,9 @@ cdef class GiacMethods_base: Ex8:convex(sqrt((1+cos(x)^2)/sin(x)),x) Ex9:convex(sqrt((1+(u')^2)/(2*g*u)),u(t)) ''' - return GiacMethods['convex'](self,*args) + return GiacMethods['convex'](self, *args) - def convexhull(self,*args): + def convexhull(self, *args): r'''From Giac's documentation: Help for convexhull: convexhull(Lst) @@ -2903,9 +2903,9 @@ cdef class GiacMethods_base: Ex2:convexhull([0,1,1+i,1+2i,-1-i,1-3i,-2+i]) Ex3: polygon(convexhull(0,1,1+i,1+2i,-1-i,1-3i,-2+i)) ''' - return GiacMethods['convexhull'](self,*args) + return GiacMethods['convexhull'](self, *args) - def convolution(self,*args): + def convolution(self, *args): r'''From Giac's documentation: Help for convolution: convolution(Lst(u),Lst(v)) @@ -2914,9 +2914,9 @@ cdef class GiacMethods_base: Ex1:convolution([1,2,3],[1,-1,1,-1]) Ex2:convolution(25*exp(2*x),x*exp(-3*x),x) ''' - return GiacMethods['convolution'](self,*args) + return GiacMethods['convolution'](self, *args) - def coordinates(self,*args): + def coordinates(self, *args): r'''From Giac's documentation: Help for coordinates: coordinates(Pnt or Cplx or Vect) @@ -2931,9 +2931,9 @@ cdef class GiacMethods_base: Ex7:coordinates(point(1,2,3)) Ex8:coordinates(vecteur([1,2,3],[4,5,6])) ''' - return GiacMethods['coordinates'](self,*args) + return GiacMethods['coordinates'](self, *args) - def copy(self,*args): + def copy(self, *args): r'''From Giac's documentation: Help for copy: copy(Mtrx,Var) @@ -2941,9 +2941,9 @@ cdef class GiacMethods_base: See also: 1/ =< Ex1: A:=copy(B) ''' - return GiacMethods['copy'](self,*args) + return GiacMethods['copy'](self, *args) - def correlation(self,*args): + def correlation(self, *args): r'''From Giac's documentation: Help for correlation: correlation(Lst||Mtrx,[Lst]) @@ -2951,9 +2951,9 @@ cdef class GiacMethods_base: See also: 1/ covariance 2/ covariance_correlation Ex1:correlation([[1,2],[1,1],[4,7]]) ''' - return GiacMethods['correlation'](self,*args) + return GiacMethods['correlation'](self, *args) - def cos(self,*args): + def cos(self, *args): r'''From Giac's documentation: Help for cos: cos(Expr or Opt) @@ -2962,9 +2962,9 @@ cdef class GiacMethods_base: Ex1:cos(0) Ex2: convert(cos(x)^4+sin(x)^2,cos) ''' - return GiacMethods['cos'](self,*args) + return GiacMethods['cos'](self, *args) - def cos2sintan(self,*args): + def cos2sintan(self, *args): r'''From Giac's documentation: Help for cos2sintan: cos2sintan(Expr) @@ -2972,9 +2972,9 @@ cdef class GiacMethods_base: See also: 1/ tan2sincos 2/ sin2costan 3/ tan2sincos2 4/ tan2cossin2 Ex1:cos2sintan(cos(x)) ''' - return GiacMethods['cos2sintan'](self,*args) + return GiacMethods['cos2sintan'](self, *args) - def cosh(self,*args): + def cosh(self, *args): r'''From Giac's documentation: Help for cosh: cosh(Expr) @@ -2982,9 +2982,9 @@ cdef class GiacMethods_base: See also: 1/ acosh Ex1:cosh(0) ''' - return GiacMethods['cosh'](self,*args) + return GiacMethods['cosh'](self, *args) - def cosine_window(self,*args): + def cosine_window(self, *args): r'''From Giac's documentation: Help for cosine_window: cosine_window(Lst,[Real(a)],[Interval(n1..n2)]) @@ -2992,9 +2992,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ bartlett_hann_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(cosine_window(randvector(1000,0..1),1.5)) ''' - return GiacMethods['cosine_window'](self,*args) + return GiacMethods['cosine_window'](self, *args) - def cot(self,*args): + def cot(self, *args): r'''From Giac's documentation: Help for cot: cot(Expr) @@ -3002,9 +3002,9 @@ cdef class GiacMethods_base: See also: 1/ acot 2/ tan Ex1:cot(pi/2) ''' - return GiacMethods['cot'](self,*args) + return GiacMethods['cot'](self, *args) - def cote(self,*args): + def cote(self, *args): r'''From Giac's documentation: Help for cote: cote(Vect) @@ -3013,9 +3013,9 @@ cdef class GiacMethods_base: Ex1:cote(point[1,2,3]) Ex2:cote(point(1,2,3)) ''' - return GiacMethods['cote'](self,*args) + return GiacMethods['cote'](self, *args) - def count(self,*args): + def count(self, *args): r'''From Giac's documentation: Help for count: count(Fnc(f)||LstIntg,(Lst||Mtrx)(l),[Opt(row||col)]) @@ -3032,9 +3032,9 @@ cdef class GiacMethods_base: Ex9:count((x)->x>2 && x<4,[[3,9/2],[4,1]]) Ex10:count((x)->x<2 || x>4,[[3,9/2],[4,1]]) ''' - return GiacMethods['count'](self,*args) + return GiacMethods['count'](self, *args) - def count_eq(self,*args): + def count_eq(self, *args): r'''From Giac's documentation: Help for count_eq: count_eq(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) @@ -3045,9 +3045,9 @@ cdef class GiacMethods_base: Ex3:count_eq(4,[[3,4],[4,1]],row) Ex4:count_eq(4,[[3,4],[4,1]],col) ''' - return GiacMethods['count_eq'](self,*args) + return GiacMethods['count_eq'](self, *args) - def count_inf(self,*args): + def count_inf(self, *args): r'''From Giac's documentation: Help for count_inf: count_inf(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) @@ -3058,9 +3058,9 @@ cdef class GiacMethods_base: Ex3:count_inf(4,[[3,5],[4,1]],row) Ex4:count_inf(4,[[3,5],[4,1]],col) ''' - return GiacMethods['count_inf'](self,*args) + return GiacMethods['count_inf'](self, *args) - def count_sup(self,*args): + def count_sup(self, *args): r'''From Giac's documentation: Help for count_sup: count_sup(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) @@ -3071,9 +3071,9 @@ cdef class GiacMethods_base: Ex3:count_sup(3,[[3,5],[4,1]],row) Ex4:count_sup(3,[[3,5],[4,1]],col) ''' - return GiacMethods['count_sup'](self,*args) + return GiacMethods['count_sup'](self, *args) - def courbe_parametrique(self,*args): + def courbe_parametrique(self, *args): r'''From Giac's documentation: Help for courbe_parametrique: courbe_parametrique(Cplx||Lst,Var||Lst(Var)) @@ -3088,9 +3088,9 @@ cdef class GiacMethods_base: Ex7:courbe_parametrique([v*cos(u),v*sin(u),v],[u,v]) Ex8:courbe_parametrique([v*cos(u),v*sin(u),v],[u=0..pi,v=0..3],ustep=0.1,vstep=0.2) ''' - return GiacMethods['courbe_parametrique'](self,*args) + return GiacMethods['courbe_parametrique'](self, *args) - def courbe_polaire(self,*args): + def courbe_polaire(self, *args): r'''From Giac's documentation: Help for courbe_polaire: courbe_polaire(Expr,Var,VarMin,VarMax) @@ -3099,9 +3099,9 @@ cdef class GiacMethods_base: Ex1:courbe_polaire(sin(2*x),x,0,pi) Ex2:courbe_polaire(sin(2*x),x,0,pi,tstep=0.1) ''' - return GiacMethods['courbe_polaire'](self,*args) + return GiacMethods['courbe_polaire'](self, *args) - def covariance(self,*args): + def covariance(self, *args): r'''From Giac's documentation: Help for covariance: covariance(Lst||Mtrx,[Lst]) @@ -3109,9 +3109,9 @@ cdef class GiacMethods_base: See also: 1/ correlation 2/ covariance_correlation Ex1:covariance([[1,2],[1,1],[4,7]]) ''' - return GiacMethods['covariance'](self,*args) + return GiacMethods['covariance'](self, *args) - def covariance_correlation(self,*args): + def covariance_correlation(self, *args): r'''From Giac's documentation: Help for covariance_correlation: covariance_correlation(Lst||Mtrx,[Lst]) @@ -3119,9 +3119,9 @@ cdef class GiacMethods_base: See also: 1/ covariance 2/ correlation Ex1:covariance_correlation([[1,2],[1,1],[4,7]]) ''' - return GiacMethods['covariance_correlation'](self,*args) + return GiacMethods['covariance_correlation'](self, *args) - def cpartfrac(self,*args): + def cpartfrac(self, *args): r'''From Giac's documentation: Help for cpartfrac: cpartfrac(RatFrac) @@ -3131,9 +3131,9 @@ cdef class GiacMethods_base: Ex2:cpartfrac((x^2-2*x+3)/(x^2-3*x+2)) Ex3:cpartfrac(a/(z*(z-b)),z) ''' - return GiacMethods['cpartfrac'](self,*args) + return GiacMethods['cpartfrac'](self, *args) - def crationalroot(self,*args): + def crationalroot(self, *args): r'''From Giac's documentation: Help for crationalroot: crationalroot(Poly(P)) @@ -3141,9 +3141,9 @@ cdef class GiacMethods_base: See also: 1/ proot 2/ froot 3/ complexroot 4/ rationalroot 5/ realroot Ex1:crationalroot(2*x^3+(-5-7*i)*x^2+(-4+14*i)*x+8-4*i) ''' - return GiacMethods['crationalroot'](self,*args) + return GiacMethods['crationalroot'](self, *args) - def crayon(self,*args): + def crayon(self, *args): r'''From Giac's documentation: Help for crayon: crayon(Color) @@ -3154,9 +3154,9 @@ cdef class GiacMethods_base: Ex3:crayon(5) Ex4:crayon(gomme) ''' - return GiacMethods['crayon'](self,*args) + return GiacMethods['crayon'](self, *args) - def createwav(self,*args): + def createwav(self, *args): r'''From Giac's documentation: Help for createwav: createwav(Lst(data),[opts]) @@ -3168,9 +3168,9 @@ cdef class GiacMethods_base: Ex4:createwav(10*sin(2*pi*440*soundsec(2)),normalize=-3) Ex5: t:=soundsec(3):;L,R:=sin(2*pi*440*t),sin(2*pi*445*t):;createwav([L,R]) ''' - return GiacMethods['createwav'](self,*args) + return GiacMethods['createwav'](self, *args) - def cross(self,*args): + def cross(self, *args): r'''From Giac's documentation: Help for cross: cross(Vect(v1),Vect(v2)) @@ -3179,9 +3179,9 @@ cdef class GiacMethods_base: Ex1:cross([1,2],[3,4]) Ex2:cross([1,2,3],[4,5,6]) ''' - return GiacMethods['cross'](self,*args) + return GiacMethods['cross'](self, *args) - def crossP(self,*args): + def crossP(self, *args): r'''From Giac's documentation: Help for crossP: crossP(Vect(v1),Vect(v2)) @@ -3190,9 +3190,9 @@ cdef class GiacMethods_base: Ex1:crossP([1,2],[3,4]) Ex2:crossP([1,2,3],[4,5,6]) ''' - return GiacMethods['crossP'](self,*args) + return GiacMethods['crossP'](self, *args) - def cross_correlation(self,*args): + def cross_correlation(self, *args): r'''From Giac's documentation: Help for cross_correlation: cross_correlation(cross_correlation(Lst(u),Lst(v))) @@ -3200,9 +3200,9 @@ cdef class GiacMethods_base: See also: 1/ auto_correlation 2/ correlation Ex1:cross_correlation([1,2],[3,4,5]) ''' - return GiacMethods['cross_correlation'](self,*args) + return GiacMethods['cross_correlation'](self, *args) - def cross_point(self,*args): + def cross_point(self, *args): r'''From Giac's documentation: Help for cross_point: cross_point(Opt) @@ -3211,9 +3211,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) ''' - return GiacMethods['cross_point'](self,*args) + return GiacMethods['cross_point'](self, *args) - def cross_ratio(self,*args): + def cross_ratio(self, *args): r'''From Giac's documentation: Help for cross_ratio: cross_ratio(Pnt or Cplx(a),Pnt or Cplx(b),Pnt or Cplx(c),Pnt or Cplx(d)) @@ -3223,9 +3223,9 @@ cdef class GiacMethods_base: Ex2:cross_ratio(0,1+i,1,i) Ex3:cross_ratio(0,1,2,3) ''' - return GiacMethods['cross_ratio'](self,*args) + return GiacMethods['cross_ratio'](self, *args) - def crossproduct(self,*args): + def crossproduct(self, *args): r'''From Giac's documentation: Help for crossproduct: crossproduct(Vect(v1),Vect(v2)) @@ -3234,9 +3234,9 @@ cdef class GiacMethods_base: Ex1:crossproduct([1,2],[3,4]) Ex2:crossproduct([1,2,3],[4,5,6]) ''' - return GiacMethods['crossproduct'](self,*args) + return GiacMethods['crossproduct'](self, *args) - def csc(self,*args): + def csc(self, *args): r'''From Giac's documentation: Help for csc: csc(Expr) @@ -3244,9 +3244,9 @@ cdef class GiacMethods_base: See also: 1/ sin 2/ acsc Ex1:csc(pi/2) ''' - return GiacMethods['csc'](self,*args) + return GiacMethods['csc'](self, *args) - def csolve(self,*args): + def csolve(self, *args): r'''From Giac's documentation: Help for csolve: csolve(LstEq,LstVar) @@ -3257,9 +3257,9 @@ cdef class GiacMethods_base: Ex3:csolve(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:csolve(u*v-u=v and v^2=u,[u,v]) ''' - return GiacMethods['csolve'](self,*args) + return GiacMethods['csolve'](self, *args) - def csv2gen(self,*args): + def csv2gen(self, *args): r'''From Giac's documentation: Help for csv2gen: csv2gen(Strng(filename),Strng(sep),Strng(nl),Strng(decsep),Strng(eof),[string]) @@ -3267,9 +3267,9 @@ cdef class GiacMethods_base: See also: 1/ read Ex1:csv2gen("mat.txt",",",char(10),".") ''' - return GiacMethods['csv2gen'](self,*args) + return GiacMethods['csv2gen'](self, *args) - def cube(self,*args): + def cube(self, *args): r'''From Giac's documentation: Help for cube: cube(Pnt(A),Pnt(B),Pnt(C)) @@ -3281,9 +3281,9 @@ cdef class GiacMethods_base: Ex4: c:=cube([0,0,0],[1,0,0],[0,1,0]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); Ex5: c:=cube([0,0,0],[0,2,0],[0,0,1]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); ''' - return GiacMethods['cube'](self,*args) + return GiacMethods['cube'](self, *args) - def cumSum(self,*args): + def cumSum(self, *args): r'''From Giac's documentation: Help for cumSum: cumSum(Lst(l)||Seq||Str) @@ -3293,9 +3293,9 @@ cdef class GiacMethods_base: Ex2:cumSum(1.2,3,4.5,6) Ex3:cumSum("a","b","c","d") ''' - return GiacMethods['cumSum'](self,*args) + return GiacMethods['cumSum'](self, *args) - def cumsum(self,*args): + def cumsum(self, *args): r'''From Giac's documentation: Help for cumsum: cumsum(Lst(l)||Seq||Str) @@ -3305,9 +3305,9 @@ cdef class GiacMethods_base: Ex2:cumsum(1.2,3,4.5,6) Ex3:cumsum("a","b","c","d") ''' - return GiacMethods['cumsum'](self,*args) + return GiacMethods['cumsum'](self, *args) - def cumulated_frequencies(self,*args): + def cumulated_frequencies(self, *args): r'''From Giac's documentation: Help for cumulated_frequencies: cumulated_frequencies(Lst || Mtrx) @@ -3319,9 +3319,9 @@ cdef class GiacMethods_base: Ex4:cumulated_frequencies([[1..2,0.3],[2..3,0.5],[3..4,0.2]]) Ex5:cumulated_frequencies([[1..2,0.3,0.5],[2..3,0.5,0.2],[3..4,0.2,0.3]]) ''' - return GiacMethods['cumulated_frequencies'](self,*args) + return GiacMethods['cumulated_frequencies'](self, *args) - def curl(self,*args): + def curl(self, *args): r'''From Giac's documentation: Help for curl: curl(Lst(A,B,C),Lst(x,y,z)) @@ -3329,9 +3329,9 @@ cdef class GiacMethods_base: See also: 1/ derive 2/ divergence Ex1:curl([2*x*y,x*z,y*z],[x,y,z]) ''' - return GiacMethods['curl'](self,*args) + return GiacMethods['curl'](self, *args) - def current_sheet(self,*args): + def current_sheet(self, *args): r'''From Giac's documentation: Help for current_sheet: current_sheet([Intg||Inter],[Intg||Letter],[Letter]) @@ -3339,9 +3339,9 @@ cdef class GiacMethods_base: Ex1:current_sheet(1,2) Ex2:current_sheet(A1..A5,B,G) ''' - return GiacMethods['current_sheet'](self,*args) + return GiacMethods['current_sheet'](self, *args) - def curvature(self,*args): + def curvature(self, *args): r'''From Giac's documentation: Help for curvature: curvature(Curve,Point) @@ -3355,18 +3355,18 @@ cdef class GiacMethods_base: Ex6:curvature([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t,7) Ex7: trigcos(curvature([2*cos(t),2*sin(t),3*t],t)) ''' - return GiacMethods['curvature'](self,*args) + return GiacMethods['curvature'](self, *args) - def curve(self,*args): + def curve(self, *args): r'''From Giac's documentation: Help for curve: curve(Expr) Reserved word. See also: 1/ ''' - return GiacMethods['curve'](self,*args) + return GiacMethods['curve'](self, *args) - def cyan(self,*args): + def cyan(self, *args): r'''From Giac's documentation: Help for cyan: cyan(Opt) @@ -3375,9 +3375,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),red) Ex2: F:=display(point(2+1.5*i),point_point+green) ''' - return GiacMethods['cyan'](self,*args) + return GiacMethods['cyan'](self, *args) - def cycle2perm(self,*args): + def cycle2perm(self, *args): r'''From Giac's documentation: Help for cycle2perm: cycle2perm(Cycle) @@ -3385,9 +3385,9 @@ cdef class GiacMethods_base: See also: 1/ cycles2permu 2/ permu2cycles Ex1:cycle2perm([1,3,5]) ''' - return GiacMethods['cycle2perm'](self,*args) + return GiacMethods['cycle2perm'](self, *args) - def cycle_graph(self,*args): + def cycle_graph(self, *args): r'''From Giac's documentation: Help for cycle_graph: cycle_graph(Intg(n)||Lst(V)) @@ -3396,9 +3396,9 @@ cdef class GiacMethods_base: Ex1:cycle_graph(4) Ex2:cycle_graph(["one","two","three","four","five"]) ''' - return GiacMethods['cycle_graph'](self,*args) + return GiacMethods['cycle_graph'](self, *args) - def cycleinv(self,*args): + def cycleinv(self, *args): r'''From Giac's documentation: Help for cycleinv: cycleinv(Cycle(c)) @@ -3406,9 +3406,9 @@ cdef class GiacMethods_base: See also: 1/ perminv Ex1:cycleinv([1,3,5]) ''' - return GiacMethods['cycleinv'](self,*args) + return GiacMethods['cycleinv'](self, *args) - def cycles2permu(self,*args): + def cycles2permu(self, *args): r'''From Giac's documentation: Help for cycles2permu: cycles2permu(Lst(Cycle)) @@ -3416,9 +3416,9 @@ cdef class GiacMethods_base: See also: 1/ permu2cycles 2/ cycle2perm Ex1:cycles2permu([[1,3,5],[3,4]]) ''' - return GiacMethods['cycles2permu'](self,*args) + return GiacMethods['cycles2permu'](self, *args) - def cyclotomic(self,*args): + def cyclotomic(self, *args): r'''From Giac's documentation: Help for cyclotomic: cyclotomic(Expr) @@ -3426,9 +3426,9 @@ cdef class GiacMethods_base: See also: 1/ none Ex1:cyclotomic(20) ''' - return GiacMethods['cyclotomic'](self,*args) + return GiacMethods['cyclotomic'](self, *args) - def cylinder(self,*args): + def cylinder(self, *args): r'''From Giac's documentation: Help for cylinder: cylinder(Pnt(A),Vect(v),Real(r),[Real(h)]) @@ -3437,9 +3437,9 @@ cdef class GiacMethods_base: Ex1:cylinder([0,0,0],[0,1,0],2) Ex2:cylinder([0,0,0],[0,1,0],2,-3) ''' - return GiacMethods['cylinder'](self,*args) + return GiacMethods['cylinder'](self, *args) - def dash_line(self,*args): + def dash_line(self, *args): r'''From Giac's documentation: Help for dash_line: dash_line(Opt) @@ -3448,9 +3448,9 @@ cdef class GiacMethods_base: Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) ''' - return GiacMethods['dash_line'](self,*args) + return GiacMethods['dash_line'](self, *args) - def dashdot_line(self,*args): + def dashdot_line(self, *args): r'''From Giac's documentation: Help for dashdot_line: dashdot_line(Opt) @@ -3459,9 +3459,9 @@ cdef class GiacMethods_base: Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) ''' - return GiacMethods['dashdot_line'](self,*args) + return GiacMethods['dashdot_line'](self, *args) - def dashdotdot_line(self,*args): + def dashdotdot_line(self, *args): r'''From Giac's documentation: Help for dashdotdot_line: dashdotdot_line(Opt) @@ -3470,9 +3470,9 @@ cdef class GiacMethods_base: Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) ''' - return GiacMethods['dashdotdot_line'](self,*args) + return GiacMethods['dashdotdot_line'](self, *args) - def dayofweek(self,*args): + def dayofweek(self, *args): r'''From Giac's documentation: Help for dayofweek: dayofweek(Int,Int,Int) @@ -3480,9 +3480,9 @@ cdef class GiacMethods_base: Ex1:dayofweek(21,4,2014) Ex2:dayofweek(15,10,1582) ''' - return GiacMethods['dayofweek'](self,*args) + return GiacMethods['dayofweek'](self, *args) - def deSolve(self,*args): + def deSolve(self, *args): r'''From Giac's documentation: Help for deSolve: deSolve(Eq,[TimeVar],FncVar) @@ -3505,9 +3505,9 @@ cdef class GiacMethods_base: Ex15:deSolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],t,z) Ex16:deSolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],z(t)) ''' - return GiacMethods['deSolve'](self,*args) + return GiacMethods['deSolve'](self, *args) - def debut_enregistrement(self,*args): + def debut_enregistrement(self, *args): r'''From Giac's documentation: Help for debut_enregistrement: debut_enregistrement(Var(nom_du_dessin)) @@ -3516,9 +3516,9 @@ cdef class GiacMethods_base: Ex1:debut_enregistrement(maison) Ex2:debut_enregistrement(arbre) ''' - return GiacMethods['debut_enregistrement'](self,*args) + return GiacMethods['debut_enregistrement'](self, *args) - def degree(self,*args): + def degree(self, *args): r'''From Giac's documentation: Help for degree: degree(Poly(P),Var(Var)) @@ -3528,9 +3528,9 @@ cdef class GiacMethods_base: Ex2:degree([1,0,1,0]) Ex3:degree(x^3+x*y,y) ''' - return GiacMethods['degree'](self,*args) + return GiacMethods['degree'](self, *args) - def degree_sequence(self,*args): + def degree_sequence(self, *args): r'''From Giac's documentation: Help for degree_sequence: degree_sequence(Graph(G)) @@ -3538,9 +3538,9 @@ cdef class GiacMethods_base: See also: 1/ is_graphic_sequence 2/ is_regular 2/ sequence_graph 3/ vertex_degree Ex1:degree_sequence(graph(trail(1,2,3,4,2))) ''' - return GiacMethods['degree_sequence'](self,*args) + return GiacMethods['degree_sequence'](self, *args) - def delcols(self,*args): + def delcols(self, *args): r'''From Giac's documentation: Help for delcols: delcols(Mtrx(A),Interval(n1..n2)||n1) @@ -3550,9 +3550,9 @@ cdef class GiacMethods_base: Ex2:delcols([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3:delcols([[1,2,3],[4,5,6],[7,8,9]],1) ''' - return GiacMethods['delcols'](self,*args) + return GiacMethods['delcols'](self, *args) - def delete_arc(self,*args): + def delete_arc(self, *args): r'''From Giac's documentation: Help for delete_arc: delete_arc(Graph(G),Edge(e)||Trail(T)||Lst(E)) @@ -3560,9 +3560,9 @@ cdef class GiacMethods_base: See also: 1/ add_arc 2/ delete_edge 3/ digraph 4/ edges 5/ has_arc 6/ trail Ex1:delete_arc(digraph(trail(1,2,3,4,5,1)),[5,1]) ''' - return GiacMethods['delete_arc'](self,*args) + return GiacMethods['delete_arc'](self, *args) - def delete_edge(self,*args): + def delete_edge(self, *args): r'''From Giac's documentation: Help for delete_edge: delete_edge(Graph(G),Edge(e)||Trail(T)||Lst(E)) @@ -3570,9 +3570,9 @@ cdef class GiacMethods_base: See also: 1/ add_edge 2/ delete_arc 3/ edges 4/ graph 5/ has_edge 6/ trail Ex1:delete_edge(cycle_graph(4),[1,2]) ''' - return GiacMethods['delete_edge'](self,*args) + return GiacMethods['delete_edge'](self, *args) - def delete_vertex(self,*args): + def delete_vertex(self, *args): r'''From Giac's documentation: Help for delete_vertex: delete_vertex(Graph(G),Vrtx(v)||Lst(V)) @@ -3580,9 +3580,9 @@ cdef class GiacMethods_base: See also: 1/ add_vertex 2/ induced_subgraph Ex1:delete_vertex(cycle_graph(5),[1,4]) ''' - return GiacMethods['delete_vertex'](self,*args) + return GiacMethods['delete_vertex'](self, *args) - def delrows(self,*args): + def delrows(self, *args): r'''From Giac's documentation: Help for delrows: delrows(Mtrx(A),Interval(n1..n2)||n1) @@ -3592,9 +3592,9 @@ cdef class GiacMethods_base: Ex2:delrows([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3:delrows([[1,2,3],[4,5,6],[7,8,9]],1) ''' - return GiacMethods['delrows'](self,*args) + return GiacMethods['delrows'](self, *args) - def deltalist(self,*args): + def deltalist(self, *args): r'''From Giac's documentation: Help for deltalist: deltalist(Lst) @@ -3603,9 +3603,9 @@ cdef class GiacMethods_base: Ex1:deltalist([1,4,8,9]) Ex2:deltalist([1,8,4,9]) ''' - return GiacMethods['deltalist'](self,*args) + return GiacMethods['deltalist'](self, *args) - def denom(self,*args): + def denom(self, *args): r'''From Giac's documentation: Help for denom: denom(Frac(a/b) or RatFrac) @@ -3615,9 +3615,9 @@ cdef class GiacMethods_base: Ex2:denom((x^3-1)/(x^2-1)) Ex3:denom(1+(x^3-1)/x^2) ''' - return GiacMethods['denom'](self,*args) + return GiacMethods['denom'](self, *args) - def densityplot(self,*args): + def densityplot(self, *args): r'''From Giac's documentation: Help for densityplot: densityplot(Expr,[x=xrange,y=yrange],[z],[xstep],[ystep]) @@ -3626,9 +3626,9 @@ cdef class GiacMethods_base: Ex1:densityplot(x^2-y^2,[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex2:densityplot(x^2-y^2,[x=-2..2,y=-2..2],z=-2..2,xstep=0.1,ystep=0.1) ''' - return GiacMethods['densityplot'](self,*args) + return GiacMethods['densityplot'](self, *args) - def departures(self,*args): + def departures(self, *args): r'''From Giac's documentation: Help for departures: departures(Graph(G),[Vrtx(v)]) @@ -3636,9 +3636,9 @@ cdef class GiacMethods_base: See also: 1/ out_degree Ex1:departures(digraph(%{[1,2],[1,3],[2,3]%}),1) ''' - return GiacMethods['departures'](self,*args) + return GiacMethods['departures'](self, *args) - def derive(self,*args): + def derive(self, *args): r'''From Giac's documentation: Help for derive: derive(Expr or Fnc,[SeqVar or LstVar],[n]) @@ -3653,9 +3653,9 @@ cdef class GiacMethods_base: Ex7:derive(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) ''' - return GiacMethods['derive'](self,*args) + return GiacMethods['derive'](self, *args) - def deriver(self,*args): + def deriver(self, *args): r'''From Giac's documentation: Help for deriver: deriver(Expr or Fnc,[SeqVar or LstVar],[n]) @@ -3670,9 +3670,9 @@ cdef class GiacMethods_base: Ex7:deriver(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) ''' - return GiacMethods['deriver'](self,*args) + return GiacMethods['deriver'](self, *args) - def desolve(self,*args): + def desolve(self, *args): r'''From Giac's documentation: Help for desolve: desolve(Eq,[TimeVar],FncVar) @@ -3695,9 +3695,9 @@ cdef class GiacMethods_base: Ex15:desolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],t,z) Ex16:desolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],z(t)) ''' - return GiacMethods['desolve'](self,*args) + return GiacMethods['desolve'](self, *args) - def dessine_tortue(self,*args): + def dessine_tortue(self, *args): r'''From Giac's documentation: Help for dessine_tortue: dessine_tortue([Intg(n)]) @@ -3707,9 +3707,9 @@ cdef class GiacMethods_base: Ex2:dessine_tortue(0) Ex3:dessine_tortue(1) ''' - return GiacMethods['dessine_tortue'](self,*args) + return GiacMethods['dessine_tortue'](self, *args) - def det(self,*args): + def det(self, *args): r'''From Giac's documentation: Help for det: det(Mtrx) @@ -3718,9 +3718,9 @@ cdef class GiacMethods_base: Ex1:det([[1,2],[3,4]]) Ex2:det([[1,2,3],[1,3,6],[2,5,7]]) ''' - return GiacMethods['det'](self,*args) + return GiacMethods['det'](self, *args) - def det_minor(self,*args): + def det_minor(self, *args): r'''From Giac's documentation: Help for det_minor: det_minor(Mtrx(A)) @@ -3728,9 +3728,9 @@ cdef class GiacMethods_base: See also: 1/ det Ex1:det_minor([[1,2],[3,4]]) ''' - return GiacMethods['det_minor'](self,*args) + return GiacMethods['det_minor'](self, *args) - def developper(self,*args): + def developper(self, *args): r'''From Giac's documentation: Help for developper: developper(Expr) @@ -3742,9 +3742,9 @@ cdef class GiacMethods_base: Ex4:developper((x+3)^4) Ex5:developper((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) ''' - return GiacMethods['developper'](self,*args) + return GiacMethods['developper'](self, *args) - def developper_transcendant(self,*args): + def developper_transcendant(self, *args): r'''From Giac's documentation: Help for developper_transcendant: developper_transcendant(Expr) @@ -3754,9 +3754,9 @@ cdef class GiacMethods_base: Ex2:developper_transcendant(cos(x+y)) Ex3:developper_transcendant(cos(3*x)) ''' - return GiacMethods['developper_transcendant'](self,*args) + return GiacMethods['developper_transcendant'](self, *args) - def dfc(self,*args): + def dfc(self, *args): r'''From Giac's documentation: Help for dfc: dfc(Real(x0),Int(n)||Real(eps)) @@ -3768,9 +3768,9 @@ cdef class GiacMethods_base: Ex4: convert(sqrt(2),confrac,'dev');dev Ex5: convert(9976/6961,confrac,'l');l ''' - return GiacMethods['dfc'](self,*args) + return GiacMethods['dfc'](self, *args) - def dfc2f(self,*args): + def dfc2f(self, *args): r'''From Giac's documentation: Help for dfc2f: dfc2f(LstFrac_Cont)) @@ -3779,9 +3779,9 @@ cdef class GiacMethods_base: Ex1:dfc2f([1,1,1]) Ex2:dfc2f([1,2,[2]]) ''' - return GiacMethods['dfc2f'](self,*args) + return GiacMethods['dfc2f'](self, *args) - def diag(self,*args): + def diag(self, *args): r'''From Giac's documentation: Help for diag: diag(Lst(l)||(Mtrx(A),[left||right||lu])||Lst(l),Lst(d),Lst(u)) @@ -3794,9 +3794,9 @@ cdef class GiacMethods_base: Ex5:diag([[1,2],[3,4]],lu) Ex6:diag([1,2],[3,4,5],[6,7]) ''' - return GiacMethods['diag'](self,*args) + return GiacMethods['diag'](self, *args) - def diff(self,*args): + def diff(self, *args): r'''From Giac's documentation: Help for diff: diff(Expr or Fnc,[SeqVar or LstVar],[n]) @@ -3811,9 +3811,9 @@ cdef class GiacMethods_base: Ex7:diff(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) ''' - return GiacMethods['diff'](self,*args) + return GiacMethods['diff'](self, *args) - def digraph(self,*args): + def digraph(self, *args): r'''From Giac's documentation: Help for digraph: digraph([Lst(V)],[Set(E)],[Mtrx(A)],[options]) @@ -3822,9 +3822,9 @@ cdef class GiacMethods_base: Ex1:digraph(%{[1,2],[2,3],[3,4],[4,1]%}) Ex2:digraph([a,b,c,d],%{[[a,b],1.0],[[a,c],2.3],[[b,d],3.1],[[c,d],4]%}) ''' - return GiacMethods['digraph'](self,*args) + return GiacMethods['digraph'](self, *args) - def dijkstra(self,*args): + def dijkstra(self, *args): r'''From Giac's documentation: Help for dijkstra: dijkstra(Graph(G),Vrtx(v),[Vrtx(w)||Lst(W)]) @@ -3832,9 +3832,9 @@ cdef class GiacMethods_base: See also: 1/ allpairs_distance 2/ shortest_path Ex1:dijkstra(graph(%{[[1,2],1],[[2,3],3],[[3,4],7],[[4,5],3],[[5,6],3],[[1,6],3]%}),1,4) ''' - return GiacMethods['dijkstra'](self,*args) + return GiacMethods['dijkstra'](self, *args) - def dim(self,*args): + def dim(self, *args): r'''From Giac's documentation: Help for dim: dim(Mtrx) @@ -3842,18 +3842,18 @@ cdef class GiacMethods_base: See also: 1/ rowdim 2/ coldim 3/ sizes 4/ size Ex1:dim([[1,2,3],[4,5,6]]) ''' - return GiacMethods['dim'](self,*args) + return GiacMethods['dim'](self, *args) - def directed(self,*args): + def directed(self, *args): r'''From Giac's documentation: Help for directed: directed(Opt) Option for graph and digraph commands. See also: 1/ weighted 2/ graph 3/ digraph ''' - return GiacMethods['directed'](self,*args) + return GiacMethods['directed'](self, *args) - def discard_edge_attribute(self,*args): + def discard_edge_attribute(self, *args): r'''From Giac's documentation: Help for discard_edge_attribute: discard_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) @@ -3861,9 +3861,9 @@ cdef class GiacMethods_base: See also: 1/ get_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes Ex1:discard_edge_attribute(cycle_graph(3),[1,2],"cost") ''' - return GiacMethods['discard_edge_attribute'](self,*args) + return GiacMethods['discard_edge_attribute'](self, *args) - def discard_graph_attribute(self,*args): + def discard_graph_attribute(self, *args): r'''From Giac's documentation: Help for discard_graph_attribute: discard_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) @@ -3871,9 +3871,9 @@ cdef class GiacMethods_base: See also: 1/ get_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes Ex1:discard_graph_attribute(cycle_graph(3),"name") ''' - return GiacMethods['discard_graph_attribute'](self,*args) + return GiacMethods['discard_graph_attribute'](self, *args) - def discard_vertex_attribute(self,*args): + def discard_vertex_attribute(self, *args): r'''From Giac's documentation: Help for discard_vertex_attribute: discard_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) @@ -3881,9 +3881,9 @@ cdef class GiacMethods_base: See also: 1/ get_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes Ex1:discard_vertex_attribute(cycle_graph(3),1,"supply") ''' - return GiacMethods['discard_vertex_attribute'](self,*args) + return GiacMethods['discard_vertex_attribute'](self, *args) - def disjoint_union(self,*args): + def disjoint_union(self, *args): r'''From Giac's documentation: Help for disjoint_union: disjoint_union(Seq(G1,G2,...)) @@ -3891,9 +3891,9 @@ cdef class GiacMethods_base: See also: 1/ graph_join 2/ graph_union Ex1:disjoint_union(is_connected(disjoint_union(cycle_graph(5),path_graph(4)))) ''' - return GiacMethods['disjoint_union'](self,*args) + return GiacMethods['disjoint_union'](self, *args) - def display(self,*args): + def display(self, *args): r'''From Giac's documentation: Help for display: display([GeoObj or legende],Intg) @@ -3910,9 +3910,9 @@ cdef class GiacMethods_base: Ex9:display(red);square(0,1); Ex10:display(red+filled);square(0,1); ''' - return GiacMethods['display'](self,*args) + return GiacMethods['display'](self, *args) - def disque(self,*args): + def disque(self, *args): r'''From Giac's documentation: Help for disque: disque(Real(r),[Real(a)],[Real(b)]) @@ -3923,9 +3923,9 @@ cdef class GiacMethods_base: Ex3:disque(40,90) Ex4:disque(40,10,100) ''' - return GiacMethods['disque'](self,*args) + return GiacMethods['disque'](self, *args) - def disque_centre(self,*args): + def disque_centre(self, *args): r'''From Giac's documentation: Help for disque_centre: disque_centre(Real(r),[Real(a)],[Real(b)]) @@ -3936,9 +3936,9 @@ cdef class GiacMethods_base: Ex3:disque_centre(40,90) Ex4:disque_centre(40,10,100) ''' - return GiacMethods['disque_centre'](self,*args) + return GiacMethods['disque_centre'](self, *args) - def distance(self,*args): + def distance(self, *args): r'''From Giac's documentation: Help for distance: distance((Pnt or Cplx),(Pnt or Cplx or Curve)) @@ -3948,9 +3948,9 @@ cdef class GiacMethods_base: Ex2:distance(1+i,segment(1-i,i)) Ex3:distance(0,1+i) ''' - return GiacMethods['distance'](self,*args) + return GiacMethods['distance'](self, *args) - def distance2(self,*args): + def distance2(self, *args): r'''From Giac's documentation: Help for distance2: distance2((Pnt or Cplx),(Pnt or Cplx or Curve)) @@ -3960,9 +3960,9 @@ cdef class GiacMethods_base: Ex2:distance2(1+i,segment(1-i,i)) Ex3:distance2(0,1+i) ''' - return GiacMethods['distance2'](self,*args) + return GiacMethods['distance2'](self, *args) - def distanceat(self,*args): + def distanceat(self, *args): r'''From Giac's documentation: Help for distanceat: distanceat(GeoObj(A),GeoObj(B),(Pnt or Cplx)) @@ -3971,9 +3971,9 @@ cdef class GiacMethods_base: Ex1: A:=point(0);B:=point(1+i);distanceat(A,B,(1+i)/2) Ex2: A:=point(0);s:=segment(1-i,i);distanceat(A,s,1) ''' - return GiacMethods['distanceat'](self,*args) + return GiacMethods['distanceat'](self, *args) - def distanceatraw(self,*args): + def distanceatraw(self, *args): r'''From Giac's documentation: Help for distanceatraw: distanceatraw(GeoObj(A),GeoObj(B),(Pnt or Cplx(z0))) @@ -3982,9 +3982,9 @@ cdef class GiacMethods_base: Ex1: A:=point(0);B:=point(1+i);distanceatraw(A,B,(1+i)/2) Ex2: A:=point(0);s:=segment(1-i,i);distanceatraw(A,s,1) ''' - return GiacMethods['distanceatraw'](self,*args) + return GiacMethods['distanceatraw'](self, *args) - def divergence(self,*args): + def divergence(self, *args): r'''From Giac's documentation: Help for divergence: divergence(Lst(A,B,C),Lst(x,y,z)) @@ -3992,9 +3992,9 @@ cdef class GiacMethods_base: See also: 1/ derive 2/ curl Ex1:divergence([x^2+y,x+z+y,z^3+x^2],[x,y,z]) ''' - return GiacMethods['divergence'](self,*args) + return GiacMethods['divergence'](self, *args) - def divide(self,*args): + def divide(self, *args): r'''From Giac's documentation: Help for divide: divide((Vect or Poly),(Vect or Poly),[Var]) @@ -4005,9 +4005,9 @@ cdef class GiacMethods_base: Ex3:divide(t^3+2t^2+3t+4,-t+2,t) Ex4:divide(t^4-1,(t+1)^2,t) ''' - return GiacMethods['divide'](self,*args) + return GiacMethods['divide'](self, *args) - def divis(self,*args): + def divis(self, *args): r'''From Giac's documentation: Help for divis: divis(Poly(P) or LstPoly) @@ -4020,9 +4020,9 @@ cdef class GiacMethods_base: Ex5:divis([x^4-1,t^2-1]) Ex6:divis(poly2symb([1,0,0,0,-1],x)) ''' - return GiacMethods['divis'](self,*args) + return GiacMethods['divis'](self, *args) - def division_point(self,*args): + def division_point(self, *args): r'''From Giac's documentation: Help for division_point: division_point(Pnt or Cplx(a),Pnt or Cplx(b),Cplx(k)) @@ -4031,9 +4031,9 @@ cdef class GiacMethods_base: Ex1:division_point(i,2+i,3+i) Ex2:division_point(i,2+i,3) ''' - return GiacMethods['division_point'](self,*args) + return GiacMethods['division_point'](self, *args) - def divisors(self,*args): + def divisors(self, *args): r'''From Giac's documentation: Help for divisors: divisors(Intg(a) or LstIntg) @@ -4042,9 +4042,9 @@ cdef class GiacMethods_base: Ex1:divisors(36) Ex2:divisors([36,49]) ''' - return GiacMethods['divisors'](self,*args) + return GiacMethods['divisors'](self, *args) - def divmod(self,*args): + def divmod(self, *args): r'''From Giac's documentation: Help for divmod: divmod(Intg(a),Intg(b)) @@ -4054,9 +4054,9 @@ cdef class GiacMethods_base: Ex2:divmod(125,41) Ex3:divmod(25+12*i,5+7*i) ''' - return GiacMethods['divmod'](self,*args) + return GiacMethods['divmod'](self, *args) - def divpc(self,*args): + def divpc(self, *args): r'''From Giac's documentation: Help for divpc: divpc(Poly,Poly,Intg(n)) @@ -4064,9 +4064,9 @@ cdef class GiacMethods_base: See also: 1/ series 2/ quorem Ex1:divpc(x^4+x+2,x^2+1,5) ''' - return GiacMethods['divpc'](self,*args) + return GiacMethods['divpc'](self, *args) - def dnewton_solver(self,*args): + def dnewton_solver(self, *args): r'''From Giac's documentation: Help for dnewton_solver: dnewton_solver(Opt) @@ -4079,9 +4079,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['dnewton_solver'](self,*args) + return GiacMethods['dnewton_solver'](self, *args) - def dodecahedron(self,*args): + def dodecahedron(self, *args): r'''From Giac's documentation: Help for dodecahedron: dodecahedron(Pnt(A),Pnt(B),Pnt(C)) @@ -4090,9 +4090,9 @@ cdef class GiacMethods_base: Ex1:dodecahedron([0,0,0],[0,2,sqrt(5)/2+3/2],[0,0,1]) Ex2:dodecahedron(evalf([0,0,0],[3,2,4],[1,1,0])) ''' - return GiacMethods['dodecahedron'](self,*args) + return GiacMethods['dodecahedron'](self, *args) - def domain(self,*args): + def domain(self, *args): r'''From Giac's documentation: Help for domain: domain(Expr) @@ -4100,9 +4100,9 @@ cdef class GiacMethods_base: Ex1:domain(log(x+1)) Ex2:domain(log(x)+asin(x)) ''' - return GiacMethods['domain'](self,*args) + return GiacMethods['domain'](self, *args) - def dot(self,*args): + def dot(self, *args): r'''From Giac's documentation: Help for dot: dot(Vect(v1),Vect(v2)) @@ -4112,9 +4112,9 @@ cdef class GiacMethods_base: Ex2:dot([3,2,4],[3,2,4]) Ex3:dot([[1,2],[3,4]],[[3,2],[4,5]]) ''' - return GiacMethods['dot'](self,*args) + return GiacMethods['dot'](self, *args) - def dotP(self,*args): + def dotP(self, *args): r'''From Giac's documentation: Help for dotP: dotP(Vect(v1),Vect(v2)) @@ -4124,9 +4124,9 @@ cdef class GiacMethods_base: Ex2:dotP([3,2,4],[3,2,4]) Ex3:dotP([[1,2],[3,4]],[[3,2],[4,5]]) ''' - return GiacMethods['dotP'](self,*args) + return GiacMethods['dotP'](self, *args) - def dot_paper(self,*args): + def dot_paper(self, *args): r'''From Giac's documentation: Help for dot_paper: dot_paper(Real(ux),Real(uy),Real(t)) @@ -4135,9 +4135,9 @@ cdef class GiacMethods_base: Ex2:dot_paper(1,pi/3,sqrt(3)/2,x=-1..4,y=-2..2) Ex3:dot_paper(0.5,3*pi/4,0.5) ''' - return GiacMethods['dot_paper'](self,*args) + return GiacMethods['dot_paper'](self, *args) - def dotprod(self,*args): + def dotprod(self, *args): r'''From Giac's documentation: Help for dotprod: dotprod(Vect(v1),Vect(v2)) @@ -4147,9 +4147,9 @@ cdef class GiacMethods_base: Ex2:dotprod([3,2,4],[3,2,4]) Ex3:dotprod([[1,2],[3,4]],[[3,2],[4,5]]) ''' - return GiacMethods['dotprod'](self,*args) + return GiacMethods['dotprod'](self, *args) - def draw_arc(self,*args): + def draw_arc(self, *args): r'''From Giac's documentation: Help for draw_arc: draw_arc(Intg(x),Intg(y),Intg(rx),Intg(ry),Real(theta1),Real(theta2),Intg(col)) @@ -4157,9 +4157,9 @@ cdef class GiacMethods_base: See also: 1/ draw_pixel 2/ draw_circle Ex1: clear(); draw_arc(100,80,40,20,0,pi,blue); show_pixels(); ''' - return GiacMethods['draw_arc'](self,*args) + return GiacMethods['draw_arc'](self, *args) - def draw_circle(self,*args): + def draw_circle(self, *args): r'''From Giac's documentation: Help for draw_circle: draw_circle(Intg(x),Intg(y),Intg(r),Intg(col)) @@ -4168,9 +4168,9 @@ cdef class GiacMethods_base: Ex1: clear(); draw_circle(100,60,20,blue); show_pixels(); Ex2: clear(); draw_circle(100,60,20,blue+filled); show_pixels(); ''' - return GiacMethods['draw_circle'](self,*args) + return GiacMethods['draw_circle'](self, *args) - def draw_graph(self,*args): + def draw_graph(self, *args): r'''From Giac's documentation: Help for draw_graph: draw_graph(Graph(G),[opts]) @@ -4182,9 +4182,9 @@ cdef class GiacMethods_base: Ex4:draw_graph(sierpinski_graph(5,3,at_triangle)) Ex5:draw_graph(graph("soccerball")) ''' - return GiacMethods['draw_graph'](self,*args) + return GiacMethods['draw_graph'](self, *args) - def draw_line(self,*args): + def draw_line(self, *args): r'''From Giac's documentation: Help for draw_line: draw_line(Intg(x1),Intg(y1),Intg(x2),Intg(y2),Intg(col)) @@ -4192,9 +4192,9 @@ cdef class GiacMethods_base: See also: 1/ draw_pixel 2/ draw_rectangle 3/ draw_polygon Ex1: clear(); draw_line(10,10,60,60,blue); show_pixels(); ''' - return GiacMethods['draw_line'](self,*args) + return GiacMethods['draw_line'](self, *args) - def draw_pixel(self,*args): + def draw_pixel(self, *args): r'''From Giac's documentation: Help for draw_pixel: draw_pixel(Intg(x),Intg(y),Intg(col)) @@ -4202,9 +4202,9 @@ cdef class GiacMethods_base: See also: 1/ clear 2/ show_pixels 3/ draw_line 4/ draw_rectangle 5/ draw_polygon Ex1: clear(); set_pixel(4); draw_pixel(1,2,red); show_pixels(); ''' - return GiacMethods['draw_pixel'](self,*args) + return GiacMethods['draw_pixel'](self, *args) - def draw_polygon(self,*args): + def draw_polygon(self, *args): r'''From Giac's documentation: Help for draw_polygon: draw_polygon(Lst(l),Intg(col)) @@ -4213,9 +4213,9 @@ cdef class GiacMethods_base: Ex1: clear(); draw_polygon([[50,30],[100,10],[20,70]],red); show_pixels(); Ex2: clear(); draw_polygon([[50,30],[100,10],[20,70]],red+filled); show_pixels(); ''' - return GiacMethods['draw_polygon'](self,*args) + return GiacMethods['draw_polygon'](self, *args) - def draw_rectangle(self,*args): + def draw_rectangle(self, *args): r'''From Giac's documentation: Help for draw_rectangle: draw_rectangle(Intg(x),Intg(y),Intg(w),Intg(h),Intg(col)) @@ -4224,9 +4224,9 @@ cdef class GiacMethods_base: Ex1: clear(); draw_rectangle(10,20,30,40,red); show_pixels(); Ex2: clear(); draw_rectangle(10,20,30,40,red+filled); show_pixels(); ''' - return GiacMethods['draw_rectangle'](self,*args) + return GiacMethods['draw_rectangle'](self, *args) - def droit(self,*args): + def droit(self, *args): r'''From Giac's documentation: Help for droit: droit(Equal(a=b) or Interval(a..b) or Str,Intg) @@ -4237,9 +4237,9 @@ cdef class GiacMethods_base: Ex3:droit(1..5) Ex4:droit("abcdefg",3) ''' - return GiacMethods['droit'](self,*args) + return GiacMethods['droit'](self, *args) - def droite_tangente(self,*args): + def droite_tangente(self, *args): r'''From Giac's documentation: Help for droite_tangente: droite_tangente(Expr(f(x)),[Var],Expr(a)) @@ -4250,9 +4250,9 @@ cdef class GiacMethods_base: Ex3:droite_tangente(sin(t),t,pi/4) Ex4:droite_tangente(x^2-x,1) ''' - return GiacMethods['droite_tangente'](self,*args) + return GiacMethods['droite_tangente'](self, *args) - def dsolve(self,*args): + def dsolve(self, *args): r'''From Giac's documentation: Help for dsolve: dsolve(Eq,[TimeVar],FncVar) @@ -4275,9 +4275,9 @@ cdef class GiacMethods_base: Ex15:dsolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],t,z) Ex16:dsolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],z(t)) ''' - return GiacMethods['dsolve'](self,*args) + return GiacMethods['dsolve'](self, *args) - def duration(self,*args): + def duration(self, *args): r'''From Giac's documentation: Help for duration: duration(Lst(clip)) @@ -4285,9 +4285,9 @@ cdef class GiacMethods_base: See also: 1/ bit_depth 2/ channels 3/ channel_data 4/ samplerate Ex1:duration(readwav("/some/file")) ''' - return GiacMethods['duration'](self,*args) + return GiacMethods['duration'](self, *args) - def e(self,*args): + def e(self, *args): r'''From Giac's documentation: Help for e: e() @@ -4295,9 +4295,9 @@ cdef class GiacMethods_base: See also: 1/ i 2/ pi Ex1: evalf(e) ''' - return GiacMethods['e'](self,*args) + return GiacMethods['e'](self, *args) - def e2r(self,*args): + def e2r(self, *args): r'''From Giac's documentation: Help for e2r: e2r(Expr, LstVar or [Var]) @@ -4310,9 +4310,9 @@ cdef class GiacMethods_base: Ex5:e2r(-x^4+x*3*y+2+y^2*z,[x,y,z]) Ex6:e2r(-x^4+x*3*y+2+y^2*z,[x,y,z]) ''' - return GiacMethods['e2r'](self,*args) + return GiacMethods['e2r'](self, *args) - def ecart_type(self,*args): + def ecart_type(self, *args): r'''From Giac's documentation: Help for ecart_type: ecart_type(Lst||Mtrx,[Lst]) @@ -4322,9 +4322,9 @@ cdef class GiacMethods_base: Ex2:ecart_type([1,2,3],[1,2,1]) Ex3:ecart_type([[1,2,3],[5,6,7]]) ''' - return GiacMethods['ecart_type'](self,*args) + return GiacMethods['ecart_type'](self, *args) - def ecart_type_population(self,*args): + def ecart_type_population(self, *args): r'''From Giac's documentation: Help for ecart_type_population: ecart_type_population(Lst||Mtrx,[Lst]) @@ -4334,18 +4334,18 @@ cdef class GiacMethods_base: Ex2:ecart_type_population([1,2,3],[1,2,1]) Ex3:ecart_type_population([[1,2,3],[5,6,7]]) ''' - return GiacMethods['ecart_type_population'](self,*args) + return GiacMethods['ecart_type_population'](self, *args) - def ecm_factor(self,*args): + def ecm_factor(self, *args): r'''From Giac's documentation: Help for ecm_factor: ecm_factor(Intg(a),[Intg(B1)]) Factorization of integer n by the Elliptic Curve Method algorithm, B1 smoothness optional parameter. Ex1:ecm_factor(1000000000000000003000000000000000000000000000000000031000000000000000093) ''' - return GiacMethods['ecm_factor'](self,*args) + return GiacMethods['ecm_factor'](self, *args) - def edge_connectivity(self,*args): + def edge_connectivity(self, *args): r'''From Giac's documentation: Help for edge_connectivity: edge_connectivity(graph(G)) @@ -4355,9 +4355,9 @@ cdef class GiacMethods_base: Ex2:edge_connectivity(graph("clebsch")) Ex3:edge_connectivity(complete_graph(5)) ''' - return GiacMethods['edge_connectivity'](self,*args) + return GiacMethods['edge_connectivity'](self, *args) - def edges(self,*args): + def edges(self, *args): r'''From Giac's documentation: Help for edges: edges(Graph(G),[weights]) @@ -4365,9 +4365,9 @@ cdef class GiacMethods_base: See also: 1/ add_edge 2/ incident_edges 3/ set_edge_weight 4/ get_edge_weight Ex1:edges(complete_graph(4)) ''' - return GiacMethods['edges'](self,*args) + return GiacMethods['edges'](self, *args) - def egcd(self,*args): + def egcd(self, *args): r'''From Giac's documentation: Help for egcd: egcd((Poly or Lst),(Poly or Lst),[Var]) @@ -4378,9 +4378,9 @@ cdef class GiacMethods_base: Ex3:egcd([1,-2,1],[1,0,0,-1]) Ex4:egcd([1,-2,1],[1,-1,2]) ''' - return GiacMethods['egcd'](self,*args) + return GiacMethods['egcd'](self, *args) - def egv(self,*args): + def egv(self, *args): r'''From Giac's documentation: Help for egv: egv(Mtrx) @@ -4389,9 +4389,9 @@ cdef class GiacMethods_base: Ex1:egv([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex2:egv([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['egv'](self,*args) + return GiacMethods['egv'](self, *args) - def egvl(self,*args): + def egvl(self, *args): r'''From Giac's documentation: Help for egvl: egvl(Mtrx(A)) @@ -4401,9 +4401,9 @@ cdef class GiacMethods_base: Ex2:egvl([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex3:egvl([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['egvl'](self,*args) + return GiacMethods['egvl'](self, *args) - def eigVc(self,*args): + def eigVc(self, *args): r'''From Giac's documentation: Help for eigVc: eigVc(Mtrx) @@ -4412,9 +4412,9 @@ cdef class GiacMethods_base: Ex1:eigVc([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex2:eigVc([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['eigVc'](self,*args) + return GiacMethods['eigVc'](self, *args) - def eigVl(self,*args): + def eigVl(self, *args): r'''From Giac's documentation: Help for eigVl: eigVl(Mtrx(A)) @@ -4424,9 +4424,9 @@ cdef class GiacMethods_base: Ex2:eigVl([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex3:eigVl([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['eigVl'](self,*args) + return GiacMethods['eigVl'](self, *args) - def eigenvals(self,*args): + def eigenvals(self, *args): r'''From Giac's documentation: Help for eigenvals: eigenvals(Mtrx) @@ -4436,9 +4436,9 @@ cdef class GiacMethods_base: Ex2:eigenvals([[1,1,3],[1,3,1],[3,1,1]]) Ex3:eigenvals([[4,1],[-4,0]]) ''' - return GiacMethods['eigenvals'](self,*args) + return GiacMethods['eigenvals'](self, *args) - def eigenvalues(self,*args): + def eigenvalues(self, *args): r'''From Giac's documentation: Help for eigenvalues: eigenvalues(Mtrx) @@ -4448,9 +4448,9 @@ cdef class GiacMethods_base: Ex2:eigenvalues([[1,1,3],[1,3,1],[3,1,1]]) Ex3:eigenvalues([[4,1],[-4,0]]) ''' - return GiacMethods['eigenvalues'](self,*args) + return GiacMethods['eigenvalues'](self, *args) - def eigenvectors(self,*args): + def eigenvectors(self, *args): r'''From Giac's documentation: Help for eigenvectors: eigenvectors(Mtrx) @@ -4459,9 +4459,9 @@ cdef class GiacMethods_base: Ex1:eigenvectors([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex2:eigenvectors([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['eigenvectors'](self,*args) + return GiacMethods['eigenvectors'](self, *args) - def eigenvects(self,*args): + def eigenvects(self, *args): r'''From Giac's documentation: Help for eigenvects: eigenvects(Mtrx) @@ -4470,9 +4470,9 @@ cdef class GiacMethods_base: Ex1:eigenvects([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex2:eigenvects([[1,1,3],[1,3,1],[3,1,1]]) ''' - return GiacMethods['eigenvects'](self,*args) + return GiacMethods['eigenvects'](self, *args) - def element(self,*args): + def element(self, *args): r'''From Giac's documentation: Help for element: element((Curve or Real_interval),[Val]) @@ -4485,9 +4485,9 @@ cdef class GiacMethods_base: Ex5: M:=element(circle(i,1)) Ex6: N:=element(circle(i,1),pi/2) ''' - return GiacMethods['element'](self,*args) + return GiacMethods['element'](self, *args) - def eliminate(self,*args): + def eliminate(self, *args): r'''From Giac's documentation: Help for eliminate: eliminate(LstEq(eqs),LstVar(vars)) @@ -4495,9 +4495,9 @@ cdef class GiacMethods_base: Ex1:eliminate([x=v0*t,y=y0-g*t^2],t) Ex2:eliminate([x+y+z+t-2,x*y*t=1,x^2+t^2=z^2],[x,z]) ''' - return GiacMethods['eliminate'](self,*args) + return GiacMethods['eliminate'](self, *args) - def ellipse(self,*args): + def ellipse(self, *args): r'''From Giac's documentation: Help for ellipse: ellipse(Pnt(F1),Pnt(F2),(Pnt(M) or Real(a))) @@ -4509,9 +4509,9 @@ cdef class GiacMethods_base: Ex4:ellipse(point(-1,0,0),point(1,0,0),point(1,1,1)) Ex5:ellipse(x^2+2y^2-y-2) ''' - return GiacMethods['ellipse'](self,*args) + return GiacMethods['ellipse'](self, *args) - def entry(self,*args): + def entry(self, *args): r'''From Giac's documentation: Help for entry: entry(Intg(n)) @@ -4521,9 +4521,9 @@ cdef class GiacMethods_base: Ex2:entry(2) Ex3:entry(-2) ''' - return GiacMethods['entry'](self,*args) + return GiacMethods['entry'](self, *args) - def envelope(self,*args): + def envelope(self, *args): r'''From Giac's documentation: Help for envelope: envelope(Expr(Xpr),Var(t)||[x,y,t]) @@ -4532,9 +4532,9 @@ cdef class GiacMethods_base: Ex1:envelope(y+x*tan(t)-2*sin(t),t) Ex2:envelope(v+u*tan(t)-3*sin(t),[u,v,t]) ''' - return GiacMethods['envelope'](self,*args) + return GiacMethods['envelope'](self, *args) - def epsilon(self,*args): + def epsilon(self, *args): r'''From Giac's documentation: Help for epsilon: epsilon(NULL) @@ -4542,9 +4542,9 @@ cdef class GiacMethods_base: See also: 1/ epsilon2zero Ex1:epsilon() ''' - return GiacMethods['epsilon'](self,*args) + return GiacMethods['epsilon'](self, *args) - def epsilon2zero(self,*args): + def epsilon2zero(self, *args): r'''From Giac's documentation: Help for epsilon2zero: epsilon2zero(Expr) @@ -4552,9 +4552,9 @@ cdef class GiacMethods_base: See also: 1/ evalf Ex1:epsilon2zero(1e-13+x+5) ''' - return GiacMethods['epsilon2zero'](self,*args) + return GiacMethods['epsilon2zero'](self, *args) - def equal(self,*args): + def equal(self, *args): r'''From Giac's documentation: Help for equal: equal(Expr,Expr) @@ -4564,9 +4564,9 @@ cdef class GiacMethods_base: Ex2:equal(2*x,4) Ex3:equal(x^2-3x+2,0) ''' - return GiacMethods['equal'](self,*args) + return GiacMethods['equal'](self, *args) - def equal2diff(self,*args): + def equal2diff(self, *args): r'''From Giac's documentation: Help for equal2diff: equal2diff(Equal) @@ -4575,9 +4575,9 @@ cdef class GiacMethods_base: Ex1:equal2diff(x=2) Ex2:equal2diff(equal(x,2)) ''' - return GiacMethods['equal2diff'](self,*args) + return GiacMethods['equal2diff'](self, *args) - def equal2list(self,*args): + def equal2list(self, *args): r'''From Giac's documentation: Help for equal2list: equal2list(Equal) @@ -4586,9 +4586,9 @@ cdef class GiacMethods_base: Ex1:equal2list(x=2) Ex2:equal2list(equal(x,2)) ''' - return GiacMethods['equal2list'](self,*args) + return GiacMethods['equal2list'](self, *args) - def equation(self,*args): + def equation(self, *args): r'''From Giac's documentation: Help for equation: equation(GeoObj, VectParam) @@ -4596,9 +4596,9 @@ cdef class GiacMethods_base: See also: 1/ parameq Ex1:equation(line(1-i,i),[x,y]) ''' - return GiacMethods['equation'](self,*args) + return GiacMethods['equation'](self, *args) - def equilateral_triangle(self,*args): + def equilateral_triangle(self, *args): r'''From Giac's documentation: Help for equilateral_triangle: equilateral_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P)],[Var(C)]) @@ -4609,9 +4609,9 @@ cdef class GiacMethods_base: Ex3:equilateral_triangle(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:equilateral_triangle(point(0,0,0),point(3,3,3),point(0,0,3),C) ''' - return GiacMethods['equilateral_triangle'](self,*args) + return GiacMethods['equilateral_triangle'](self, *args) - def erf(self,*args): + def erf(self, *args): r'''From Giac's documentation: Help for erf: erf(Real(x0)) @@ -4620,9 +4620,9 @@ cdef class GiacMethods_base: Ex1:erf(1) Ex2:erf(1/(sqrt(2)))*1/2 ''' - return GiacMethods['erf'](self,*args) + return GiacMethods['erf'](self, *args) - def erfc(self,*args): + def erfc(self, *args): r'''From Giac's documentation: Help for erfc: erfc(Real(x0)) @@ -4631,9 +4631,9 @@ cdef class GiacMethods_base: Ex1:erfc(1) Ex2:erfc(1/(sqrt(2)))*1/2 ''' - return GiacMethods['erfc'](self,*args) + return GiacMethods['erfc'](self, *args) - def error(self,*args): + def error(self, *args): r'''From Giac's documentation: Help for error: error(Str) @@ -4642,9 +4642,9 @@ cdef class GiacMethods_base: Ex1:error("Argument should be integer") Ex2:error("je provoque une erreur") ''' - return GiacMethods['error'](self,*args) + return GiacMethods['error'](self, *args) - def est_permu(self,*args): + def est_permu(self, *args): r'''From Giac's documentation: Help for est_permu: est_permu(Lst) @@ -4653,9 +4653,9 @@ cdef class GiacMethods_base: Ex1:est_permu([4,2,3,1]) Ex2:est_permu([4,2,3,1,0]) ''' - return GiacMethods['est_permu'](self,*args) + return GiacMethods['est_permu'](self, *args) - def euler(self,*args): + def euler(self, *args): r'''From Giac's documentation: Help for euler: euler(Intg(n)) @@ -4664,18 +4664,18 @@ cdef class GiacMethods_base: Ex1:euler(11) Ex2:euler(6) ''' - return GiacMethods['euler'](self,*args) + return GiacMethods['euler'](self, *args) - def euler_gamma(self,*args): + def euler_gamma(self, *args): r'''From Giac's documentation: Help for euler_gamma: euler_gamma() Euler's constant=euler_gamma=limit(sum(1/k,k,1,n)-ln(n),n,+infinity). Ex1: evalf(euler_gamma) ''' - return GiacMethods['euler_gamma'](self,*args) + return GiacMethods['euler_gamma'](self, *args) - def euler_lagrange(self,*args): + def euler_lagrange(self, *args): r'''From Giac's documentation: Help for euler_lagrange: euler_lagrange(Expr(f),[(Var(x),[Var||Lst(y)]) || y(x) || Lst(y(x))]) @@ -4685,9 +4685,9 @@ cdef class GiacMethods_base: Ex2:euler_lagrange(sqrt(x'^2+y'^2),[x(t),y(t)]) Ex3: assume(y>=0):; euler_lagrange(sqrt((1+y'^2)/y),t,y) ''' - return GiacMethods['euler_lagrange'](self,*args) + return GiacMethods['euler_lagrange'](self, *args) - def eval_level(self,*args): + def eval_level(self, *args): r'''From Giac's documentation: Help for eval_level: eval_level([Intg(n)]) @@ -4698,9 +4698,9 @@ cdef class GiacMethods_base: Ex4: purge(a,b,c);eval_level(2);a:=b+1; b:=c+1;c:=3; Ex5: purge(a,b,c);eval_level(3);a:=b+1; b:=c+1;c:=3; ''' - return GiacMethods['eval_level'](self,*args) + return GiacMethods['eval_level'](self, *args) - def evala(self,*args): + def evala(self, *args): r'''From Giac's documentation: Help for evala: evala(Expr) @@ -4710,9 +4710,9 @@ cdef class GiacMethods_base: Ex2:evala(2*x*2) Ex3:evala((2*x+1)^2) ''' - return GiacMethods['evala'](self,*args) + return GiacMethods['evala'](self, *args) - def evalb(self,*args): + def evalb(self, *args): r'''From Giac's documentation: Help for evalb: evalb(Expr) @@ -4721,9 +4721,9 @@ cdef class GiacMethods_base: Ex1:evalb(a==2) Ex2:evalb(sqrt(2)+pi>a) ''' - return GiacMethods['evalb'](self,*args) + return GiacMethods['evalb'](self, *args) - def evalc(self,*args): + def evalc(self, *args): r'''From Giac's documentation: Help for evalc: evalc(Expr) @@ -4732,9 +4732,9 @@ cdef class GiacMethods_base: Ex1:evalc(-3+4*i+exp(i)) Ex2:evalc(1/(x+y*i)) ''' - return GiacMethods['evalc'](self,*args) + return GiacMethods['evalc'](self, *args) - def evalf(self,*args): + def evalf(self, *args): r'''From Giac's documentation: Help for evalf: evalf(Expr,[Int]) @@ -4747,9 +4747,9 @@ cdef class GiacMethods_base: Ex5:evalf(sqrt(2)+pi) Ex6:evalf(sqrt(2)+pi,30) ''' - return GiacMethods['evalf'](self,*args) + return GiacMethods['evalf'](self, *args) - def evalm(self,*args): + def evalm(self, *args): r'''From Giac's documentation: Help for evalm: evalm(Expr) @@ -4757,9 +4757,9 @@ cdef class GiacMethods_base: See also: 1/ evalf Ex1:evalm(2*sin(pi)) ''' - return GiacMethods['evalm'](self,*args) + return GiacMethods['evalm'](self, *args) - def even(self,*args): + def even(self, *args): r'''From Giac's documentation: Help for even: even(Intg(n)) @@ -4768,9 +4768,9 @@ cdef class GiacMethods_base: Ex1:even(6) Ex2:even(1251) ''' - return GiacMethods['even'](self,*args) + return GiacMethods['even'](self, *args) - def evolute(self,*args): + def evolute(self, *args): r'''From Giac's documentation: Help for evolute: evolute(Curve) @@ -4780,9 +4780,9 @@ cdef class GiacMethods_base: Ex2:evolute([t,t^2],t) Ex3:evolute([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t) ''' - return GiacMethods['evolute'](self,*args) + return GiacMethods['evolute'](self, *args) - def exact(self,*args): + def exact(self, *args): r'''From Giac's documentation: Help for exact: exact(Expr) @@ -4793,9 +4793,9 @@ cdef class GiacMethods_base: Ex3:exact(1.4141) Ex4:exact(0.156381102937) ''' - return GiacMethods['exact'](self,*args) + return GiacMethods['exact'](self, *args) - def exbisector(self,*args): + def exbisector(self, *args): r'''From Giac's documentation: Help for exbisector: exbisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx)) @@ -4803,9 +4803,9 @@ cdef class GiacMethods_base: See also: 1/ angle 2/ bisector Ex1:exbisector(0,1,i) ''' - return GiacMethods['exbisector'](self,*args) + return GiacMethods['exbisector'](self, *args) - def excircle(self,*args): + def excircle(self, *args): r'''From Giac's documentation: Help for excircle: excircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -4813,9 +4813,9 @@ cdef class GiacMethods_base: See also: 1/ incircle 2/ circumcircle Ex1:excircle(0,1,1+i) ''' - return GiacMethods['excircle'](self,*args) + return GiacMethods['excircle'](self, *args) - def execute(self,*args): + def execute(self, *args): r'''From Giac's documentation: Help for execute: execute(Str) @@ -4826,9 +4826,9 @@ cdef class GiacMethods_base: Ex3:execute("0123") Ex4:execute(sin,x) ''' - return GiacMethods['execute'](self,*args) + return GiacMethods['execute'](self, *args) - def exp(self,*args): + def exp(self, *args): r'''From Giac's documentation: Help for exp: exp(Expr or Opt) @@ -4837,9 +4837,9 @@ cdef class GiacMethods_base: Ex1:exp(0) Ex2: convert(cos(x),exp) ''' - return GiacMethods['exp'](self,*args) + return GiacMethods['exp'](self, *args) - def exp2list(self,*args): + def exp2list(self, *args): r'''From Giac's documentation: Help for exp2list: exp2list(Expr) @@ -4848,9 +4848,9 @@ cdef class GiacMethods_base: Ex1:exp2list((x=2) or (x=0)) Ex2:exp2list((x=3 and y=9) or (x=-1 and y=1) ) ''' - return GiacMethods['exp2list'](self,*args) + return GiacMethods['exp2list'](self, *args) - def exp2pow(self,*args): + def exp2pow(self, *args): r'''From Giac's documentation: Help for exp2pow: exp2pow(Expr) @@ -4859,9 +4859,9 @@ cdef class GiacMethods_base: Ex1:exp2pow(exp(3*ln(x))) Ex2:exp2pow(exp(x*ln(x))) ''' - return GiacMethods['exp2pow'](self,*args) + return GiacMethods['exp2pow'](self, *args) - def exp2trig(self,*args): + def exp2trig(self, *args): r'''From Giac's documentation: Help for exp2trig: exp2trig(Expr) @@ -4870,9 +4870,9 @@ cdef class GiacMethods_base: Ex1:exp2trig(exp(i*x)) Ex2:exp2trig(exp(-i*x)) ''' - return GiacMethods['exp2trig'](self,*args) + return GiacMethods['exp2trig'](self, *args) - def expand(self,*args): + def expand(self, *args): r'''From Giac's documentation: Help for expand: expand(Expr) @@ -4884,9 +4884,9 @@ cdef class GiacMethods_base: Ex4:expand((x+3)^4) Ex5:expand((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) ''' - return GiacMethods['expand'](self,*args) + return GiacMethods['expand'](self, *args) - def expexpand(self,*args): + def expexpand(self, *args): r'''From Giac's documentation: Help for expexpand: expexpand(Expr) @@ -4894,9 +4894,9 @@ cdef class GiacMethods_base: See also: 1/ texpand 2/ lnexpand 3/ trigexpand Ex1:expexpand(exp(3*x)) ''' - return GiacMethods['expexpand'](self,*args) + return GiacMethods['expexpand'](self, *args) - def expln(self,*args): + def expln(self, *args): r'''From Giac's documentation: Help for expln: expln(Opt) @@ -4904,9 +4904,9 @@ cdef class GiacMethods_base: See also: 1/ exp 2/ ln 3/ convert 4/ trig2exp Ex1: convert(cos(x),expln) ''' - return GiacMethods['expln'](self,*args) + return GiacMethods['expln'](self, *args) - def exponential(self,*args): + def exponential(self, *args): r'''From Giac's documentation: Help for exponential: exponential(Real(lambda),Real(x)) @@ -4917,9 +4917,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,exponential,1.2) Ex4: ranm(4,3,exponential,1.2) ''' - return GiacMethods['exponential'](self,*args) + return GiacMethods['exponential'](self, *args) - def exponential_cdf(self,*args): + def exponential_cdf(self, *args): r'''From Giac's documentation: Help for exponential_cdf: exponential_cdf(Real(lambda),Real(x0),[Real(y0)]) @@ -4928,9 +4928,9 @@ cdef class GiacMethods_base: Ex1:exponential_cdf(4.2,2.1) Ex2:exponential_cdf(4.2,2.1,3.2) ''' - return GiacMethods['exponential_cdf'](self,*args) + return GiacMethods['exponential_cdf'](self, *args) - def exponential_icdf(self,*args): + def exponential_icdf(self, *args): r'''From Giac's documentation: Help for exponential_icdf: exponential_icdf(Real(lambda),Real(x0),Real(p)) @@ -4939,9 +4939,9 @@ cdef class GiacMethods_base: Ex1:exponential_icdf(4.2,0.95) Ex2:exponential_icdf(4.2,0.6) ''' - return GiacMethods['exponential_icdf'](self,*args) + return GiacMethods['exponential_icdf'](self, *args) - def exponential_regression(self,*args): + def exponential_regression(self, *args): r'''From Giac's documentation: Help for exponential_regression: exponential_regression(Lst||Mtrx(A),[Lst]) @@ -4950,9 +4950,9 @@ cdef class GiacMethods_base: Ex1:exponential_regression([[1.0,2.0],[0.0,1.0],[4.0,7.0]]) Ex2:exponential_regression([1.0,0.0,4.0],[2.0,1.0,7.0]) ''' - return GiacMethods['exponential_regression'](self,*args) + return GiacMethods['exponential_regression'](self, *args) - def exponential_regression_plot(self,*args): + def exponential_regression_plot(self, *args): r'''From Giac's documentation: Help for exponential_regression_plot: exponential_regression_plot(Lst||Mtrx(A),[Lst]) @@ -4961,9 +4961,9 @@ cdef class GiacMethods_base: Ex1:exponential_regression_plot([[1.0,2.0],[0.0,1.0],[4.0,7.0]]) Ex2:exponential_regression_plot([1.0,0.0,4.0],[2.0,1.0,7.0]) ''' - return GiacMethods['exponential_regression_plot'](self,*args) + return GiacMethods['exponential_regression_plot'](self, *args) - def exponentiald(self,*args): + def exponentiald(self, *args): r'''From Giac's documentation: Help for exponentiald: exponentiald(Real(lambda),Real(x)) @@ -4974,9 +4974,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,exponential,1.2) Ex4: ranm(4,3,exponential,1.2) ''' - return GiacMethods['exponentiald'](self,*args) + return GiacMethods['exponentiald'](self, *args) - def exponentiald_cdf(self,*args): + def exponentiald_cdf(self, *args): r'''From Giac's documentation: Help for exponentiald_cdf: exponentiald_cdf(Real(lambda),Real(x0),[Real(y0)]) @@ -4985,9 +4985,9 @@ cdef class GiacMethods_base: Ex1:exponentiald_cdf(4.2,2.1) Ex2:exponentiald_cdf(4.2,2.1,3.2) ''' - return GiacMethods['exponentiald_cdf'](self,*args) + return GiacMethods['exponentiald_cdf'](self, *args) - def exponentiald_icdf(self,*args): + def exponentiald_icdf(self, *args): r'''From Giac's documentation: Help for exponentiald_icdf: exponentiald_icdf(Real(lambda),Real(x0),Real(p)) @@ -4996,9 +4996,9 @@ cdef class GiacMethods_base: Ex1:exponentiald_icdf(4.2,0.95) Ex2:exponentiald_icdf(4.2,0.6) ''' - return GiacMethods['exponentiald_icdf'](self,*args) + return GiacMethods['exponentiald_icdf'](self, *args) - def export_graph(self,*args): + def export_graph(self, *args): r'''From Giac's documentation: Help for export_graph: export_graph(Graph(G),Str("path/to/graphname")) @@ -5006,9 +5006,9 @@ cdef class GiacMethods_base: See also: 1/ import_graph Ex1:export_graph(complete_graph(5),"K5") ''' - return GiacMethods['export_graph'](self,*args) + return GiacMethods['export_graph'](self, *args) - def export_mathml(self,*args): + def export_mathml(self, *args): r'''From Giac's documentation: Help for export_mathml: export_mathml(Expr,[display||content]) @@ -5018,9 +5018,9 @@ cdef class GiacMethods_base: Ex2:export_mathml(a+2*b,display) Ex3:export_mathml(a+2*b,content) ''' - return GiacMethods['export_mathml'](self,*args) + return GiacMethods['export_mathml'](self, *args) - def expovariate(self,*args): + def expovariate(self, *args): r'''From Giac's documentation: Help for expovariate: expovariate(Real(a)) @@ -5029,9 +5029,9 @@ cdef class GiacMethods_base: Ex1:expovariate(1) Ex2:expovariate(2) ''' - return GiacMethods['expovariate'](self,*args) + return GiacMethods['expovariate'](self, *args) - def expr(self,*args): + def expr(self, *args): r'''From Giac's documentation: Help for expr: expr(Str) @@ -5042,9 +5042,9 @@ cdef class GiacMethods_base: Ex3:expr("0123") Ex4:expr(sin,x) ''' - return GiacMethods['expr'](self,*args) + return GiacMethods['expr'](self, *args) - def extend(self,*args): + def extend(self, *args): r'''From Giac's documentation: Help for extend: extend(Lst,Lst||Seq,Seq||Str,Str||Mtrx,Mtrx) @@ -5056,9 +5056,9 @@ cdef class GiacMethods_base: Ex4: L:=[1,2];L.concat([3,4,5]) Ex5: S:="abcd";S.concat("efghi") ''' - return GiacMethods['extend'](self,*args) + return GiacMethods['extend'](self, *args) - def extract_measure(self,*args): + def extract_measure(self, *args): r'''From Giac's documentation: Help for extract_measure: extract_measure(Var) @@ -5068,9 +5068,9 @@ cdef class GiacMethods_base: Ex2:extract_measure(angleatraw(0,1,1+i,1)) Ex3: A:=point(0);B:=point(1+i);a:=distanceatraw(A,B,(1+i)/2);extract_measure(a) ''' - return GiacMethods['extract_measure'](self,*args) + return GiacMethods['extract_measure'](self, *args) - def extrema(self,*args): + def extrema(self, *args): r'''From Giac's documentation: Help for extrema: extrema(Expr,Var,a,b) @@ -5133,9 +5133,9 @@ cdef class GiacMethods_base: Ex56:extrema((1+y*sinh(x))/(1+y^2+tanh(x)^2),[x,y]) Ex57:extrema((1+y*sinh(x))/(1+y^2+tanh(x)^2),y=x^2,[x,y]) ''' - return GiacMethods['extrema'](self,*args) + return GiacMethods['extrema'](self, *args) - def ezgcd(self,*args): + def ezgcd(self, *args): r'''From Giac's documentation: Help for ezgcd: ezgcd(Poly,Poly) @@ -5145,9 +5145,9 @@ cdef class GiacMethods_base: Ex2:ezgcd((x+1)^4-y^4,(x+1-y)^2) Ex3:ezgcd((x+y-1)*(x+y+1),(x+y+1)^2) ''' - return GiacMethods['ezgcd'](self,*args) + return GiacMethods['ezgcd'](self, *args) - def f2nd(self,*args): + def f2nd(self, *args): r'''From Giac's documentation: Help for f2nd: f2nd(Frac or RatFrac) @@ -5156,9 +5156,9 @@ cdef class GiacMethods_base: Ex1:f2nd(42/12) Ex2:f2nd((x^2+2*x+1)/(x^2-1)) ''' - return GiacMethods['f2nd'](self,*args) + return GiacMethods['f2nd'](self, *args) - def fMax(self,*args): + def fMax(self, *args): r'''From Giac's documentation: Help for fMax: fMax(Expr,[Var]) @@ -5167,9 +5167,9 @@ cdef class GiacMethods_base: Ex1:fMax(-x^2+2*x+1,x) Ex2:fMax(-x^2+2*x+1,x=1..2) ''' - return GiacMethods['fMax'](self,*args) + return GiacMethods['fMax'](self, *args) - def fMin(self,*args): + def fMin(self, *args): r'''From Giac's documentation: Help for fMin: fMin(Expr,[Var]) @@ -5180,9 +5180,9 @@ cdef class GiacMethods_base: Ex3:fMin((x-3)^2+(y-5)^2+1,[],[x,y],[1,1]) Ex4:fMin((x-3)^2+(y-5)^2+1,[x+y^2=1],[x,y],[1,1]) ''' - return GiacMethods['fMin'](self,*args) + return GiacMethods['fMin'](self, *args) - def fPart(self,*args): + def fPart(self, *args): r'''From Giac's documentation: Help for fPart: fPart(Real||LstReal) @@ -5194,9 +5194,9 @@ cdef class GiacMethods_base: Ex4:fPart(-1.2) Ex5:fPart([3.4,sqrt(2)]) ''' - return GiacMethods['fPart'](self,*args) + return GiacMethods['fPart'](self, *args) - def faces(self,*args): + def faces(self, *args): r'''From Giac's documentation: Help for faces: faces(Polygon or Polyedr(P)) @@ -5205,9 +5205,9 @@ cdef class GiacMethods_base: Ex1:faces(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex2:faces(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6]))[2] ''' - return GiacMethods['faces'](self,*args) + return GiacMethods['faces'](self, *args) - def facteurs_premiers(self,*args): + def facteurs_premiers(self, *args): r'''From Giac's documentation: Help for facteurs_premiers: facteurs_premiers(Intg(a) or LstIntg) @@ -5216,9 +5216,9 @@ cdef class GiacMethods_base: Ex1:facteurs_premiers(36) Ex2:facteurs_premiers([36,52]) ''' - return GiacMethods['facteurs_premiers'](self,*args) + return GiacMethods['facteurs_premiers'](self, *args) - def factor(self,*args): + def factor(self, *args): r'''From Giac's documentation: Help for factor: factor(Expr) @@ -5228,9 +5228,9 @@ cdef class GiacMethods_base: Ex2:factor(x^4-4,sqrt(2)) Ex3:factor(x^4+12*x^3+54*x^2+108*x+81) ''' - return GiacMethods['factor'](self,*args) + return GiacMethods['factor'](self, *args) - def factor_xn(self,*args): + def factor_xn(self, *args): r'''From Giac's documentation: Help for factor_xn: factor_xn(Poly(P)) @@ -5239,9 +5239,9 @@ cdef class GiacMethods_base: Ex1:factor_xn(x^4-1) Ex2:factor_xn(x^4+12*x^3+54*x^2+108*x+81) ''' - return GiacMethods['factor_xn'](self,*args) + return GiacMethods['factor_xn'](self, *args) - def factorial(self,*args): + def factorial(self, *args): r'''From Giac's documentation: Help for factorial: factorial(Intg(n)|| Real(a)) @@ -5250,9 +5250,9 @@ cdef class GiacMethods_base: Ex1:factorial(4) Ex2:factorial(1.2) ''' - return GiacMethods['factorial'](self,*args) + return GiacMethods['factorial'](self, *args) - def factoriser(self,*args): + def factoriser(self, *args): r'''From Giac's documentation: Help for factoriser: factoriser(Expr) @@ -5262,9 +5262,9 @@ cdef class GiacMethods_base: Ex2:factoriser(x^4-4,sqrt(2)) Ex3:factoriser(x^4+12*x^3+54*x^2+108*x+81) ''' - return GiacMethods['factoriser'](self,*args) + return GiacMethods['factoriser'](self, *args) - def factoriser_entier(self,*args): + def factoriser_entier(self, *args): r'''From Giac's documentation: Help for factoriser_entier: factoriser_entier(Intg(a)) @@ -5273,9 +5273,9 @@ cdef class GiacMethods_base: Ex1:factoriser_entier(50) Ex2:factoriser_entier(123456789) ''' - return GiacMethods['factoriser_entier'](self,*args) + return GiacMethods['factoriser_entier'](self, *args) - def factoriser_sur_C(self,*args): + def factoriser_sur_C(self, *args): r'''From Giac's documentation: Help for factoriser_sur_C: factoriser_sur_C(Expr) @@ -5285,9 +5285,9 @@ cdef class GiacMethods_base: Ex2:factoriser_sur_C(x^2*y^2+y^2+4*x^2+4) Ex3:factoriser_sur_C(x^2*y^2+y^2+2*x^2+2) ''' - return GiacMethods['factoriser_sur_C'](self,*args) + return GiacMethods['factoriser_sur_C'](self, *args) - def factors(self,*args): + def factors(self, *args): r'''From Giac's documentation: Help for factors: factors(Poly or LstPoly) @@ -5296,9 +5296,9 @@ cdef class GiacMethods_base: Ex1:factors(x^4-1) Ex2:factors([x^2,x^2-1]) ''' - return GiacMethods['factors'](self,*args) + return GiacMethods['factors'](self, *args) - def fadeev(self,*args): + def fadeev(self, *args): r'''From Giac's documentation: Help for fadeev: fadeev(Opt) @@ -5306,9 +5306,9 @@ cdef class GiacMethods_base: See also: 1/ pcar Ex1: pcar([[4,1,-2],[1,2,-1],[2,1,0]],fadeev) ''' - return GiacMethods['fadeev'](self,*args) + return GiacMethods['fadeev'](self, *args) - def false(self,*args): + def false(self, *args): r'''From Giac's documentation: Help for false: false() @@ -5316,9 +5316,9 @@ cdef class GiacMethods_base: See also: 1/ true Ex1: a:=false ''' - return GiacMethods['false'](self,*args) + return GiacMethods['false'](self, *args) - def falsepos_solver(self,*args): + def falsepos_solver(self, *args): r'''From Giac's documentation: Help for falsepos_solver: falsepos_solver(Opt) @@ -5331,9 +5331,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['falsepos_solver'](self,*args) + return GiacMethods['falsepos_solver'](self, *args) - def fclose(self,*args): + def fclose(self, *args): r'''From Giac's documentation: Help for fclose: fclose(File(f)) @@ -5341,9 +5341,9 @@ cdef class GiacMethods_base: See also: 1/ fprint 2/ fopen Ex1:fclose(f) ''' - return GiacMethods['fclose'](self,*args) + return GiacMethods['fclose'](self, *args) - def fcoeff(self,*args): + def fcoeff(self, *args): r'''From Giac's documentation: Help for fcoeff: fcoeff(Lst(root||pole,order)) @@ -5351,9 +5351,9 @@ cdef class GiacMethods_base: See also: 1/ pcoeff 2/ froot 3/ proot Ex1:fcoeff([1,2,0,1,3,-1]) ''' - return GiacMethods['fcoeff'](self,*args) + return GiacMethods['fcoeff'](self, *args) - def fdistrib(self,*args): + def fdistrib(self, *args): r'''From Giac's documentation: Help for fdistrib: fdistrib(Expr) @@ -5365,9 +5365,9 @@ cdef class GiacMethods_base: Ex4:fdistrib((x+3)^4) Ex5:fdistrib((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) ''' - return GiacMethods['fdistrib'](self,*args) + return GiacMethods['fdistrib'](self, *args) - def fft(self,*args): + def fft(self, *args): r'''From Giac's documentation: Help for fft: fft(Vect or (Vect(L),Intg(a),Intg(p)) @@ -5376,9 +5376,9 @@ cdef class GiacMethods_base: Ex1:fft([1,2,3,4,0,0,0,0]) Ex2:fft(ranm(128),22798,35969) ''' - return GiacMethods['fft'](self,*args) + return GiacMethods['fft'](self, *args) - def fieldplot(self,*args): + def fieldplot(self, *args): r'''From Giac's documentation: Help for fieldplot: fieldplot(Expr,VectVar,[Opt]) @@ -5390,9 +5390,9 @@ cdef class GiacMethods_base: Ex4:fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) Ex5:fieldplot(-t*y,[t=-6.868..6.868,y=-6.868..6.868],normalize) ''' - return GiacMethods['fieldplot'](self,*args) + return GiacMethods['fieldplot'](self, *args) - def find(self,*args): + def find(self, *args): r'''From Giac's documentation: Help for find: find(Expr,Vect) @@ -5404,9 +5404,9 @@ cdef class GiacMethods_base: Ex4:find("ab","abracadabrant") Ex5:find(1,%{4,3,1,2%}) ''' - return GiacMethods['find'](self,*args) + return GiacMethods['find'](self, *args) - def find_cycles(self,*args): + def find_cycles(self, *args): r'''From Giac's documentation: Help for find_cycles: find_cycles(Graph(G,[length=k||l..u])) @@ -5416,9 +5416,9 @@ cdef class GiacMethods_base: Ex2:find_cycles(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%}),length=3) Ex3:find_cycles(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%}),length=3..4) ''' - return GiacMethods['find_cycles'](self,*args) + return GiacMethods['find_cycles'](self, *args) - def findhelp(self,*args): + def findhelp(self, *args): r'''From Giac's documentation: Help for findhelp: findhelp(Cmd) @@ -5426,9 +5426,9 @@ cdef class GiacMethods_base: See also: 1/ ifte 2/ when Ex1:findhelp(ifactor) ''' - return GiacMethods['findhelp'](self,*args) + return GiacMethods['findhelp'](self, *args) - def fisher(self,*args): + def fisher(self, *args): r'''From Giac's documentation: Help for fisher: fisher(Intg(n),Intg(m),Real(x0)) @@ -5439,9 +5439,9 @@ cdef class GiacMethods_base: Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) ''' - return GiacMethods['fisher'](self,*args) + return GiacMethods['fisher'](self, *args) - def fisher_cdf(self,*args): + def fisher_cdf(self, *args): r'''From Giac's documentation: Help for fisher_cdf: fisher_cdf(Intg(n),Intg(m),Real(x0)) @@ -5450,9 +5450,9 @@ cdef class GiacMethods_base: Ex1:fisher_cdf(4,4,2.1) Ex2:fisher_cdf(4,10,3.5) ''' - return GiacMethods['fisher_cdf'](self,*args) + return GiacMethods['fisher_cdf'](self, *args) - def fisher_icdf(self,*args): + def fisher_icdf(self, *args): r'''From Giac's documentation: Help for fisher_icdf: fisher_icdf(Intg(n),Intg(m),Real(p)) @@ -5461,9 +5461,9 @@ cdef class GiacMethods_base: Ex1:fisher_icdf(4,10,0.95) Ex2:fisher_icdf(4,10,0.05) ''' - return GiacMethods['fisher_icdf'](self,*args) + return GiacMethods['fisher_icdf'](self, *args) - def fisherd(self,*args): + def fisherd(self, *args): r'''From Giac's documentation: Help for fisherd: fisherd(Intg(n),Intg(m),Real(x0)) @@ -5474,9 +5474,9 @@ cdef class GiacMethods_base: Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) ''' - return GiacMethods['fisherd'](self,*args) + return GiacMethods['fisherd'](self, *args) - def fisherd_cdf(self,*args): + def fisherd_cdf(self, *args): r'''From Giac's documentation: Help for fisherd_cdf: fisherd_cdf(Intg(n),Intg(m),Real(x0)) @@ -5485,9 +5485,9 @@ cdef class GiacMethods_base: Ex1:fisherd_cdf(4,4,2.1) Ex2:fisherd_cdf(4,10,3.5) ''' - return GiacMethods['fisherd_cdf'](self,*args) + return GiacMethods['fisherd_cdf'](self, *args) - def fisherd_icdf(self,*args): + def fisherd_icdf(self, *args): r'''From Giac's documentation: Help for fisherd_icdf: fisherd_icdf(Intg(n),Intg(m),Real(p)) @@ -5496,9 +5496,9 @@ cdef class GiacMethods_base: Ex1:fisherd_icdf(4,10,0.95) Ex2:fisherd_icdf(4,10,0.05) ''' - return GiacMethods['fisherd_icdf'](self,*args) + return GiacMethods['fisherd_icdf'](self, *args) - def fitdistr(self,*args): + def fitdistr(self, *args): r'''From Giac's documentation: Help for fitdistr: fitdistr(Lst(L),Fnc(D)) @@ -5508,9 +5508,9 @@ cdef class GiacMethods_base: Ex2: X:=randvar(normal,stddev=9.5):;Y:=randvar(normal,stddev=1.5):;S:=sample(eval(X/Y,0),1000):;Z:=fitdistr(S,cauchy) Ex3: X:=randvar(normal,mean=5,variance=2):;S:=sample(exp(X),1000):;fitdistr(log(S),normal) ''' - return GiacMethods['fitdistr'](self,*args) + return GiacMethods['fitdistr'](self, *args) - def flatten(self,*args): + def flatten(self, *args): r'''From Giac's documentation: Help for flatten: flatten(Lst) @@ -5518,9 +5518,9 @@ cdef class GiacMethods_base: See also: 1/ mat2list Ex1:flatten([[1,[2,3],4],[5,6]]) ''' - return GiacMethods['flatten'](self,*args) + return GiacMethods['flatten'](self, *args) - def float2rational(self,*args): + def float2rational(self, *args): r'''From Giac's documentation: Help for float2rational: float2rational(Expr) @@ -5531,9 +5531,9 @@ cdef class GiacMethods_base: Ex3:float2rational(1.4141) Ex4:float2rational(0.156381102937) ''' - return GiacMethods['float2rational'](self,*args) + return GiacMethods['float2rational'](self, *args) - def floor(self,*args): + def floor(self, *args): r'''From Giac's documentation: Help for floor: floor(Real or Cplx) @@ -5542,9 +5542,9 @@ cdef class GiacMethods_base: Ex1:floor(-2.5) Ex2:floor(2.5-4.2*i) ''' - return GiacMethods['floor'](self,*args) + return GiacMethods['floor'](self, *args) - def flow_polynomial(self,*args): + def flow_polynomial(self, *args): r'''From Giac's documentation: Help for flow_polynomial: flow_polynomial(Graph(G),[Var(x)]) @@ -5553,18 +5553,18 @@ cdef class GiacMethods_base: Ex1:flow_polynomial(graph("tetrahedron")) Ex2:flow_polynomial(graph("tetrahedron"),5) ''' - return GiacMethods['flow_polynomial'](self,*args) + return GiacMethods['flow_polynomial'](self, *args) - def fmod(self,*args): + def fmod(self, *args): r'''From Giac's documentation: Help for fmod: fmod(Real(a),Real(b)) Returns a mod b for a and b floats. Ex1:fmod(10.0,pi) ''' - return GiacMethods['fmod'](self,*args) + return GiacMethods['fmod'](self, *args) - def foldl(self,*args): + def foldl(self, *args): r'''From Giac's documentation: Help for foldl: foldl(op,id,Seq(r1,r2,...)) @@ -5572,9 +5572,9 @@ cdef class GiacMethods_base: See also: 1/ apply 2/ foldr 3/ map Ex1:foldl(F,init,a,b,c) ''' - return GiacMethods['foldl'](self,*args) + return GiacMethods['foldl'](self, *args) - def foldr(self,*args): + def foldr(self, *args): r'''From Giac's documentation: Help for foldr: foldr(op,id,Seq(r1,r2,...)) @@ -5582,9 +5582,9 @@ cdef class GiacMethods_base: See also: 1/ apply 2/ foldl 3/ map Ex1:foldr(F,init,a,b,c) ''' - return GiacMethods['foldr'](self,*args) + return GiacMethods['foldr'](self, *args) - def fonction_derivee(self,*args): + def fonction_derivee(self, *args): r'''From Giac's documentation: Help for fonction_derivee: fonction_derivee(Fnc(f)) @@ -5596,9 +5596,9 @@ cdef class GiacMethods_base: Ex4:fonction_derivee(ln)([x,y]) Ex5: (function_diff @@3)(ln)('x') ''' - return GiacMethods['fonction_derivee'](self,*args) + return GiacMethods['fonction_derivee'](self, *args) - def forward(self,*args): + def forward(self, *args): r'''From Giac's documentation: Help for forward: forward(NULL or Real(n)) @@ -5607,9 +5607,9 @@ cdef class GiacMethods_base: Ex1: avance 30 Ex2:forward(30) ''' - return GiacMethods['forward'](self,*args) + return GiacMethods['forward'](self, *args) - def fourier(self,*args): + def fourier(self, *args): r'''From Giac's documentation: Help for fourier: fourier(Expr(f(x)),[Var(x),[Var(s)]]) @@ -5632,9 +5632,9 @@ cdef class GiacMethods_base: Ex15:fourier(atan(x/4)/x,x,s) Ex16:fourier(piecewise(x<=-1,exp(x+1),x<=1,1,exp(2-2x)),x,s) ''' - return GiacMethods['fourier'](self,*args) + return GiacMethods['fourier'](self, *args) - def fourier_an(self,*args): + def fourier_an(self, *args): r'''From Giac's documentation: Help for fourier_an: fourier_an(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) @@ -5643,9 +5643,9 @@ cdef class GiacMethods_base: Ex1:fourier_an(x^2,x,2,0,-1) Ex2:fourier_an(x^2,x,2,n,-1) ''' - return GiacMethods['fourier_an'](self,*args) + return GiacMethods['fourier_an'](self, *args) - def fourier_bn(self,*args): + def fourier_bn(self, *args): r'''From Giac's documentation: Help for fourier_bn: fourier_bn(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) @@ -5654,9 +5654,9 @@ cdef class GiacMethods_base: Ex1:fourier_bn(x^2,x,2,0,-1) Ex2:fourier_bn(x^2,x,2,n,-1) ''' - return GiacMethods['fourier_bn'](self,*args) + return GiacMethods['fourier_bn'](self, *args) - def fourier_cn(self,*args): + def fourier_cn(self, *args): r'''From Giac's documentation: Help for fourier_cn: fourier_cn(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) @@ -5665,9 +5665,9 @@ cdef class GiacMethods_base: Ex1:fourier_cn(x^2,x,2,0,-1) Ex2:fourier_cn(x^2,x,2,n,-1) ''' - return GiacMethods['fourier_cn'](self,*args) + return GiacMethods['fourier_cn'](self, *args) - def fprint(self,*args): + def fprint(self, *args): r'''From Giac's documentation: Help for fprint: fprint(File(f),Var,[Var,Var...]) @@ -5677,9 +5677,9 @@ cdef class GiacMethods_base: Ex2:fprint(f,"blabla") Ex3:fprint(f,Unquoted,"blabla") ''' - return GiacMethods['fprint'](self,*args) + return GiacMethods['fprint'](self, *args) - def frac(self,*args): + def frac(self, *args): r'''From Giac's documentation: Help for frac: frac(Real||LstReal) @@ -5691,9 +5691,9 @@ cdef class GiacMethods_base: Ex4:frac(-1.2) Ex5:frac([3.4,sqrt(2)]) ''' - return GiacMethods['frac'](self,*args) + return GiacMethods['frac'](self, *args) - def fracmod(self,*args): + def fracmod(self, *args): r'''From Giac's documentation: Help for fracmod: fracmod(Expr(Xpr),Intg(n)) @@ -5701,9 +5701,9 @@ cdef class GiacMethods_base: See also: 1/ mod 2/ smod Ex1:fracmod(41,121) ''' - return GiacMethods['fracmod'](self,*args) + return GiacMethods['fracmod'](self, *args) - def frame_2d(self,*args): + def frame_2d(self, *args): r'''From Giac's documentation: Help for frame_2d: frame_2d(NULL) @@ -5711,9 +5711,9 @@ cdef class GiacMethods_base: See also: 1/ frame_3d 2/ Ox_2d_unit_vector 3/ Oy_2d_unit_vector Ex1:frame_2d() ''' - return GiacMethods['frame_2d'](self,*args) + return GiacMethods['frame_2d'](self, *args) - def frequencies(self,*args): + def frequencies(self, *args): r'''From Giac's documentation: Help for frequencies: frequencies(Lst) @@ -5722,9 +5722,9 @@ cdef class GiacMethods_base: Ex1:frequencies([1,2,1,1,2,1,2,4,3,3]) Ex2:frequencies([(rand(6)+1)$(k=1..100)]) ''' - return GiacMethods['frequencies'](self,*args) + return GiacMethods['frequencies'](self, *args) - def frobenius_norm(self,*args): + def frobenius_norm(self, *args): r'''From Giac's documentation: Help for frobenius_norm: frobenius_norm(Mtrx) @@ -5732,9 +5732,9 @@ cdef class GiacMethods_base: See also: 1/ l1norm 2/ l2 norm 3/ linfnorm 4/ matrix_norm Ex1:frobenius_norm([[1,2,3],[3,-9,6],[4,5,6]]) ''' - return GiacMethods['frobenius_norm'](self,*args) + return GiacMethods['frobenius_norm'](self, *args) - def froot(self,*args): + def froot(self, *args): r'''From Giac's documentation: Help for froot: froot(RatPoly(F)) @@ -5743,9 +5743,9 @@ cdef class GiacMethods_base: Ex1:froot((x^5-2*x^4+x^3)/(x-3)) Ex2:froot((x^5-2*x^4+x^3)/(x-1)) ''' - return GiacMethods['froot'](self,*args) + return GiacMethods['froot'](self, *args) - def fsolve(self,*args): + def fsolve(self, *args): r'''From Giac's documentation: Help for fsolve: fsolve(Expr,Var,[Guess or Interval],[Method]) @@ -5756,9 +5756,9 @@ cdef class GiacMethods_base: Ex3:fsolve([x^2+y-2,x+y^2-2],[x,y],[0,0],newtonj_solver) Ex4:fsolve([x^2+y-2,x+y^2-2],[x,y]) ''' - return GiacMethods['fsolve'](self,*args) + return GiacMethods['fsolve'](self, *args) - def fullparfrac(self,*args): + def fullparfrac(self, *args): r'''From Giac's documentation: Help for fullparfrac: fullparfrac(Opt) @@ -5767,9 +5767,9 @@ cdef class GiacMethods_base: Ex1: convert(1/(x^2-1),parfrac) Ex2: convert(1/(x^2-1),fullparfrac) ''' - return GiacMethods['fullparfrac'](self,*args) + return GiacMethods['fullparfrac'](self, *args) - def funcplot(self,*args): + def funcplot(self, *args): r'''From Giac's documentation: Help for funcplot: funcplot(Expr,[Var(x) or VectVar] ,[Intg(color)]) @@ -5781,9 +5781,9 @@ cdef class GiacMethods_base: Ex4:funcplot(x^2+y^2,[x=-1..1,y=-2..2],nstep=900) Ex5:funcplot((x+i*y)^2,[x=-1..1,y=-2..2],nstep=900,affichage=rempli) ''' - return GiacMethods['funcplot'](self,*args) + return GiacMethods['funcplot'](self, *args) - def function_diff(self,*args): + def function_diff(self, *args): r'''From Giac's documentation: Help for function_diff: function_diff(Fnc(f)) @@ -5795,9 +5795,9 @@ cdef class GiacMethods_base: Ex4:function_diff(ln)([x,y]) Ex5: (function_diff @@3)(ln)('x') ''' - return GiacMethods['function_diff'](self,*args) + return GiacMethods['function_diff'](self, *args) - def fxnd(self,*args): + def fxnd(self, *args): r'''From Giac's documentation: Help for fxnd: fxnd(Frac or RatFrac) @@ -5806,9 +5806,9 @@ cdef class GiacMethods_base: Ex1:fxnd(42/12) Ex2:fxnd((x^2+2*x+1)/(x^2-1)) ''' - return GiacMethods['fxnd'](self,*args) + return GiacMethods['fxnd'](self, *args) - def gammad(self,*args): + def gammad(self, *args): r'''From Giac's documentation: Help for gammad: gammad(Real(a>0),Real(b>0),Real(x>=0)) @@ -5816,9 +5816,9 @@ cdef class GiacMethods_base: See also: 1/ gammad_cdf; 2/ gammad_icdf Ex1:gammad(2.2,1.5,0.8) ''' - return GiacMethods['gammad'](self,*args) + return GiacMethods['gammad'](self, *args) - def gammad_cdf(self,*args): + def gammad_cdf(self, *args): r'''From Giac's documentation: Help for gammad_cdf: gammad_cdf(Real(a>0),Real(b>0),Real(x0>=0),[Real(y0>=0)]) @@ -5827,9 +5827,9 @@ cdef class GiacMethods_base: Ex1:gammad_cdf(2,1,2.96) Ex2:gammad_cdf(2,1,1.4,2.96) ''' - return GiacMethods['gammad_cdf'](self,*args) + return GiacMethods['gammad_cdf'](self, *args) - def gammad_icdf(self,*args): + def gammad_icdf(self, *args): r'''From Giac's documentation: Help for gammad_icdf: gammad_icdf(Real(a>0),Real(b>0),Real(0<=p<=1)) @@ -5838,9 +5838,9 @@ cdef class GiacMethods_base: Ex1:gammad_icdf(2,1,0.95) Ex2:gammad_icdf(2,1,0.5) ''' - return GiacMethods['gammad_icdf'](self,*args) + return GiacMethods['gammad_icdf'](self, *args) - def gammavariate(self,*args): + def gammavariate(self, *args): r'''From Giac's documentation: Help for gammavariate: gammavariate(Real(a),Real(b)) @@ -5849,9 +5849,9 @@ cdef class GiacMethods_base: Ex1:gammavariate(1,2) Ex2:gammavariate(1.5,4) ''' - return GiacMethods['gammavariate'](self,*args) + return GiacMethods['gammavariate'](self, *args) - def gauss(self,*args): + def gauss(self, *args): r'''From Giac's documentation: Help for gauss: gauss(Expr,VectVar) @@ -5859,9 +5859,9 @@ cdef class GiacMethods_base: See also: 1/ cholesky Ex1:gauss(x^2+2*a*x*y,[x,y]) ''' - return GiacMethods['gauss'](self,*args) + return GiacMethods['gauss'](self, *args) - def gauss15(self,*args): + def gauss15(self, *args): r'''From Giac's documentation: Help for gauss15: gauss15(Opt) @@ -5872,9 +5872,9 @@ cdef class GiacMethods_base: Ex3: area(x^2,x=0..1,5,rombergm) Ex4:gauss15(area(x^2,x=0..1,5,gauss15)) ''' - return GiacMethods['gauss15'](self,*args) + return GiacMethods['gauss15'](self, *args) - def gauss_seidel_linsolve(self,*args): + def gauss_seidel_linsolve(self, *args): r'''From Giac's documentation: Help for gauss_seidel_linsolve: gauss_seidel_linsolve([Real(omega)],Mtrx(A),Vect(b),Real(eps),[Int(maxiter)]) @@ -5885,9 +5885,9 @@ cdef class GiacMethods_base: Ex3: a:=[[100,2],[2,100]];gauss_seidel_linsolve(1.5,a,[0,1],1e-12); Ex4: a:=[[100,2],[2,100]];gauss_seidel_linsolve(1.5,table(a),[0,1],1e-12); ''' - return GiacMethods['gauss_seidel_linsolve'](self,*args) + return GiacMethods['gauss_seidel_linsolve'](self, *args) - def gaussian_window(self,*args): + def gaussian_window(self, *args): r'''From Giac's documentation: Help for gaussian_window: gaussian_window(Lst,[Real(a)],[Interval(n1..n2)]) @@ -5895,9 +5895,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ bartlett_hann_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(gaussian_window(randvector(1000,0..1),0.4)) ''' - return GiacMethods['gaussian_window'](self,*args) + return GiacMethods['gaussian_window'](self, *args) - def gaussjord(self,*args): + def gaussjord(self, *args): r'''From Giac's documentation: Help for gaussjord: gaussjord(Mtrx(M),[Intg(k)]||Opt) @@ -5908,9 +5908,9 @@ cdef class GiacMethods_base: Ex3:gaussjord([[2,1,1,-1],[1,1,2,-1],[1,2,1,-4]],2) Ex4:gaussjord([[1,1,0,0,-a1],[0,1,1,0,-a2],[0,0,1,1,-a3],[1,0,0,1,-a4]],keep_pivot) ''' - return GiacMethods['gaussjord'](self,*args) + return GiacMethods['gaussjord'](self, *args) - def gaussquad(self,*args): + def gaussquad(self, *args): r'''From Giac's documentation: Help for gaussquad: gaussquad(Expr(f(x)),Var(x),Real(a),Real(b)) @@ -5920,9 +5920,9 @@ cdef class GiacMethods_base: Ex2:gaussquad(x^2,x,0,1) Ex3:gaussquad(exp(-x^2),x,-1,1) ''' - return GiacMethods['gaussquad'](self,*args) + return GiacMethods['gaussquad'](self, *args) - def gbasis(self,*args): + def gbasis(self, *args): r'''From Giac's documentation: Help for gbasis: gbasis(LstPoly,LstVar,[order]) @@ -5934,9 +5934,9 @@ cdef class GiacMethods_base: Ex4:gbasis([x1+x2+x3,x1*x2+x1*x3+x2*x3,x1*x2*x3-1],[x1,x2,x3],plex) Ex5:gbasis([x1+x2+x3,x1*x2+x1*x3+x2*x3,x1*x2*x3-1] mod 29,[x1,x2,x3]) ''' - return GiacMethods['gbasis'](self,*args) + return GiacMethods['gbasis'](self, *args) - def gbasis_max_pairs(self,*args): + def gbasis_max_pairs(self, *args): r'''From Giac's documentation: Help for gbasis_max_pairs: gbasis_max_pairs(Intg) @@ -5945,9 +5945,9 @@ cdef class GiacMethods_base: Ex1:gbasis_max_pairs(4096) Ex2:gbasis_max_pairs(0) ''' - return GiacMethods['gbasis_max_pairs'](self,*args) + return GiacMethods['gbasis_max_pairs'](self, *args) - def gbasis_reinject(self,*args): + def gbasis_reinject(self, *args): r'''From Giac's documentation: Help for gbasis_reinject: gbasis_reinject(Real(a),[Real(b)]) @@ -5956,9 +5956,9 @@ cdef class GiacMethods_base: Ex1:gbasis_reinject(0.1) Ex2:gbasis_reinject(0.1,0.05) ''' - return GiacMethods['gbasis_reinject'](self,*args) + return GiacMethods['gbasis_reinject'](self, *args) - def gbasis_simult_primes(self,*args): + def gbasis_simult_primes(self, *args): r'''From Giac's documentation: Help for gbasis_simult_primes: gbasis_simult_primes(Intg) @@ -5966,9 +5966,9 @@ cdef class GiacMethods_base: See also: 1/ gbasis 2/ gbasis_max_pairs 3/ gbasis_reinject Ex1:gbasis_simult_primes(3) ''' - return GiacMethods['gbasis_simult_primes'](self,*args) + return GiacMethods['gbasis_simult_primes'](self, *args) - def gcd(self,*args): + def gcd(self, *args): r'''From Giac's documentation: Help for gcd: gcd((Intg(a) or Poly),(Intg(b) or Poly)) @@ -5980,9 +5980,9 @@ cdef class GiacMethods_base: Ex4:gcd(t^2-2*t+1,t^2+t-2) Ex5:gcd((x^2-1)*(y^2-1)*z^2,x^3*y^3*z+(-(y^3))*z+x^3*z-z) ''' - return GiacMethods['gcd'](self,*args) + return GiacMethods['gcd'](self, *args) - def gcdex(self,*args): + def gcdex(self, *args): r'''From Giac's documentation: Help for gcdex: gcdex((Poly or Lst),(Poly or Lst),[Var]) @@ -5993,9 +5993,9 @@ cdef class GiacMethods_base: Ex3:gcdex([1,-2,1],[1,0,0,-1]) Ex4:gcdex([1,-2,1],[1,-1,2]) ''' - return GiacMethods['gcdex'](self,*args) + return GiacMethods['gcdex'](self, *args) - def genpoly(self,*args): + def genpoly(self, *args): r'''From Giac's documentation: Help for genpoly: genpoly(Poly(P),Intg(b),Var) @@ -6005,9 +6005,9 @@ cdef class GiacMethods_base: Ex2:genpoly(7*y+5,6,x) Ex3:genpoly(7*y-5*z,10,x) ''' - return GiacMethods['genpoly'](self,*args) + return GiacMethods['genpoly'](self, *args) - def geometric(self,*args): + def geometric(self, *args): r'''From Giac's documentation: Help for geometric: geometric(Real(p),Intg(k)) @@ -6018,9 +6018,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,geometric,0.3) Ex4: ranm(4,3,geometric,0.3) ''' - return GiacMethods['geometric'](self,*args) + return GiacMethods['geometric'](self, *args) - def geometric_cdf(self,*args): + def geometric_cdf(self, *args): r'''From Giac's documentation: Help for geometric_cdf: geometric_cdf(Real(p),Intg(k),[Intg(m)]) @@ -6029,9 +6029,9 @@ cdef class GiacMethods_base: Ex1:geometric_cdf(0.3,4) Ex2:geometric_cdf(0.3,4,5) ''' - return GiacMethods['geometric_cdf'](self,*args) + return GiacMethods['geometric_cdf'](self, *args) - def geometric_icdf(self,*args): + def geometric_icdf(self, *args): r'''From Giac's documentation: Help for geometric_icdf: geometric_icdf(Real(p),Real(x)) @@ -6039,9 +6039,9 @@ cdef class GiacMethods_base: See also: 1/ geometric_cdf 2/ geometric Ex1:geometric_icdf(0.3,0.95) ''' - return GiacMethods['geometric_icdf'](self,*args) + return GiacMethods['geometric_icdf'](self, *args) - def getDenom(self,*args): + def getDenom(self, *args): r'''From Giac's documentation: Help for getDenom: getDenom(Expr) @@ -6051,9 +6051,9 @@ cdef class GiacMethods_base: Ex2:getDenom((x^3-1)/(x^2-1)) Ex3:getDenom(1+(x^3-1)/x^2) ''' - return GiacMethods['getDenom'](self,*args) + return GiacMethods['getDenom'](self, *args) - def getKey(self,*args): + def getKey(self, *args): r'''From Giac's documentation: Help for getKey: getKey(NULL) @@ -6061,9 +6061,9 @@ cdef class GiacMethods_base: See also: 1/ getType Ex1:getKey() ''' - return GiacMethods['getKey'](self,*args) + return GiacMethods['getKey'](self, *args) - def getNum(self,*args): + def getNum(self, *args): r'''From Giac's documentation: Help for getNum: getNum(Expr) @@ -6073,9 +6073,9 @@ cdef class GiacMethods_base: Ex2:getNum((x^3-1)/(x^2-1)) Ex3:getNum(1+(x^3-1)/x^2) ''' - return GiacMethods['getNum'](self,*args) + return GiacMethods['getNum'](self, *args) - def getType(self,*args): + def getType(self, *args): r'''From Giac's documentation: Help for getType: getType(Expr) @@ -6086,9 +6086,9 @@ cdef class GiacMethods_base: Ex3:getType(x->cos(2*x)) Ex4:getType(1.414) ''' - return GiacMethods['getType'](self,*args) + return GiacMethods['getType'](self, *args) - def get_edge_attribute(self,*args): + def get_edge_attribute(self, *args): r'''From Giac's documentation: Help for get_edge_attribute: get_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) @@ -6096,9 +6096,9 @@ cdef class GiacMethods_base: See also: 1/ discard_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes Ex1:get_edge_attribute(cycle_graph(3),[1,2],"cost") ''' - return GiacMethods['get_edge_attribute'](self,*args) + return GiacMethods['get_edge_attribute'](self, *args) - def get_edge_weight(self,*args): + def get_edge_weight(self, *args): r'''From Giac's documentation: Help for get_edge_weight: get_edge_weight(Graph(G),Edge(e)) @@ -6106,9 +6106,9 @@ cdef class GiacMethods_base: See also: 1/ is_weighted 2/ make_weighted 3/ set_edge_weight 4/ weight_matrix Ex1:get_edge_weight(graph(%{[[1,2],5],[[2,3],6]%}),[1,2]) ''' - return GiacMethods['get_edge_weight'](self,*args) + return GiacMethods['get_edge_weight'](self, *args) - def get_graph_attribute(self,*args): + def get_graph_attribute(self, *args): r'''From Giac's documentation: Help for get_graph_attribute: get_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) @@ -6116,9 +6116,9 @@ cdef class GiacMethods_base: See also: 1/ discard_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes Ex1:get_graph_attribute(cycle_graph(3),"name") ''' - return GiacMethods['get_graph_attribute'](self,*args) + return GiacMethods['get_graph_attribute'](self, *args) - def get_vertex_attribute(self,*args): + def get_vertex_attribute(self, *args): r'''From Giac's documentation: Help for get_vertex_attribute: get_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) @@ -6126,9 +6126,9 @@ cdef class GiacMethods_base: See also: 1/ discard_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes Ex1:get_vertex_attribute(cycle_graph(3),1,"supply") ''' - return GiacMethods['get_vertex_attribute'](self,*args) + return GiacMethods['get_vertex_attribute'](self, *args) - def girth(self,*args): + def girth(self, *args): r'''From Giac's documentation: Help for girth: girth(Graph(G)) @@ -6137,9 +6137,9 @@ cdef class GiacMethods_base: Ex1:girth(graph("petersen")) Ex2:girth(hypercube_graph(3)) ''' - return GiacMethods['girth'](self,*args) + return GiacMethods['girth'](self, *args) - def gl_showaxes(self,*args): + def gl_showaxes(self, *args): r'''From Giac's documentation: Help for gl_showaxes: gl_showaxes(Opt=Boolean) @@ -6148,9 +6148,9 @@ cdef class GiacMethods_base: Ex1: gl_showaxes=true;plot(sin(x)) Ex2: gl_showaxes=false;plot(sin(x)) ''' - return GiacMethods['gl_showaxes'](self,*args) + return GiacMethods['gl_showaxes'](self, *args) - def grad(self,*args): + def grad(self, *args): r'''From Giac's documentation: Help for grad: grad(Expr(Xpr),LstVar) @@ -6158,9 +6158,9 @@ cdef class GiacMethods_base: See also: 1/ hessian Ex1:grad(2*x^2*y-x*z^3,[x,y,z]) ''' - return GiacMethods['grad'](self,*args) + return GiacMethods['grad'](self, *args) - def gramschmidt(self,*args): + def gramschmidt(self, *args): r'''From Giac's documentation: Help for gramschmidt: gramschmidt(Basis(B),ScalarProd(Sp)) @@ -6169,9 +6169,9 @@ cdef class GiacMethods_base: Ex1:gramschmidt(-2) Ex2:gramschmidt([1,1+x],(p,q)->integrate(p*q,x,-1,1)) ''' - return GiacMethods['gramschmidt'](self,*args) + return GiacMethods['gramschmidt'](self, *args) - def graph(self,*args): + def graph(self, *args): r'''From Giac's documentation: Help for graph: graph([Lst(V)],[Set(E)],[Mtrx(A)],[options]) @@ -6185,9 +6185,9 @@ cdef class GiacMethods_base: Ex6:graph("petersen") Ex7:graph([[0,1,1,0],[1,0,0,1],[1,0,0,0],[0,1,0,0]]) ''' - return GiacMethods['graph'](self,*args) + return GiacMethods['graph'](self, *args) - def graph_automorphisms(self,*args): + def graph_automorphisms(self, *args): r'''From Giac's documentation: Help for graph_automorphisms: graph_automorphisms(Graph(G)) @@ -6195,9 +6195,9 @@ cdef class GiacMethods_base: See also: 1/ cycles2permu 2/ isomorphic_copy 3/ permute_vertices Ex1:graph_automorphisms(graph("petersen")) ''' - return GiacMethods['graph_automorphisms'](self,*args) + return GiacMethods['graph_automorphisms'](self, *args) - def graph_charpoly(self,*args): + def graph_charpoly(self, *args): r'''From Giac's documentation: Help for graph_charpoly: graph_charpoly(Graph(G),[Var(x)]) @@ -6206,9 +6206,9 @@ cdef class GiacMethods_base: Ex1:graph_charpoly(graph(%{[1,2],[2,3]%})) Ex2:graph_charpoly(graph("shrikhande")) ''' - return GiacMethods['graph_charpoly'](self,*args) + return GiacMethods['graph_charpoly'](self, *args) - def graph_complement(self,*args): + def graph_complement(self, *args): r'''From Giac's documentation: Help for graph_complement: graph_complement(Graph(G)) @@ -6216,9 +6216,9 @@ cdef class GiacMethods_base: See also: 1/ edges Ex1:graph_complement(cycle_graph(5)) ''' - return GiacMethods['graph_complement'](self,*args) + return GiacMethods['graph_complement'](self, *args) - def graph_diameter(self,*args): + def graph_diameter(self, *args): r'''From Giac's documentation: Help for graph_diameter: graph_diameter(Graph(G)) @@ -6226,9 +6226,9 @@ cdef class GiacMethods_base: See also: 1/ allpairs_distance 2/ dijkstra 3/ shortest_path 4/ vertex_distance Ex1:graph_diameter(graph("petersen")) ''' - return GiacMethods['graph_diameter'](self,*args) + return GiacMethods['graph_diameter'](self, *args) - def graph_equal(self,*args): + def graph_equal(self, *args): r'''From Giac's documentation: Help for graph_equal: graph_equal(Graph(G1),Graph(G2)) @@ -6236,9 +6236,9 @@ cdef class GiacMethods_base: See also: 1/ edges 2/ graph_vertices Ex1:graph_equal(graph([1,2,3],%{[1,2],[2,3],[3,1]%}),graph(trail(1,2,3,1))) ''' - return GiacMethods['graph_equal'](self,*args) + return GiacMethods['graph_equal'](self, *args) - def graph_join(self,*args): + def graph_join(self, *args): r'''From Giac's documentation: Help for graph_join: graph_join(Graph(G),Graph(H)) @@ -6246,9 +6246,9 @@ cdef class GiacMethods_base: See also: 1/ disjoint_union 2/ graph_union Ex1:graph_join(edges(graph_join(cycle_graph(3),graph(2)))) ''' - return GiacMethods['graph_join'](self,*args) + return GiacMethods['graph_join'](self, *args) - def graph_power(self,*args): + def graph_power(self, *args): r'''From Giac's documentation: Help for graph_power: graph_power(Graph(G),Intg(k)) @@ -6256,9 +6256,9 @@ cdef class GiacMethods_base: See also: 1/ adjacency matrix 2/ graph_diameter 3/ shortest_path Ex1:graph_power(edges(graph_power(path_graph(5),3))) ''' - return GiacMethods['graph_power'](self,*args) + return GiacMethods['graph_power'](self, *args) - def graph_rank(self,*args): + def graph_rank(self, *args): r'''From Giac's documentation: Help for graph_rank: graph_rank(Graph(G),[Lst(E)]) @@ -6267,9 +6267,9 @@ cdef class GiacMethods_base: Ex1:graph_rank(graph(%{[1,2],[3,4],[4,5]%})) Ex2:graph_rank(graph(%{[1,2],[3,4],[4,5]%}),[[1,2],[3,4]) ''' - return GiacMethods['graph_rank'](self,*args) + return GiacMethods['graph_rank'](self, *args) - def graph_spectrum(self,*args): + def graph_spectrum(self, *args): r'''From Giac's documentation: Help for graph_spectrum: graph_spectrum(Graph(G)) @@ -6277,9 +6277,9 @@ cdef class GiacMethods_base: See also: 1/ graph_charpoly 2/ seidel_spectrum 3/ is_integer_graph Ex1:graph_spectrum(cycle_graph(5)) ''' - return GiacMethods['graph_spectrum'](self,*args) + return GiacMethods['graph_spectrum'](self, *args) - def graph_union(self,*args): + def graph_union(self, *args): r'''From Giac's documentation: Help for graph_union: graph_union(Seq(G1,G2,...)) @@ -6287,9 +6287,9 @@ cdef class GiacMethods_base: See also: 1/ disjoint_union 2/ graph_join Ex1:graph_union(edges(graph_union(cycle_graph(4),path_graph(5)))) ''' - return GiacMethods['graph_union'](self,*args) + return GiacMethods['graph_union'](self, *args) - def graph_vertices(self,*args): + def graph_vertices(self, *args): r'''From Giac's documentation: Help for graph_vertices: graph_vertices(Graph(G)) @@ -6297,9 +6297,9 @@ cdef class GiacMethods_base: See also: 1/ add_vertex 2/ graph 3/ neighbors 4/ permute_vertices 5/ relabel_vertices Ex1:graph_vertices(graph(%{[a,c],[b,c],[a,b]%})) ''' - return GiacMethods['graph_vertices'](self,*args) + return GiacMethods['graph_vertices'](self, *args) - def greduce(self,*args): + def greduce(self, *args): r'''From Giac's documentation: Help for greduce: greduce(Poly,LstPoly,LstVar,[order]) @@ -6309,9 +6309,9 @@ cdef class GiacMethods_base: Ex2:greduce(x1^2*x3^2,[x3^3-1,-x2^2-x2*x3-x3^2,x1+x2+x3],[x1,x2,x3],tdeg) Ex3:greduce(x1^2*x3^2-x2,[x3^3-1,-x2^2-x2*x3-x3^2,x1+x2+x3],[x1,x2,x3]) ''' - return GiacMethods['greduce'](self,*args) + return GiacMethods['greduce'](self, *args) - def greedy_color(self,*args): + def greedy_color(self, *args): r'''From Giac's documentation: Help for greedy_color: greedy_color(Graph(G),[Permu(p)]) @@ -6319,9 +6319,9 @@ cdef class GiacMethods_base: See also: 1/ is_vertex_colorable 2/ chromatic_number Ex1:greedy_color(graph("petersen")) ''' - return GiacMethods['greedy_color'](self,*args) + return GiacMethods['greedy_color'](self, *args) - def grid_graph(self,*args): + def grid_graph(self, *args): r'''From Giac's documentation: Help for grid_graph: grid_graph(Intg(m),Intg(n),[triangle]) @@ -6329,9 +6329,9 @@ cdef class GiacMethods_base: See also: 1/ torus_grid_graph Ex1:grid_graph(5,8) ''' - return GiacMethods['grid_graph'](self,*args) + return GiacMethods['grid_graph'](self, *args) - def groupermu(self,*args): + def groupermu(self, *args): r'''From Giac's documentation: Help for groupermu: groupermu(Permut(a),Permut(b)) @@ -6339,9 +6339,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:groupermu([1,2,0],[3,1,2,0]) ''' - return GiacMethods['groupermu'](self,*args) + return GiacMethods['groupermu'](self, *args) - def hadamard(self,*args): + def hadamard(self, *args): r'''From Giac's documentation: Help for hadamard: hadamard(Mtrx,Mtrx) @@ -6350,9 +6350,9 @@ cdef class GiacMethods_base: Ex1:hadamard([[1,2],[3,4]]) Ex2:hadamard([[1,2],[3,4]],[[3,4],[5,6]]) ''' - return GiacMethods['hadamard'](self,*args) + return GiacMethods['hadamard'](self, *args) - def half_cone(self,*args): + def half_cone(self, *args): r'''From Giac's documentation: Help for half_cone: half_cone(Pnt(A),Vect(v),Real(t),[Real(h)]) @@ -6361,9 +6361,9 @@ cdef class GiacMethods_base: Ex1:half_cone([0,0,0],[0,0,1],pi/6) Ex2:half_cone([0,0,0],[0,1,1],pi/6,-4) ''' - return GiacMethods['half_cone'](self,*args) + return GiacMethods['half_cone'](self, *args) - def half_line(self,*args): + def half_line(self, *args): r'''From Giac's documentation: Help for half_line: half_line((Pnt or Cplx),(Pnt or Cplx)) @@ -6372,9 +6372,9 @@ cdef class GiacMethods_base: Ex1:half_line(i,1+i) Ex2:half_line(point(i),point(1+i)) ''' - return GiacMethods['half_line'](self,*args) + return GiacMethods['half_line'](self, *args) - def halftan(self,*args): + def halftan(self, *args): r'''From Giac's documentation: Help for halftan: halftan(Expr) @@ -6383,9 +6383,9 @@ cdef class GiacMethods_base: Ex2:halftan(cos(x)) Ex3:halftan(tan(x)) ''' - return GiacMethods['halftan'](self,*args) + return GiacMethods['halftan'](self, *args) - def halftan_hyp2exp(self,*args): + def halftan_hyp2exp(self, *args): r'''From Giac's documentation: Help for halftan_hyp2exp: halftan_hyp2exp(ExprTrig) @@ -6393,9 +6393,9 @@ cdef class GiacMethods_base: See also: 1/ hyp2exp 2/ halftan Ex1:halftan_hyp2exp(sin(x)+sinh(x)) ''' - return GiacMethods['halftan_hyp2exp'](self,*args) + return GiacMethods['halftan_hyp2exp'](self, *args) - def halt(self,*args): + def halt(self, *args): r'''From Giac's documentation: Help for halt: halt(NULL) @@ -6403,18 +6403,18 @@ cdef class GiacMethods_base: See also: 1/ Ex1:halt() ''' - return GiacMethods['halt'](self,*args) + return GiacMethods['halt'](self, *args) - def hamdist(self,*args): + def hamdist(self, *args): r'''From Giac's documentation: Help for hamdist: hamdist(Intg,Intg) Bitwise Hamming distance. Ex1:hamdist(0x12,0x38) ''' - return GiacMethods['hamdist'](self,*args) + return GiacMethods['hamdist'](self, *args) - def hamming_window(self,*args): + def hamming_window(self, *args): r'''From Giac's documentation: Help for hamming_window: hamming_window(Lst,[Interval(n1..n2)]) @@ -6422,9 +6422,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ bartlett_hann_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hamming_window(randvector(1000,0..1))) ''' - return GiacMethods['hamming_window'](self,*args) + return GiacMethods['hamming_window'](self, *args) - def hann_poisson_window(self,*args): + def hann_poisson_window(self, *args): r'''From Giac's documentation: Help for hann_poisson_window: hann_poisson_window(Lst,[Interval(n1..n2)]) @@ -6432,9 +6432,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ bartlett_hann_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hann_poisson_window(randvector(1000,0..1),2)) ''' - return GiacMethods['hann_poisson_window'](self,*args) + return GiacMethods['hann_poisson_window'](self, *args) - def hann_window(self,*args): + def hann_window(self, *args): r'''From Giac's documentation: Help for hann_window: hann_window(Lst,[Interval(n1..n2)]) @@ -6442,9 +6442,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ bartlett_hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hann_window(randvector(1000,0..1))) ''' - return GiacMethods['hann_window'](self,*args) + return GiacMethods['hann_window'](self, *args) - def harmonic_conjugate(self,*args): + def harmonic_conjugate(self, *args): r'''From Giac's documentation: Help for harmonic_conjugate: harmonic_conjugate(Line or Pnt(A),Line or Pnt(B),Line or Pnt(C)) @@ -6455,9 +6455,9 @@ cdef class GiacMethods_base: Ex3:harmonic_conjugate(line(0,1+i),line(0,3+i),line(0,i)) Ex4:harmonic_conjugate(line(0,1+i),line(0,3+i),point(3/2+i)) ''' - return GiacMethods['harmonic_conjugate'](self,*args) + return GiacMethods['harmonic_conjugate'](self, *args) - def harmonic_division(self,*args): + def harmonic_division(self, *args): r'''From Giac's documentation: Help for harmonic_division: harmonic_division(Pnt or Line,Pnt or Line,Pnt or Line,Var) @@ -6468,9 +6468,9 @@ cdef class GiacMethods_base: Ex3:harmonic_division(line(i,0),line(i,1+i),line(i,3+2*i),D) Ex4:harmonic_division(line(0,1+i),line(0,3+i),line(0,i),D) ''' - return GiacMethods['harmonic_division'](self,*args) + return GiacMethods['harmonic_division'](self, *args) - def has(self,*args): + def has(self, *args): r'''From Giac's documentation: Help for has: has(Expr,Var) @@ -6479,9 +6479,9 @@ cdef class GiacMethods_base: Ex1:has(x+y,x) Ex2:has(x+y,n) ''' - return GiacMethods['has'](self,*args) + return GiacMethods['has'](self, *args) - def has_arc(self,*args): + def has_arc(self, *args): r'''From Giac's documentation: Help for has_arc: has_arc(Graph(G),Edge(e)) @@ -6490,9 +6490,9 @@ cdef class GiacMethods_base: Ex1:has_arc(digraph(trail(1,2,3,4,1)),[4,2]) Ex2:has_arc(digraph(trail(1,2,3,4,1)),%{4,2%}) ''' - return GiacMethods['has_arc'](self,*args) + return GiacMethods['has_arc'](self, *args) - def has_edge(self,*args): + def has_edge(self, *args): r'''From Giac's documentation: Help for has_edge: has_edge(Graph(G),Edge(e)) @@ -6500,9 +6500,9 @@ cdef class GiacMethods_base: See also: 1/ edges 2/ has_arc Ex1:has_edge(graph(trail(1,2,3,4,1)),[2,4]) ''' - return GiacMethods['has_edge'](self,*args) + return GiacMethods['has_edge'](self, *args) - def hasard(self,*args): + def hasard(self, *args): r'''From Giac's documentation: Help for hasard: hasard(Intg(n) or Interval(p..n) or NULL,[Intg(b1) or Lst(L)],[Intg(b2)]) @@ -6516,9 +6516,9 @@ cdef class GiacMethods_base: Ex6:hasard(3,1,10) Ex7:hasard(3,["r","r","r","b","n"]) ''' - return GiacMethods['hasard'](self,*args) + return GiacMethods['hasard'](self, *args) - def head(self,*args): + def head(self, *args): r'''From Giac's documentation: Help for head: head(Vect or Seq or Str) @@ -6528,9 +6528,9 @@ cdef class GiacMethods_base: Ex2:head([1,2,3]) Ex3:head("bonjour") ''' - return GiacMethods['head'](self,*args) + return GiacMethods['head'](self, *args) - def heading(self,*args): + def heading(self, *args): r'''From Giac's documentation: Help for heading: heading(NULL or Real) @@ -6540,36 +6540,36 @@ cdef class GiacMethods_base: Ex2:heading() Ex3:heading(cap 90) ''' - return GiacMethods['heading'](self,*args) + return GiacMethods['heading'](self, *args) - def heapify(self,*args): + def heapify(self, *args): r'''From Giac's documentation: Help for heapify: heapify(List) Partial ordering of a list as a heap. See also: 1/ heappush 2/ heappop ''' - return GiacMethods['heapify'](self,*args) + return GiacMethods['heapify'](self, *args) - def heappop(self,*args): + def heappop(self, *args): r'''From Giac's documentation: Help for heappop: heappop(List) Removes and returns the root node of a heap. See also: 1/ heapify 2/ heappush ''' - return GiacMethods['heappop'](self,*args) + return GiacMethods['heappop'](self, *args) - def heappush(self,*args): + def heappush(self, *args): r'''From Giac's documentation: Help for heappush: heappush(List,Object) Adds an object in a heap. See also: 1/ heapify 2/ heappop ''' - return GiacMethods['heappush'](self,*args) + return GiacMethods['heappush'](self, *args) - def hermite(self,*args): + def hermite(self, *args): r'''From Giac's documentation: Help for hermite: hermite(Intg(n)||Matr(A)) @@ -6578,9 +6578,9 @@ cdef class GiacMethods_base: Ex1:hermite(3) Ex2: n:=5; a:=ranm(n,n) % 17; l,u:=hermite(x-a);normal(l*(x-a)-u); ''' - return GiacMethods['hermite'](self,*args) + return GiacMethods['hermite'](self, *args) - def hessenberg(self,*args): + def hessenberg(self, *args): r'''From Giac's documentation: Help for hessenberg: hessenberg(Mtrx(A),[Intg(n)]) @@ -6592,9 +6592,9 @@ cdef class GiacMethods_base: Ex4:hessenberg([[1,2,3],[4,5,6],[7,8,1]],-2) Ex5:hessenberg([[1,2,3],[4,5,6],[7,8,1]],3) ''' - return GiacMethods['hessenberg'](self,*args) + return GiacMethods['hessenberg'](self, *args) - def hessian(self,*args): + def hessian(self, *args): r'''From Giac's documentation: Help for hessian: hessian(Expr(Xpr),LstVar) @@ -6602,9 +6602,9 @@ cdef class GiacMethods_base: See also: 1/ grad Ex1:hessian(2*x^2*y-x*z,[x,y,z]) ''' - return GiacMethods['hessian'](self,*args) + return GiacMethods['hessian'](self, *args) - def heugcd(self,*args): + def heugcd(self, *args): r'''From Giac's documentation: Help for heugcd: heugcd(Poly,Poly) @@ -6612,9 +6612,9 @@ cdef class GiacMethods_base: See also: 1/ gcd 2/ modgcd 3/ ezgcd 4/ psrgcd Ex1:heugcd(x^4-1,(x-1)^2) ''' - return GiacMethods['heugcd'](self,*args) + return GiacMethods['heugcd'](self, *args) - def hexagon(self,*args): + def hexagon(self, *args): r'''From Giac's documentation: Help for hexagon: hexagon(Pnt(A)||Cplx,Pnt(B)||Cplx,[Pnt(P)],[Var(C)],[Var(D)],[Var(E)],[Var(F)]) @@ -6625,9 +6625,9 @@ cdef class GiacMethods_base: Ex3:hexagon(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:hexagon(point(0,0,0),point(3,3,3),point(0,0,3),C,D,E,F) ''' - return GiacMethods['hexagon'](self,*args) + return GiacMethods['hexagon'](self, *args) - def highlight_edges(self,*args): + def highlight_edges(self, *args): r'''From Giac's documentation: Help for highlight_edges: highlight_edges(Graph(G),Edge(e)||Lst(E),[Color(c)||Lst(C)]) @@ -6635,9 +6635,9 @@ cdef class GiacMethods_base: See also: 1/ highlight_vertex 2/ highlight_subgraph 3/ highlight_trail Ex1: draw_graph(highlight_edges(cycle_graph(3),[1,2])) ''' - return GiacMethods['highlight_edges'](self,*args) + return GiacMethods['highlight_edges'](self, *args) - def highlight_subgraph(self,*args): + def highlight_subgraph(self, *args): r'''From Giac's documentation: Help for highlight_subgraph: highlight_subgraph(Graph(G),Graph(S)||Lst(S1,S2,..),Seq(c1,c2)) @@ -6645,9 +6645,9 @@ cdef class GiacMethods_base: See also: 1/ highlight_edges 2/ highlight_vertex 3/ highlight_trail Ex1: draw_graph(highlight_subgraph(cycle_graph(5),path_graph(3))) ''' - return GiacMethods['highlight_subgraph'](self,*args) + return GiacMethods['highlight_subgraph'](self, *args) - def highlight_trail(self,*args): + def highlight_trail(self, *args): r'''From Giac's documentation: Help for highlight_trail: highlight_trail(Graph(G),Trail(t)||Lst(T),[Color(c)||Lst(C)]) @@ -6655,9 +6655,9 @@ cdef class GiacMethods_base: See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_vertex Ex1: draw_graph(highlight_trail(cycle_graph(5),trail(1,2,3),green) ''' - return GiacMethods['highlight_trail'](self,*args) + return GiacMethods['highlight_trail'](self, *args) - def highlight_vertex(self,*args): + def highlight_vertex(self, *args): r'''From Giac's documentation: Help for highlight_vertex: highlight_vertex(Graph(G),Vrtx(v)||Lst(V),[Color(c)||Lst(C)]) @@ -6665,9 +6665,9 @@ cdef class GiacMethods_base: See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_trail Ex1: draw_graph(highlight_vertex(cycle_graph(3),1)) ''' - return GiacMethods['highlight_vertex'](self,*args) + return GiacMethods['highlight_vertex'](self, *args) - def highpass(self,*args): + def highpass(self, *args): r'''From Giac's documentation: Help for highpass: highpass(Lst(s),Real(c),[Intg(samplerate)]) @@ -6675,9 +6675,9 @@ cdef class GiacMethods_base: See also: 1/ lowpass 2/ moving_average Ex1: f:=unapply(periodic(sign(x),x,-1/880,1/880),x):;s:=createwav(apply(f,soundsec(1))):;playsnd(highpass(s,5000)) ''' - return GiacMethods['highpass'](self,*args) + return GiacMethods['highpass'](self, *args) - def hilbert(self,*args): + def hilbert(self, *args): r'''From Giac's documentation: Help for hilbert: hilbert(Intg(n)) @@ -6685,9 +6685,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:hilbert(4) ''' - return GiacMethods['hilbert'](self,*args) + return GiacMethods['hilbert'](self, *args) - def histogram(self,*args): + def histogram(self, *args): r'''From Giac's documentation: Help for histogram: histogram(Lst(data),[Lst(eff) || Intg(nc) || Real(classmin)],[Real(classsize)]) @@ -6702,9 +6702,9 @@ cdef class GiacMethods_base: Ex7:histogram(seq(rand(1000),k,0,100),0,100) Ex8:histogram(seq(rand(1000),k,0,100),10) ''' - return GiacMethods['histogram'](self,*args) + return GiacMethods['histogram'](self, *args) - def hold(self,*args): + def hold(self, *args): r'''From Giac's documentation: Help for hold: hold(Expr) @@ -6714,9 +6714,9 @@ cdef class GiacMethods_base: Ex2:hold(1/x+1/(x-1)) Ex3:hold((x+1)*(x-1)) ''' - return GiacMethods['hold'](self,*args) + return GiacMethods['hold'](self, *args) - def homogeneize(self,*args): + def homogeneize(self, *args): r'''From Giac's documentation: Help for homogeneize: homogeneize(Expr(P),[Var(t)]) @@ -6724,9 +6724,9 @@ cdef class GiacMethods_base: Ex1:homogeneize(x^2-1) Ex2:homogeneize(x^2-y,z) ''' - return GiacMethods['homogeneize'](self,*args) + return GiacMethods['homogeneize'](self, *args) - def homothety(self,*args): + def homothety(self, *args): r'''From Giac's documentation: Help for homothety: homothety(Pnt(C),Real(k),Pnt(A)) @@ -6737,9 +6737,9 @@ cdef class GiacMethods_base: Ex3: h:=homothety(1+i,1/3);h(i) Ex4: h:=homothety(point(1,1,1),1/3);h(point(0,1,0)) ''' - return GiacMethods['homothety'](self,*args) + return GiacMethods['homothety'](self, *args) - def horner(self,*args): + def horner(self, *args): r'''From Giac's documentation: Help for horner: horner(Poly(P),Real(a)) @@ -6750,9 +6750,9 @@ cdef class GiacMethods_base: Ex3:horner(x^2+y*x+y^3-1,2,y) Ex4: X:=[0.0,1.0,2.0]; A:=lagrange(X,exp,lagrange); horner(A,X,1.5); ''' - return GiacMethods['horner'](self,*args) + return GiacMethods['horner'](self, *args) - def hybrid_solver(self,*args): + def hybrid_solver(self, *args): r'''From Giac's documentation: Help for hybrid_solver: hybrid_solver(Opt) @@ -6765,9 +6765,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['hybrid_solver'](self,*args) + return GiacMethods['hybrid_solver'](self, *args) - def hybridj_solver(self,*args): + def hybridj_solver(self, *args): r'''From Giac's documentation: Help for hybridj_solver: hybridj_solver(Opt) @@ -6780,9 +6780,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['hybridj_solver'](self,*args) + return GiacMethods['hybridj_solver'](self, *args) - def hybrids_solver(self,*args): + def hybrids_solver(self, *args): r'''From Giac's documentation: Help for hybrids_solver: hybrids_solver(Opt) @@ -6795,9 +6795,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['hybrids_solver'](self,*args) + return GiacMethods['hybrids_solver'](self, *args) - def hybridsj_solver(self,*args): + def hybridsj_solver(self, *args): r'''From Giac's documentation: Help for hybridsj_solver: hybridsj_solver(Opt) @@ -6810,9 +6810,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['hybridsj_solver'](self,*args) + return GiacMethods['hybridsj_solver'](self, *args) - def hyp2exp(self,*args): + def hyp2exp(self, *args): r'''From Giac's documentation: Help for hyp2exp: hyp2exp(ExprHyperb) @@ -6820,9 +6820,9 @@ cdef class GiacMethods_base: See also: 1/ halftan_hyp2exp Ex1:hyp2exp(cosh(x)) ''' - return GiacMethods['hyp2exp'](self,*args) + return GiacMethods['hyp2exp'](self, *args) - def hyperbola(self,*args): + def hyperbola(self, *args): r'''From Giac's documentation: Help for hyperbola: hyperbola(Focus(F1),Focus(F2),(Pnt(M) or Real(a))) @@ -6833,9 +6833,9 @@ cdef class GiacMethods_base: Ex3:hyperbola(point(-1,0,0),point(1,0,0),point(1,1,1)) Ex4:hyperbola(x^2-y^2+y+2) ''' - return GiacMethods['hyperbola'](self,*args) + return GiacMethods['hyperbola'](self, *args) - def hypercube_graph(self,*args): + def hypercube_graph(self, *args): r'''From Giac's documentation: Help for hypercube_graph: hypercube_graph(Intg(n)) @@ -6843,9 +6843,9 @@ cdef class GiacMethods_base: See also: 1/ graph Ex1:hypercube_graph(3) ''' - return GiacMethods['hypercube_graph'](self,*args) + return GiacMethods['hypercube_graph'](self, *args) - def iPart(self,*args): + def iPart(self, *args): r'''From Giac's documentation: Help for iPart: iPart(Real||LstReal) @@ -6855,9 +6855,9 @@ cdef class GiacMethods_base: Ex2:iPart(sqrt(2)) Ex3:iPart(4.3,sqrt(2)) ''' - return GiacMethods['iPart'](self,*args) + return GiacMethods['iPart'](self, *args) - def iabcuv(self,*args): + def iabcuv(self, *args): r'''From Giac's documentation: Help for iabcuv: iabcuv(Intg(a),Intg(b),Intg(c)) @@ -6867,9 +6867,9 @@ cdef class GiacMethods_base: Ex2:iabcuv(21,28,14) Ex3:iabcuv(21,28,1) ''' - return GiacMethods['iabcuv'](self,*args) + return GiacMethods['iabcuv'](self, *args) - def ibasis(self,*args): + def ibasis(self, *args): r'''From Giac's documentation: Help for ibasis: ibasis(Lst(Vect,..,Vect),Lst(Vect,..,Vect)) @@ -6877,9 +6877,9 @@ cdef class GiacMethods_base: See also: 1/ basis Ex1:ibasis([[1,0,0],[0,1,0]],[[1,1,1],[0,0,1]]) ''' - return GiacMethods['ibasis'](self,*args) + return GiacMethods['ibasis'](self, *args) - def ibpdv(self,*args): + def ibpdv(self, *args): r'''From Giac's documentation: Help for ibpdv: ibpdv(Expr(f(x)),Expr(v(x)),[Var(x)],[Real(a)],[Real(b)]) @@ -6891,9 +6891,9 @@ cdef class GiacMethods_base: Ex4:ibpdv([x*ln(x),-1],0) Ex5:ibpdv(ibpdv(ln(x),x,x,2,3),0,x,2,3) ''' - return GiacMethods['ibpdv'](self,*args) + return GiacMethods['ibpdv'](self, *args) - def ibpu(self,*args): + def ibpu(self, *args): r'''From Giac's documentation: Help for ibpu: ibpu(Expr(f(x)),Expr(u(x)),[Var(x)],[Real(a)],[Real(b)]) @@ -6905,9 +6905,9 @@ cdef class GiacMethods_base: Ex4:ibpu([x*ln(x),-1],0) Ex5:ibpu(ibpu(ln(x),ln(x),x,2,3),0,x,2,3) ''' - return GiacMethods['ibpu'](self,*args) + return GiacMethods['ibpu'](self, *args) - def icdf(self,*args): + def icdf(self, *args): r'''From Giac's documentation: Help for icdf: icdf(Func,FuncParams) @@ -6916,9 +6916,9 @@ cdef class GiacMethods_base: Ex1:icdf(binomial,10,0.5,0.6) Ex2:icdf(normald,0.0,1.0,0.975) ''' - return GiacMethods['icdf'](self,*args) + return GiacMethods['icdf'](self, *args) - def ichinrem(self,*args): + def ichinrem(self, *args): r'''From Giac's documentation: Help for ichinrem: ichinrem(LstIntg(a,p),LstIntg(b,q)) @@ -6929,9 +6929,9 @@ cdef class GiacMethods_base: Ex3:ichinrem([2%7,3%5,1%9]) Ex4:ichinrem([(x+1)%2,(x+2)%3,(3*x-1)%5]) ''' - return GiacMethods['ichinrem'](self,*args) + return GiacMethods['ichinrem'](self, *args) - def ichrem(self,*args): + def ichrem(self, *args): r'''From Giac's documentation: Help for ichrem: ichrem(LstIntg(a,p),LstIntg(b,q)) @@ -6942,9 +6942,9 @@ cdef class GiacMethods_base: Ex3:ichrem([2%7,3%5,1%9]) Ex4:ichrem([(x+1)%2,(x+2)%3,(3*x-1)%5]) ''' - return GiacMethods['ichrem'](self,*args) + return GiacMethods['ichrem'](self, *args) - def icomp(self,*args): + def icomp(self, *args): r'''From Giac's documentation: Help for icomp: icomp(Intg(n),Intg(k),[zeros=true||false]) @@ -6953,9 +6953,9 @@ cdef class GiacMethods_base: Ex1:icomp(4,2) Ex2:icomp(6,3,zeros=false) ''' - return GiacMethods['icomp'](self,*args) + return GiacMethods['icomp'](self, *args) - def icontent(self,*args): + def icontent(self, *args): r'''From Giac's documentation: Help for icontent: icontent(Poly,[Var]) @@ -6964,9 +6964,9 @@ cdef class GiacMethods_base: Ex1:icontent(24x^3+6x^2-12x+18) Ex2:icontent(24t^3+6t^2-12t+18,t) ''' - return GiacMethods['icontent'](self,*args) + return GiacMethods['icontent'](self, *args) - def icosahedron(self,*args): + def icosahedron(self, *args): r'''From Giac's documentation: Help for icosahedron: icosahedron(Pnt(A),Pnt(B),Pnt(C)) @@ -6975,9 +6975,9 @@ cdef class GiacMethods_base: Ex1:icosahedron([0,0,0],[sqrt(5),0,0],[1,2,0]) Ex2:icosahedron(evalf([0,0,0],[3,2,4],[1,1,0])) ''' - return GiacMethods['icosahedron'](self,*args) + return GiacMethods['icosahedron'](self, *args) - def id(self,*args): + def id(self, *args): r'''From Giac's documentation: Help for id: id(Seq) @@ -6985,9 +6985,9 @@ cdef class GiacMethods_base: See also: 1/ sq 2/ sqrt Ex1:id(1,2,3) ''' - return GiacMethods['id'](self,*args) + return GiacMethods['id'](self, *args) - def identity(self,*args): + def identity(self, *args): r'''From Giac's documentation: Help for identity: identity(Intg(n)) @@ -6996,9 +6996,9 @@ cdef class GiacMethods_base: Ex1:identity(3) Ex2:identity(5) ''' - return GiacMethods['identity'](self,*args) + return GiacMethods['identity'](self, *args) - def idivis(self,*args): + def idivis(self, *args): r'''From Giac's documentation: Help for idivis: idivis(Intg(a) or LstIntg) @@ -7007,9 +7007,9 @@ cdef class GiacMethods_base: Ex1:idivis(36) Ex2:idivis([36,49]) ''' - return GiacMethods['idivis'](self,*args) + return GiacMethods['idivis'](self, *args) - def idn(self,*args): + def idn(self, *args): r'''From Giac's documentation: Help for idn: idn(Intg(n)) @@ -7018,9 +7018,9 @@ cdef class GiacMethods_base: Ex1:idn(3) Ex2:idn(5) ''' - return GiacMethods['idn'](self,*args) + return GiacMethods['idn'](self, *args) - def iegcd(self,*args): + def iegcd(self, *args): r'''From Giac's documentation: Help for iegcd: iegcd(Intg,Intg) @@ -7030,9 +7030,9 @@ cdef class GiacMethods_base: Ex2:iegcd(21,28) Ex3:iegcd(30,49) ''' - return GiacMethods['iegcd'](self,*args) + return GiacMethods['iegcd'](self, *args) - def ifactor(self,*args): + def ifactor(self, *args): r'''From Giac's documentation: Help for ifactor: ifactor(Intg(a)) @@ -7041,9 +7041,9 @@ cdef class GiacMethods_base: Ex1:ifactor(50) Ex2:ifactor(123456789) ''' - return GiacMethods['ifactor'](self,*args) + return GiacMethods['ifactor'](self, *args) - def ifactors(self,*args): + def ifactors(self, *args): r'''From Giac's documentation: Help for ifactors: ifactors(Intg(a) or LstIntg) @@ -7052,9 +7052,9 @@ cdef class GiacMethods_base: Ex1:ifactors(36) Ex2:ifactors([36,52]) ''' - return GiacMethods['ifactors'](self,*args) + return GiacMethods['ifactors'](self, *args) - def ifourier(self,*args): + def ifourier(self, *args): r'''From Giac's documentation: Help for ifourier: ifourier(Expr(F(s)),[Var(s),[Var(x)]]) @@ -7068,9 +7068,9 @@ cdef class GiacMethods_base: Ex6:ifourier(fourier(exp(-abs(x)),x,s)^2,s,x) Ex7:ifourier(sinc(s),s,x) ''' - return GiacMethods['ifourier'](self,*args) + return GiacMethods['ifourier'](self, *args) - def igamma(self,*args): + def igamma(self, *args): r'''From Giac's documentation: Help for igamma: igamma(Real(a),Real(x),[1]) @@ -7080,9 +7080,9 @@ cdef class GiacMethods_base: Ex2:igamma(-5.1,2.1) Ex3:igamma(5.0,2.0,1) ''' - return GiacMethods['igamma'](self,*args) + return GiacMethods['igamma'](self, *args) - def igcd(self,*args): + def igcd(self, *args): r'''From Giac's documentation: Help for igcd: igcd((Intg(a) or Poly),(Intg(b) or Poly)) @@ -7094,9 +7094,9 @@ cdef class GiacMethods_base: Ex4:igcd(t^2-2*t+1,t^2+t-2) Ex5:igcd((x^2-1)*(y^2-1)*z^2,x^3*y^3*z+(-(y^3))*z+x^3*z-z) ''' - return GiacMethods['igcd'](self,*args) + return GiacMethods['igcd'](self, *args) - def igcdex(self,*args): + def igcdex(self, *args): r'''From Giac's documentation: Help for igcdex: igcdex(Intg,Intg) @@ -7106,9 +7106,9 @@ cdef class GiacMethods_base: Ex2:igcdex(21,28) Ex3:igcdex(30,49) ''' - return GiacMethods['igcdex'](self,*args) + return GiacMethods['igcdex'](self, *args) - def ihermite(self,*args): + def ihermite(self, *args): r'''From Giac's documentation: Help for ihermite: ihermite(Mtrx(A)) @@ -7117,9 +7117,9 @@ cdef class GiacMethods_base: Ex1:ihermite([[9,-36,30], [-36,192,-180], [30,-180,180]]) Ex2:ihermite([[1,2,3],[4,5,6],[7,8,9]]) ''' - return GiacMethods['ihermite'](self,*args) + return GiacMethods['ihermite'](self, *args) - def ilaplace(self,*args): + def ilaplace(self, *args): r'''From Giac's documentation: Help for ilaplace: ilaplace(Expr,[Var],[IlapVar]) @@ -7129,9 +7129,9 @@ cdef class GiacMethods_base: Ex2:ilaplace(s/(s^4-1),s,x) Ex3:ilaplace(exp(-s)/s,s,x) ''' - return GiacMethods['ilaplace'](self,*args) + return GiacMethods['ilaplace'](self, *args) - def im(self,*args): + def im(self, *args): r'''From Giac's documentation: Help for im: im(Cplx) @@ -7141,9 +7141,9 @@ cdef class GiacMethods_base: Ex2:im((1+2*i)^2) Ex3:im([1+2*i,(1+2*i)^2]) ''' - return GiacMethods['im'](self,*args) + return GiacMethods['im'](self, *args) - def imag(self,*args): + def imag(self, *args): r'''From Giac's documentation: Help for imag: imag(Cplx) @@ -7153,9 +7153,9 @@ cdef class GiacMethods_base: Ex2:imag((1+2*i)^2) Ex3:imag([1+2*i,(1+2*i)^2]) ''' - return GiacMethods['imag'](self,*args) + return GiacMethods['imag'](self, *args) - def image(self,*args): + def image(self, *args): r'''From Giac's documentation: Help for image: image(Mtrx(M)) @@ -7164,9 +7164,9 @@ cdef class GiacMethods_base: Ex1:image([[1,2],[3,6]]) Ex2:image([[1,2,3],[1,3,6],[2,5,9]]) ''' - return GiacMethods['image'](self,*args) + return GiacMethods['image'](self, *args) - def implicitdiff(self,*args): + def implicitdiff(self, *args): r'''From Giac's documentation: Help for implicitdiff: implicitdiff(constr,[depvars],y,diffvars) @@ -7191,9 +7191,9 @@ cdef class GiacMethods_base: Ex17:implicitdiff(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,z,y],order=2,[1,-1,0]) Ex18: pd:=implicitdiff(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,z,y],order=4,[0,z,0]);pd[4,0,0] ''' - return GiacMethods['implicitdiff'](self,*args) + return GiacMethods['implicitdiff'](self, *args) - def implicitplot(self,*args): + def implicitplot(self, *args): r'''From Giac's documentation: Help for implicitplot: implicitplot(Expr,Var1,Var2) @@ -7209,18 +7209,18 @@ cdef class GiacMethods_base: Ex8:implicitplot((x+5)^2+(y+4)^2-1,x=-6..-4,y=-5..-3) Ex9:implicitplot((x+5)^2+(y+4)^2-1,[x=-6..-4,y=-5..-3]) ''' - return GiacMethods['implicitplot'](self,*args) + return GiacMethods['implicitplot'](self, *args) - def import_graph(self,*args): + def import_graph(self, *args): r'''From Giac's documentation: Help for import_graph: import_graph(Str("path/to/graphname[.dot]")) Returns the graph constructed from instructions in the file 'path/to/graphname.dot' (in dot format), or "undef" on failure. Ex1:import_graph("K5.dot") ''' - return GiacMethods['import_graph'](self,*args) + return GiacMethods['import_graph'](self, *args) - def inString(self,*args): + def inString(self, *args): r'''From Giac's documentation: Help for inString: inString(Str(l),Elem(e)) @@ -7229,9 +7229,9 @@ cdef class GiacMethods_base: Ex1:inString("abcd","b") Ex2:inString("abcd","e") ''' - return GiacMethods['inString'](self,*args) + return GiacMethods['inString'](self, *args) - def in_ideal(self,*args): + def in_ideal(self, *args): r'''From Giac's documentation: Help for in_ideal: in_ideal(Poly,Lst,LstVar,[order]) @@ -7240,9 +7240,9 @@ cdef class GiacMethods_base: Ex1:in_ideal((x+y)^2,[y^2,x^2+2*x*y],[x,y]) Ex2:in_ideal(x+y,[y^2,x^2+2*x*y],[x,y]) ''' - return GiacMethods['in_ideal'](self,*args) + return GiacMethods['in_ideal'](self, *args) - def incidence_matrix(self,*args): + def incidence_matrix(self, *args): r'''From Giac's documentation: Help for incidence_matrix: incidence_matrix(Graph(G)) @@ -7250,9 +7250,9 @@ cdef class GiacMethods_base: See also: 1/ incident_edges Ex1:incidence_matrix(graph("tetrahedron")) ''' - return GiacMethods['incidence_matrix'](self,*args) + return GiacMethods['incidence_matrix'](self, *args) - def incident_edges(self,*args): + def incident_edges(self, *args): r'''From Giac's documentation: Help for incident_edges: incident_edges(Graph(G),Vrtx(v)) @@ -7260,9 +7260,9 @@ cdef class GiacMethods_base: See also: 1/ adjacency_matrix 2/ vertex_degree 3/ incidence_matrix 4/ neighbors Ex1:incident_edges(cycle_graph(8),[1,5,7]) ''' - return GiacMethods['incident_edges'](self,*args) + return GiacMethods['incident_edges'](self, *args) - def incircle(self,*args): + def incircle(self, *args): r'''From Giac's documentation: Help for incircle: incircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -7270,9 +7270,9 @@ cdef class GiacMethods_base: See also: 1/ excircle 2/ circumcircle Ex1:incircle(0,1,1+i) ''' - return GiacMethods['incircle'](self,*args) + return GiacMethods['incircle'](self, *args) - def increasing_power(self,*args): + def increasing_power(self, *args): r'''From Giac's documentation: Help for increasing_power: increasing_power(:=Intg(0 or 1)) @@ -7281,9 +7281,9 @@ cdef class GiacMethods_base: Ex1: increasing_power:=1 Ex2: increasing_power:=0 ''' - return GiacMethods['increasing_power'](self,*args) + return GiacMethods['increasing_power'](self, *args) - def independence_number(self,*args): + def independence_number(self, *args): r'''From Giac's documentation: Help for independence_number: independence_number(Graph(G)) @@ -7291,9 +7291,9 @@ cdef class GiacMethods_base: See also: 1/ clique_number 2/ graph_complement 3/ maximum_clique 4/ maximum_independent_set Ex1:independence_number(complete_graph(3,4)) ''' - return GiacMethods['independence_number'](self,*args) + return GiacMethods['independence_number'](self, *args) - def indets(self,*args): + def indets(self, *args): r'''From Giac's documentation: Help for indets: indets(Expr) @@ -7301,9 +7301,9 @@ cdef class GiacMethods_base: See also: 1/ has 2/ lvar Ex1:indets(exp(x)*2*sin(y)) ''' - return GiacMethods['indets'](self,*args) + return GiacMethods['indets'](self, *args) - def index(self,*args): + def index(self, *args): r'''From Giac's documentation: Help for index: index(Vect,Expr) @@ -7314,9 +7314,9 @@ cdef class GiacMethods_base: Ex3:index(%{4,3,1,2%},1) Ex4:index("abracadabrant","c") ''' - return GiacMethods['index'](self,*args) + return GiacMethods['index'](self, *args) - def induced_subgraph(self,*args): + def induced_subgraph(self, *args): r'''From Giac's documentation: Help for induced_subgraph: induced_subgraph(Graph(G),Lst(V)) @@ -7324,9 +7324,9 @@ cdef class GiacMethods_base: See also: 1/ subgraph Ex1:induced_subgraph(cycle_graph(6),[1,2,6]) ''' - return GiacMethods['induced_subgraph'](self,*args) + return GiacMethods['induced_subgraph'](self, *args) - def inequationplot(self,*args): + def inequationplot(self, *args): r'''From Giac's documentation: Help for inequationplot: inequationplot(Expr,[x=xrange,y=yrange],[xstep],[ystep]) @@ -7337,27 +7337,27 @@ cdef class GiacMethods_base: Ex3:inequationplot(3-(x^2-y^2),[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex4:inequationplot([x+y>3,x^2ifte(x<5,"A","B"),1,10) ''' - return GiacMethods['makelist'](self,*args) + return GiacMethods['makelist'](self, *args) - def makemat(self,*args): + def makemat(self, *args): r'''From Giac's documentation: Help for makemat: makemat(Fnct(f),RowsNumb,ColsNumb) @@ -9669,9 +9669,9 @@ cdef class GiacMethods_base: Ex2:makemat((j,k)->1/(j+k+1),2,3) Ex3:makemat(sqrt(2),2,3) ''' - return GiacMethods['makemat'](self,*args) + return GiacMethods['makemat'](self, *args) - def makesuite(self,*args): + def makesuite(self, *args): r'''From Giac's documentation: Help for makesuite: makesuite(Vect||Lst) @@ -9679,9 +9679,9 @@ cdef class GiacMethods_base: See also: 1/ makevector 2/ op Ex1:makesuite([1,2,3]) ''' - return GiacMethods['makesuite'](self,*args) + return GiacMethods['makesuite'](self, *args) - def makevector(self,*args): + def makevector(self, *args): r'''From Giac's documentation: Help for makevector: makevector(Seq) @@ -9689,9 +9689,9 @@ cdef class GiacMethods_base: See also: 1/ makesuite Ex1:makevector(1,2,3) ''' - return GiacMethods['makevector'](self,*args) + return GiacMethods['makevector'](self, *args) - def map(self,*args): + def map(self, *args): r'''From Giac's documentation: Help for map: map(Lst(l),Fnc(f)) @@ -9701,27 +9701,27 @@ cdef class GiacMethods_base: Ex2:map([1,2,3],unapply(x^3,x)) Ex3:map(%%%{1,[2,0]%%%}+%%%{2,[1,1]%%%},(a,b,c)->a*(b+2*c)) ''' - return GiacMethods['map'](self,*args) + return GiacMethods['map'](self, *args) - def maple2mupad(self,*args): + def maple2mupad(self, *args): r'''From Giac's documentation: Help for maple2mupad: maple2mupad(Str("Name_Maplefile"),Str("Name_Mupadfile")) maple2mupad("file1","file2") translates file1(Maple) to file2(MuPAD). See also: 1/ maple2xcas ''' - return GiacMethods['maple2mupad'](self,*args) + return GiacMethods['maple2mupad'](self, *args) - def maple2xcas(self,*args): + def maple2xcas(self, *args): r'''From Giac's documentation: Help for maple2xcas: maple2xcas(Str("NameMapleFile"),Str("NameXcasFile")) maple2xcas("file1","file2") translates file1(Maple) to file2(Xcas). See also: 1/ maple2mupad ''' - return GiacMethods['maple2xcas'](self,*args) + return GiacMethods['maple2xcas'](self, *args) - def maple_ifactors(self,*args): + def maple_ifactors(self, *args): r'''From Giac's documentation: Help for maple_ifactors: maple_ifactors(Intg(n)) @@ -9729,9 +9729,9 @@ cdef class GiacMethods_base: See also: 1/ ifactors Ex1:maple_ifactors(120) ''' - return GiacMethods['maple_ifactors'](self,*args) + return GiacMethods['maple_ifactors'](self, *args) - def maple_mode(self,*args): + def maple_mode(self, *args): r'''From Giac's documentation: Help for maple_mode: maple_mode(Intg(0) or 1 or 2 or 3) @@ -9740,9 +9740,9 @@ cdef class GiacMethods_base: Ex1:maple_mode(1) Ex2:maple_mode(0) ''' - return GiacMethods['maple_mode'](self,*args) + return GiacMethods['maple_mode'](self, *args) - def markov(self,*args): + def markov(self, *args): r'''From Giac's documentation: Help for markov: markov(Mtrx(M),[Real(eps)]) @@ -9750,9 +9750,9 @@ cdef class GiacMethods_base: See also: 1/ randmarkov 2/ plotproba Ex1:markov([[0,0,1/2,0,1/2],[0,0,1,0,0],[1/4,1/4,0,1/4,1/4],[0,0,1/2,0,1/2],[0,0,0,0,1]]) ''' - return GiacMethods['markov'](self,*args) + return GiacMethods['markov'](self, *args) - def mat2list(self,*args): + def mat2list(self, *args): r'''From Giac's documentation: Help for mat2list: mat2list(Mtrx) @@ -9760,9 +9760,9 @@ cdef class GiacMethods_base: See also: 1/ list2mat 2/ flatten Ex1:mat2list([[1,8],[4,9]]) ''' - return GiacMethods['mat2list'](self,*args) + return GiacMethods['mat2list'](self, *args) - def mathml(self,*args): + def mathml(self, *args): r'''From Giac's documentation: Help for mathml: mathml(Expr) @@ -9770,9 +9770,9 @@ cdef class GiacMethods_base: See also: 1/ export_mathml 2/ latex Ex1:mathml(1/2) ''' - return GiacMethods['mathml'](self,*args) + return GiacMethods['mathml'](self, *args) - def matpow(self,*args): + def matpow(self, *args): r'''From Giac's documentation: Help for matpow: matpow(Mtrx,Intg(n)) @@ -9780,9 +9780,9 @@ cdef class GiacMethods_base: See also: 1/ &^ 2/ ^ Ex1:matpow([[1,2],[3,4]],n) ''' - return GiacMethods['matpow'](self,*args) + return GiacMethods['matpow'](self, *args) - def matrix(self,*args): + def matrix(self, *args): r'''From Giac's documentation: Help for matrix: matrix(Intg(p),Intg(q),(Fnc(f) or Val(a))) @@ -9793,9 +9793,9 @@ cdef class GiacMethods_base: Ex3:matrix(2,3,4) Ex4: A[0..2,0..2]:=1;A[0..1,1..2]:=2;a:=matrix(A) ''' - return GiacMethods['matrix'](self,*args) + return GiacMethods['matrix'](self, *args) - def matrix_norm(self,*args): + def matrix_norm(self, *args): r'''From Giac's documentation: Help for matrix_norm: matrix_norm(Mtrx,[2]||[inf]) @@ -9806,9 +9806,9 @@ cdef class GiacMethods_base: Ex3:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]],2) Ex4:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]],inf) ''' - return GiacMethods['matrix_norm'](self,*args) + return GiacMethods['matrix_norm'](self, *args) - def max(self,*args): + def max(self, *args): r'''From Giac's documentation: Help for max: max(Seq||Lst) @@ -9816,9 +9816,9 @@ cdef class GiacMethods_base: See also: 1/ min Ex1:max(25,35) ''' - return GiacMethods['max'](self,*args) + return GiacMethods['max'](self, *args) - def maxflow(self,*args): + def maxflow(self, *args): r'''From Giac's documentation: Help for maxflow: maxflow(Graph(G),Vrtx(s),Vrtx(t)) @@ -9826,9 +9826,9 @@ cdef class GiacMethods_base: See also: 1/ minimum_cut Ex1:maxflow(digraph(%{[[1,2],2],[[2,3],4],[[3,4],3],[[1,5],3],[[5,2],1],[[5,4],2]%}),1,4) ''' - return GiacMethods['maxflow'](self,*args) + return GiacMethods['maxflow'](self, *args) - def maximal_independent_set(self,*args): + def maximal_independent_set(self, *args): r'''From Giac's documentation: Help for maximal_independent_set: maximal_independent_set(Graph(G)) @@ -9836,9 +9836,9 @@ cdef class GiacMethods_base: See also: 1/ maximum_independent_set Ex1:maximal_independent_set(graph("petersen")) ''' - return GiacMethods['maximal_independent_set'](self,*args) + return GiacMethods['maximal_independent_set'](self, *args) - def maximize(self,*args): + def maximize(self, *args): r'''From Giac's documentation: Help for maximize: maximize(Expr,[Constr],Vars,[Options]) @@ -9852,9 +9852,9 @@ cdef class GiacMethods_base: Ex7:maximize((1+x^2+3y+5x-4*x*y)/(1+x^2+y^2),x^2/4+y^2/3=9,[x,y]) Ex8:maximize(cos(x)^2+cos(y)^2,x+y=pi/4,[x,y],locus) ''' - return GiacMethods['maximize'](self,*args) + return GiacMethods['maximize'](self, *args) - def maximum_clique(self,*args): + def maximum_clique(self, *args): r'''From Giac's documentation: Help for maximum_clique: maximum_clique(Graph(G)) @@ -9862,9 +9862,9 @@ cdef class GiacMethods_base: See also: 1/ clique_number 2/ is_clique 3/ maximum_independent_set Ex1:maximum_clique(graph_complement(complete_graph(3,4))) ''' - return GiacMethods['maximum_clique'](self,*args) + return GiacMethods['maximum_clique'](self, *args) - def maximum_degree(self,*args): + def maximum_degree(self, *args): r'''From Giac's documentation: Help for maximum_degree: maximum_degree(Graph(G)) @@ -9872,9 +9872,9 @@ cdef class GiacMethods_base: See also: 1/ minimum_degree 2/ vertex_degree Ex1:maximum_degree(digraph(trail(1,2,3,4,5,6,4,7,8,2))) ''' - return GiacMethods['maximum_degree'](self,*args) + return GiacMethods['maximum_degree'](self, *args) - def maximum_independent_set(self,*args): + def maximum_independent_set(self, *args): r'''From Giac's documentation: Help for maximum_independent_set: maximum_independent_set(Graph(G)) @@ -9882,9 +9882,9 @@ cdef class GiacMethods_base: See also: 1/ clique_number 2/ graph_complement 3/ independence_number 4/ maximum_clique Ex1:maximum_independent_set(complete_graph(3,4)) ''' - return GiacMethods['maximum_independent_set'](self,*args) + return GiacMethods['maximum_independent_set'](self, *args) - def maximum_matching(self,*args): + def maximum_matching(self, *args): r'''From Giac's documentation: Help for maximum_matching: maximum_matching(Graph(G)) @@ -9892,9 +9892,9 @@ cdef class GiacMethods_base: See also: 1/ maximum_independent_set Ex1: G:=graph("soccerball"); draw_graph(highlight_edges(G,maximum_matching(G))) ''' - return GiacMethods['maximum_matching'](self,*args) + return GiacMethods['maximum_matching'](self, *args) - def maxnorm(self,*args): + def maxnorm(self, *args): r'''From Giac's documentation: Help for maxnorm: maxnorm(Vect or Mtrx) @@ -9904,9 +9904,9 @@ cdef class GiacMethods_base: Ex2:maxnorm([1,2,3,-4]) Ex3:maxnorm([[1,2],[3,-4]]) ''' - return GiacMethods['maxnorm'](self,*args) + return GiacMethods['maxnorm'](self, *args) - def mean(self,*args): + def mean(self, *args): r'''From Giac's documentation: Help for mean: mean(Lst||Mtrx,[Lst]) @@ -9916,9 +9916,9 @@ cdef class GiacMethods_base: Ex2:mean([1,2,3],[1,2,3]) Ex3:mean([[1,2,3],[1,2,3]]) ''' - return GiacMethods['mean'](self,*args) + return GiacMethods['mean'](self, *args) - def median(self,*args): + def median(self, *args): r'''From Giac's documentation: Help for median: median(Lst||Mtrx,[Lst]) @@ -9927,9 +9927,9 @@ cdef class GiacMethods_base: Ex1:median([1,2,3,5,10,4]) Ex2:median([1,2,3,5,10,4],[1,2,3,1,2,3]) ''' - return GiacMethods['median'](self,*args) + return GiacMethods['median'](self, *args) - def median_line(self,*args): + def median_line(self, *args): r'''From Giac's documentation: Help for median_line: median_line((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -9937,9 +9937,9 @@ cdef class GiacMethods_base: See also: 1/ midpoint 2/ perpen_bisector Ex1:median_line(-1,1-i,i) ''' - return GiacMethods['median_line'](self,*args) + return GiacMethods['median_line'](self, *args) - def member(self,*args): + def member(self, *args): r'''From Giac's documentation: Help for member: member(Elem(e),(Lst(l) or Set(l))) @@ -9948,9 +9948,9 @@ cdef class GiacMethods_base: Ex1:member(1,[4,3,1,2]) Ex2:member(1,%{4,3,1,2%}) ''' - return GiacMethods['member'](self,*args) + return GiacMethods['member'](self, *args) - def mgf(self,*args): + def mgf(self, *args): r'''From Giac's documentation: Help for mgf: mgf(Func,[Real(Param_1),Real(Param_2)]) @@ -9959,9 +9959,9 @@ cdef class GiacMethods_base: Ex2:mgf(poisson,5) Ex3:mgf(binomial,n,p) ''' - return GiacMethods['mgf'](self,*args) + return GiacMethods['mgf'](self, *args) - def mid(self,*args): + def mid(self, *args): r'''From Giac's documentation: Help for mid: mid(Lst(l) or Str(l),Intg(d),Intg(n)) @@ -9973,9 +9973,9 @@ cdef class GiacMethods_base: Ex4:mid("azertyuiop",2) Ex5:mid([[1,2],[3,4],[5,6]],1) ''' - return GiacMethods['mid'](self,*args) + return GiacMethods['mid'](self, *args) - def middle_point(self,*args): + def middle_point(self, *args): r'''From Giac's documentation: Help for middle_point: middle_point(Opt) @@ -9988,9 +9988,9 @@ cdef class GiacMethods_base: Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) ''' - return GiacMethods['middle_point'](self,*args) + return GiacMethods['middle_point'](self, *args) - def midpoint(self,*args): + def midpoint(self, *args): r'''From Giac's documentation: Help for midpoint: midpoint((Pnt or Cplx),(Pnt or Cplx)) @@ -9998,9 +9998,9 @@ cdef class GiacMethods_base: See also: 1/ median_line 2/ perpen_bisector Ex1:midpoint(-2,2i) ''' - return GiacMethods['midpoint'](self,*args) + return GiacMethods['midpoint'](self, *args) - def min(self,*args): + def min(self, *args): r'''From Giac's documentation: Help for min: min(Seq||Lst) @@ -10008,9 +10008,9 @@ cdef class GiacMethods_base: See also: 1/ max Ex1:min(25,35) ''' - return GiacMethods['min'](self,*args) + return GiacMethods['min'](self, *args) - def minimal_edge_coloring(self,*args): + def minimal_edge_coloring(self, *args): r'''From Giac's documentation: Help for minimal_edge_coloring: minimal_edge_coloring(Graph(G),[sto]) @@ -10019,9 +10019,9 @@ cdef class GiacMethods_base: Ex1:minimal_edge_coloring(graph("petersen")) Ex2: G:=minimal_edge_coloring(graph("dodecahedron"),sto); draw_graph(G) ''' - return GiacMethods['minimal_edge_coloring'](self,*args) + return GiacMethods['minimal_edge_coloring'](self, *args) - def minimal_spanning_tree(self,*args): + def minimal_spanning_tree(self, *args): r'''From Giac's documentation: Help for minimal_spanning_tree: minimal_spanning_tree(Graph(G)) @@ -10029,9 +10029,9 @@ cdef class GiacMethods_base: See also: 1/ spanning_tree Ex1:minimal_spanning_tree(graph([[0,1,0,4,0,0],[1,0,1,0,4,0],[0,1,0,3,0,1],[4,0,3,0,1,0],[0,4,0,1,0,4],[0,0,1,0,4,0]])) ''' - return GiacMethods['minimal_spanning_tree'](self,*args) + return GiacMethods['minimal_spanning_tree'](self, *args) - def minimal_vertex_coloring(self,*args): + def minimal_vertex_coloring(self, *args): r'''From Giac's documentation: Help for minimal_vertex_coloring: minimal_vertex_coloring(Graph(G),[sto]) @@ -10040,9 +10040,9 @@ cdef class GiacMethods_base: Ex1:minimal_vertex_coloring(graph("petersen")) Ex2: draw_graph(minimal_vertex_coloring(graph("petersen"),sto)) ''' - return GiacMethods['minimal_vertex_coloring'](self,*args) + return GiacMethods['minimal_vertex_coloring'](self, *args) - def minimax(self,*args): + def minimax(self, *args): r'''From Giac's documentation: Help for minimax: minimax(Expr,Var=a..b,n,[Options]) @@ -10058,9 +10058,9 @@ cdef class GiacMethods_base: Ex9:minimax(min(1/cosh(3*sin(x)),sin(9x/10)),x=-3..4,30) Ex10:minimax(when(x==0,0,exp(-1/x^2)),x=-1..1,25) ''' - return GiacMethods['minimax'](self,*args) + return GiacMethods['minimax'](self, *args) - def minimize(self,*args): + def minimize(self, *args): r'''From Giac's documentation: Help for minimize: minimize(Expr,[Constr],Vars,[Options]) @@ -10074,9 +10074,9 @@ cdef class GiacMethods_base: Ex7:minimize((1+x^2+3y+5x-4*x*y)/(1+x^2+y^2),x^2/4+y^2/3=9,[x,y]) Ex8:minimize(cos(x)^2+cos(y)^2,x+y=pi/4,[x,y],locus) ''' - return GiacMethods['minimize'](self,*args) + return GiacMethods['minimize'](self, *args) - def minimum_cut(self,*args): + def minimum_cut(self, *args): r'''From Giac's documentation: Help for minimum_cut: minimum_cut(Graph(G),Vrtx(s),Vrtx(t)) @@ -10084,9 +10084,9 @@ cdef class GiacMethods_base: See also: 1/ maxflow Ex1:minimum_cut(digraph(%{[[1,2],2],[[2,3],4],[[3,4],3],[[1,5],3],[[5,2],1],[[5,4],2]%}),1,4) ''' - return GiacMethods['minimum_cut'](self,*args) + return GiacMethods['minimum_cut'](self, *args) - def minimum_degree(self,*args): + def minimum_degree(self, *args): r'''From Giac's documentation: Help for minimum_degree: minimum_degree(Graph(G)) @@ -10094,9 +10094,9 @@ cdef class GiacMethods_base: See also: 1/ maximum_degree 2/ vertex_degree Ex1:minimum_degree(digraph(trail(1,2,3,4,5,6,4,7,8,2))) ''' - return GiacMethods['minimum_degree'](self,*args) + return GiacMethods['minimum_degree'](self, *args) - def mkisom(self,*args): + def mkisom(self, *args): r'''From Giac's documentation: Help for mkisom: mkisom(Vect,(Sign(1) or -1)) @@ -10106,9 +10106,9 @@ cdef class GiacMethods_base: Ex2:mkisom([[1,0,0],pi/3],-1) Ex3:mkisom(pi,1) ''' - return GiacMethods['mkisom'](self,*args) + return GiacMethods['mkisom'](self, *args) - def mksa(self,*args): + def mksa(self, *args): r'''From Giac's documentation: Help for mksa: mksa(Unit) @@ -10116,9 +10116,9 @@ cdef class GiacMethods_base: See also: 1/ convert 2/ ufactor Ex1:mksa(1_N) ''' - return GiacMethods['mksa'](self,*args) + return GiacMethods['mksa'](self, *args) - def modgcd(self,*args): + def modgcd(self, *args): r'''From Giac's documentation: Help for modgcd: modgcd(Poly,Poly) @@ -10126,9 +10126,9 @@ cdef class GiacMethods_base: See also: 1/ gcd 2/ heugcd 3/ ezgcd 4/ psrgcd Ex1:modgcd(x^4-1,(x-1)^2) ''' - return GiacMethods['modgcd'](self,*args) + return GiacMethods['modgcd'](self, *args) - def mods(self,*args): + def mods(self, *args): r'''From Giac's documentation: Help for mods: mods(Intg,Intg) @@ -10138,18 +10138,18 @@ cdef class GiacMethods_base: Ex2:mods(10,4) Ex3:mods(11,7) ''' - return GiacMethods['mods'](self,*args) + return GiacMethods['mods'](self, *args) - def monotonic(self,*args): + def monotonic(self, *args): r'''From Giac's documentation: Help for monotonic: monotonic() Returns a real that increases as time passes Ex1:monotonic() ''' - return GiacMethods['monotonic'](self,*args) + return GiacMethods['monotonic'](self, *args) - def montre_tortue(self,*args): + def montre_tortue(self, *args): r'''From Giac's documentation: Help for montre_tortue: montre_tortue(NULL) @@ -10157,9 +10157,9 @@ cdef class GiacMethods_base: See also: 1/ cache_tortue Ex1:montre_tortue() ''' - return GiacMethods['montre_tortue'](self,*args) + return GiacMethods['montre_tortue'](self, *args) - def moustache(self,*args): + def moustache(self, *args): r'''From Giac's documentation: Help for moustache: moustache(Lst,[Lst],[x=a..b||y=a..b]) @@ -10170,9 +10170,9 @@ cdef class GiacMethods_base: Ex3:moustache([1,2,3,5,10,4],[1,2,3,1,2,3]) Ex4:moustache([[6,0,1,3,4,2,5],[0,1,3,4,2,5,6],[1,3,4,2,5,6,0],[3,4,2,5,6,0,1],[4,2,5,6,0,1,3],[2,5,6,0,1,3,4]]) ''' - return GiacMethods['moustache'](self,*args) + return GiacMethods['moustache'](self, *args) - def moving_average(self,*args): + def moving_average(self, *args): r'''From Giac's documentation: Help for moving_average: moving_average(Lst(A),Intg(n)) @@ -10180,9 +10180,9 @@ cdef class GiacMethods_base: See also: 1/ lowpass Ex1: snd:=soundsec(2):;data:=0.5*threshold(3*sin(2*pi*220*snd),[-1.0,1.0])+randvector(length(snd),normald,0,0.05):;moving_average(data,25) ''' - return GiacMethods['moving_average'](self,*args) + return GiacMethods['moving_average'](self, *args) - def moyal(self,*args): + def moyal(self, *args): r'''From Giac's documentation: Help for moyal: moyal(Expr,Expr,VectVar) @@ -10190,9 +10190,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:moyal(x^2+y^4,x^4-y^2,[x,y],5) ''' - return GiacMethods['moyal'](self,*args) + return GiacMethods['moyal'](self, *args) - def moyenne(self,*args): + def moyenne(self, *args): r'''From Giac's documentation: Help for moyenne: moyenne(Lst||Mtrx,[Lst]) @@ -10202,9 +10202,9 @@ cdef class GiacMethods_base: Ex2:moyenne([1,2,3],[1,2,3]) Ex3:moyenne([[1,2,3],[1,2,3]]) ''' - return GiacMethods['moyenne'](self,*args) + return GiacMethods['moyenne'](self, *args) - def mul(self,*args): + def mul(self, *args): r'''From Giac's documentation: Help for mul: mul(Expr||Lst,[Var||Lst],[Intg(a)],[Intg(b)],[Intg(p)]) @@ -10218,9 +10218,9 @@ cdef class GiacMethods_base: Ex6:mul([2,3,4],[5,6,7]) Ex7:mul([[2,3,4],[5,6,7]],[[2,3,4],[5,6,7]]) ''' - return GiacMethods['mul'](self,*args) + return GiacMethods['mul'](self, *args) - def mult_c_conjugate(self,*args): + def mult_c_conjugate(self, *args): r'''From Giac's documentation: Help for mult_c_conjugate: mult_c_conjugate(Expr) @@ -10229,9 +10229,9 @@ cdef class GiacMethods_base: Ex1:mult_c_conjugate(1/(3+i*2)) Ex2:mult_c_conjugate(3+i*2) ''' - return GiacMethods['mult_c_conjugate'](self,*args) + return GiacMethods['mult_c_conjugate'](self, *args) - def mult_conjugate(self,*args): + def mult_conjugate(self, *args): r'''From Giac's documentation: Help for mult_conjugate: mult_conjugate(Expr) @@ -10240,9 +10240,9 @@ cdef class GiacMethods_base: Ex1:mult_conjugate(sqrt(3)-sqrt(2)) Ex2:mult_conjugate(1/(sqrt(3)-sqrt(2))) ''' - return GiacMethods['mult_conjugate'](self,*args) + return GiacMethods['mult_conjugate'](self, *args) - def multinomial(self,*args): + def multinomial(self, *args): r'''From Giac's documentation: Help for multinomial: multinomial(Intg(n),Vect(p),Vect(k)) @@ -10253,9 +10253,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,multinomial,[1/2,1/3,1/6]) Ex4: ranm(4,3,multinomial,[1/2,1/3,1/6]) ''' - return GiacMethods['multinomial'](self,*args) + return GiacMethods['multinomial'](self, *args) - def multiplier_conjugue(self,*args): + def multiplier_conjugue(self, *args): r'''From Giac's documentation: Help for multiplier_conjugue: multiplier_conjugue(Expr) @@ -10264,9 +10264,9 @@ cdef class GiacMethods_base: Ex1:multiplier_conjugue(sqrt(3)-sqrt(2)) Ex2:multiplier_conjugue(1/(sqrt(3)-sqrt(2))) ''' - return GiacMethods['multiplier_conjugue'](self,*args) + return GiacMethods['multiplier_conjugue'](self, *args) - def multiplier_conjugue_complexe(self,*args): + def multiplier_conjugue_complexe(self, *args): r'''From Giac's documentation: Help for multiplier_conjugue_complexe: multiplier_conjugue_complexe(Expr) @@ -10275,9 +10275,9 @@ cdef class GiacMethods_base: Ex1:multiplier_conjugue_complexe(1/(3+i*2)) Ex2:multiplier_conjugue_complexe(3+i*2) ''' - return GiacMethods['multiplier_conjugue_complexe'](self,*args) + return GiacMethods['multiplier_conjugue_complexe'](self, *args) - def multiply(self,*args): + def multiply(self, *args): r'''From Giac's documentation: Help for multiply: multiply(Intg or Lst, Intg or Lst) @@ -10287,27 +10287,27 @@ cdef class GiacMethods_base: Ex2:multiply([4,1],[-4,2]) Ex3:multiply([[4,1],[-4,1]],[[4,1],[-4,1]]) ''' - return GiacMethods['multiply'](self,*args) + return GiacMethods['multiply'](self, *args) - def mupad2maple(self,*args): + def mupad2maple(self, *args): r'''From Giac's documentation: Help for mupad2maple: mupad2maple(Str("NameMupadFile"),Str("NameMapleFile")) mupad2maple("file1","file2") translates file1(MuPAD) to file2(Maple). See also: 1/ mupad2xcas ''' - return GiacMethods['mupad2maple'](self,*args) + return GiacMethods['mupad2maple'](self, *args) - def mupad2xcas(self,*args): + def mupad2xcas(self, *args): r'''From Giac's documentation: Help for mupad2xcas: mupad2xcas(Str("NameMupadFile"),Str("NameXcasFile")) mupad2xcas("file1","file2") translates file1(MuPAD) to file2(Xcas). See also: 1/ mupad2maple ''' - return GiacMethods['mupad2xcas'](self,*args) + return GiacMethods['mupad2xcas'](self, *args) - def mycielski(self,*args): + def mycielski(self, *args): r'''From Giac's documentation: Help for mycielski: mycielski(Graph(G)) @@ -10316,9 +10316,9 @@ cdef class GiacMethods_base: Ex1:mycielski(graph("petersen")) Ex2: is_isomorphic(mycielski(mycielski(path_graph(2))),graph("grotzsch")) ''' - return GiacMethods['mycielski'](self,*args) + return GiacMethods['mycielski'](self, *args) - def nCr(self,*args): + def nCr(self, *args): r'''From Giac's documentation: Help for nCr: nCr(Intg(n),Intg(r)) @@ -10326,9 +10326,9 @@ cdef class GiacMethods_base: See also: 1/ factorial 2/ perm Ex1:nCr(4,2) ''' - return GiacMethods['nCr'](self,*args) + return GiacMethods['nCr'](self, *args) - def nDeriv(self,*args): + def nDeriv(self, *args): r'''From Giac's documentation: Help for nDeriv: nDeriv(Expr(Xpr),Var(Var),[Real(h)]) @@ -10338,9 +10338,9 @@ cdef class GiacMethods_base: Ex2:nDeriv(x^2,x,0.1) Ex3:nDeriv(x^2,x) ''' - return GiacMethods['nDeriv'](self,*args) + return GiacMethods['nDeriv'](self, *args) - def nInt(self,*args): + def nInt(self, *args): r'''From Giac's documentation: Help for nInt: nInt(Expr(f(x)),Var(x),Real(a),Real(b)) @@ -10350,9 +10350,9 @@ cdef class GiacMethods_base: Ex2:nInt(x^2,x,0,1) Ex3:nInt(exp(-x^2),x,-1,1) ''' - return GiacMethods['nInt'](self,*args) + return GiacMethods['nInt'](self, *args) - def nPr(self,*args): + def nPr(self, *args): r'''From Giac's documentation: Help for nPr: nPr(Intg(n),Intg(p)) @@ -10360,9 +10360,9 @@ cdef class GiacMethods_base: See also: 1/ comb 2/ factorial Ex1:nPr(4,2) ''' - return GiacMethods['nPr'](self,*args) + return GiacMethods['nPr'](self, *args) - def nSolve(self,*args): + def nSolve(self, *args): r'''From Giac's documentation: Help for nSolve: nSolve(Expr,Var,[Guess or Interval],[Method]) @@ -10371,9 +10371,9 @@ cdef class GiacMethods_base: Ex1:nSolve(cos(x)=x,x) Ex2:nSolve(cos(x)=x,x=1.3) ''' - return GiacMethods['nSolve'](self,*args) + return GiacMethods['nSolve'](self, *args) - def ncols(self,*args): + def ncols(self, *args): r'''From Giac's documentation: Help for ncols: ncols(Mtrx) @@ -10382,9 +10382,9 @@ cdef class GiacMethods_base: Ex1:ncols([[1,2,3],[4,5,6]]) Ex2:ncols([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['ncols'](self,*args) + return GiacMethods['ncols'](self, *args) - def negbinomial(self,*args): + def negbinomial(self, *args): r'''From Giac's documentation: Help for negbinomial: negbinomial(Intg(n),Intg(k),Real(p in 0..1)) @@ -10394,9 +10394,9 @@ cdef class GiacMethods_base: Ex2:negbinomial(4,2,0.6) Ex3:negbinomial(4,6,0.3) ''' - return GiacMethods['negbinomial'](self,*args) + return GiacMethods['negbinomial'](self, *args) - def negbinomial_cdf(self,*args): + def negbinomial_cdf(self, *args): r'''From Giac's documentation: Help for negbinomial_cdf: negbinomial_cdf(Intg(n),Real(p),Real(x),[Real(y)]) @@ -10406,9 +10406,9 @@ cdef class GiacMethods_base: Ex2:negbinomial_cdf(4,0.1,2) Ex3:negbinomial_cdf(4,0.5,2,3) ''' - return GiacMethods['negbinomial_cdf'](self,*args) + return GiacMethods['negbinomial_cdf'](self, *args) - def negbinomial_icdf(self,*args): + def negbinomial_icdf(self, *args): r'''From Giac's documentation: Help for negbinomial_icdf: negbinomial_icdf(Intg(n),Real(p),Real(t)) @@ -10417,9 +10417,9 @@ cdef class GiacMethods_base: Ex1:negbinomial_icdf(4,0.5,0.68) Ex2:negbinomial_icdf(4,0.1,0.95) ''' - return GiacMethods['negbinomial_icdf'](self,*args) + return GiacMethods['negbinomial_icdf'](self, *args) - def neighbors(self,*args): + def neighbors(self, *args): r'''From Giac's documentation: Help for neighbors: neighbors(Graph(G),[Vrtx(v)]) @@ -10427,9 +10427,9 @@ cdef class GiacMethods_base: See also: 1/ adjacency_matrix 2/ vertex_degree 3/ in_degree 3/ out_degree Ex1:neighbors(digraph(trail(1,2,3,4,5,6,4,7,8,2)),4) ''' - return GiacMethods['neighbors'](self,*args) + return GiacMethods['neighbors'](self, *args) - def network_transitivity(self,*args): + def network_transitivity(self, *args): r'''From Giac's documentation: Help for network_transitivity: network_transitivity(Graph(G)) @@ -10437,9 +10437,9 @@ cdef class GiacMethods_base: See also: 1/ clustering_coefficient 2/ number_of_triangles Ex1:network_transitivity(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%})) ''' - return GiacMethods['network_transitivity'](self,*args) + return GiacMethods['network_transitivity'](self, *args) - def newList(self,*args): + def newList(self, *args): r'''From Giac's documentation: Help for newList: newList(Intg(n)) @@ -10447,9 +10447,9 @@ cdef class GiacMethods_base: See also: 1/ newMat 2/ makelist Ex1:newList(4) ''' - return GiacMethods['newList'](self,*args) + return GiacMethods['newList'](self, *args) - def newMat(self,*args): + def newMat(self, *args): r'''From Giac's documentation: Help for newMat: newMat(Intg(n),Intg(p)) @@ -10457,9 +10457,9 @@ cdef class GiacMethods_base: See also: 1/ newList 2/ makemat Ex1:newMat(2,3) ''' - return GiacMethods['newMat'](self,*args) + return GiacMethods['newMat'](self, *args) - def newton(self,*args): + def newton(self, *args): r'''From Giac's documentation: Help for newton: newton(Expr(f(x)),Var(x),[ApproxVal(a),NumIter(p)]) @@ -10470,9 +10470,9 @@ cdef class GiacMethods_base: Ex3:newton(x^2-2,x,-2) Ex4:newton(x^2-2,x,2,5,1e-7) ''' - return GiacMethods['newton'](self,*args) + return GiacMethods['newton'](self, *args) - def newton_solver(self,*args): + def newton_solver(self, *args): r'''From Giac's documentation: Help for newton_solver: newton_solver(Opt) @@ -10485,9 +10485,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['newton_solver'](self,*args) + return GiacMethods['newton_solver'](self, *args) - def newtonj_solver(self,*args): + def newtonj_solver(self, *args): r'''From Giac's documentation: Help for newtonj_solver: newtonj_solver(Opt) @@ -10500,9 +10500,9 @@ cdef class GiacMethods_base: Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) ''' - return GiacMethods['newtonj_solver'](self,*args) + return GiacMethods['newtonj_solver'](self, *args) - def nextperm(self,*args): + def nextperm(self, *args): r'''From Giac's documentation: Help for nextperm: nextperm(Intg(n)) @@ -10511,9 +10511,9 @@ cdef class GiacMethods_base: Ex1:nextperm([0,2,1,3]) Ex2:nextperm([0,3,2,1]) ''' - return GiacMethods['nextperm'](self,*args) + return GiacMethods['nextperm'](self, *args) - def nextprime(self,*args): + def nextprime(self, *args): r'''From Giac's documentation: Help for nextprime: nextprime(Intg(a)) @@ -10522,9 +10522,9 @@ cdef class GiacMethods_base: Ex1:nextprime(9856989898990) Ex2:nextprime(97160249868928888261606009) ''' - return GiacMethods['nextprime'](self,*args) + return GiacMethods['nextprime'](self, *args) - def nlpsolve(self,*args): + def nlpsolve(self, *args): r'''From Giac's documentation: Help for nlpsolve: nlpsolve(objective, [constr], [bd], [opts]) @@ -10541,18 +10541,18 @@ cdef class GiacMethods_base: Ex9:nlpsolve(w^3*(v-w)^2+(w-x-1)^2+(x-y-2)^2+(y-z-3)^2,[w+x+y+z<=5,3z+2v=3],assume=nlp_nonnegative) Ex10:nlpsolve(sin(x)*Psi(x),x=1..20,nlp_initialpoint=[x=16]) ''' - return GiacMethods['nlpsolve'](self,*args) + return GiacMethods['nlpsolve'](self, *args) - def nodisp(self,*args): + def nodisp(self, *args): r'''From Giac's documentation: Help for nodisp: nodisp(Expr) Displays Done in place of a value. Ex1:nodisp(A:=ranm(50,50)) ''' - return GiacMethods['nodisp'](self,*args) + return GiacMethods['nodisp'](self, *args) - def non_recursive_normal(self,*args): + def non_recursive_normal(self, *args): r'''From Giac's documentation: Help for non_recursive_normal: non_recursive_normal(Expr) @@ -10561,9 +10561,9 @@ cdef class GiacMethods_base: Ex1:non_recursive_normal(sin(x+x)+sin(2*x)+x+x) Ex2:non_recursive_normal(sin(2*x)+sin(2*x)+x+x) ''' - return GiacMethods['non_recursive_normal'](self,*args) + return GiacMethods['non_recursive_normal'](self, *args) - def nop(self,*args): + def nop(self, *args): r'''From Giac's documentation: Help for nop: nop(NULL) @@ -10571,9 +10571,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:nop() ''' - return GiacMethods['nop'](self,*args) + return GiacMethods['nop'](self, *args) - def nops(self,*args): + def nops(self, *args): r'''From Giac's documentation: Help for nops: nops(Lst or Str or Seq) @@ -10583,9 +10583,9 @@ cdef class GiacMethods_base: Ex2:nops("bonjour") Ex3:nops(1,2,3) ''' - return GiacMethods['nops'](self,*args) + return GiacMethods['nops'](self, *args) - def norm(self,*args): + def norm(self, *args): r'''From Giac's documentation: Help for norm: norm(Vect or Mtrx) @@ -10596,9 +10596,9 @@ cdef class GiacMethods_base: Ex3:norm([[1,2],[3,-4]]) Ex4:norm([[1,2,3],[3,-9,6],[4,5,6]]) ''' - return GiacMethods['norm'](self,*args) + return GiacMethods['norm'](self, *args) - def normal(self,*args): + def normal(self, *args): r'''From Giac's documentation: Help for normal: normal(Expr) @@ -10608,9 +10608,9 @@ cdef class GiacMethods_base: Ex2:normal(2*x*2) Ex3:normal((2*x+1)^2) ''' - return GiacMethods['normal'](self,*args) + return GiacMethods['normal'](self, *args) - def normal_cdf(self,*args): + def normal_cdf(self, *args): r'''From Giac's documentation: Help for normal_cdf: normal_cdf(Real(mu),Real(sigma),Real(x0),[Real(y0)]) @@ -10620,9 +10620,9 @@ cdef class GiacMethods_base: Ex2:normal_cdf(1,2,2.96*sqrt(2)) Ex3:normal_cdf(1,2,1.4*sqrt(2),2.96*sqrt(2)) ''' - return GiacMethods['normal_cdf'](self,*args) + return GiacMethods['normal_cdf'](self, *args) - def normal_icdf(self,*args): + def normal_icdf(self, *args): r'''From Giac's documentation: Help for normal_icdf: normal_icdf(Real(mu),Real(sigma),Real(p)) @@ -10631,9 +10631,9 @@ cdef class GiacMethods_base: Ex1:normal_icdf(0.95) Ex2:normal_icdf(1,2,0.95) ''' - return GiacMethods['normal_icdf'](self,*args) + return GiacMethods['normal_icdf'](self, *args) - def normald(self,*args): + def normald(self, *args): r'''From Giac's documentation: Help for normald: normald(Real(mu),Real(sigma),Real(x0)) @@ -10644,9 +10644,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,normald,1,0.5) Ex4: ranm(4,3,normald,1,0.5) ''' - return GiacMethods['normald'](self,*args) + return GiacMethods['normald'](self, *args) - def normald_cdf(self,*args): + def normald_cdf(self, *args): r'''From Giac's documentation: Help for normald_cdf: normald_cdf(Real(mu),Real(sigma),Real(x0),[Real(y0)]) @@ -10656,9 +10656,9 @@ cdef class GiacMethods_base: Ex2:normald_cdf(1,2,2.96*sqrt(2)) Ex3:normald_cdf(1,2,1.4*sqrt(2),2.96*sqrt(2)) ''' - return GiacMethods['normald_cdf'](self,*args) + return GiacMethods['normald_cdf'](self, *args) - def normald_icdf(self,*args): + def normald_icdf(self, *args): r'''From Giac's documentation: Help for normald_icdf: normald_icdf(Real(mu),Real(sigma),Real(p)) @@ -10667,9 +10667,9 @@ cdef class GiacMethods_base: Ex1:normald_icdf(0.95) Ex2:normald_icdf(1,2,0.95) ''' - return GiacMethods['normald_icdf'](self,*args) + return GiacMethods['normald_icdf'](self, *args) - def normalize(self,*args): + def normalize(self, *args): r'''From Giac's documentation: Help for normalize: normalize(Lst||Cplx) @@ -10680,9 +10680,9 @@ cdef class GiacMethods_base: Ex3: fieldplot(-t*y,[t,y],normalize) Ex4: fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) ''' - return GiacMethods['normalize'](self,*args) + return GiacMethods['normalize'](self, *args) - def normalt(self,*args): + def normalt(self, *args): r'''From Giac's documentation: Help for normalt: normalt(Lst,Real,[Real],Fnc,[Real]) @@ -10691,9 +10691,9 @@ cdef class GiacMethods_base: Ex1:normalt([10,30],.5,.02,'!=',0.1) Ex2:normalt([0.48,50],0.5,0.1,'<') ''' - return GiacMethods['normalt'](self,*args) + return GiacMethods['normalt'](self, *args) - def normalvariate(self,*args): + def normalvariate(self, *args): r'''From Giac's documentation: Help for normalvariate: normalvariate(Real(mu),Real(sigma)) @@ -10702,9 +10702,9 @@ cdef class GiacMethods_base: Ex1:normalvariate(0,1) Ex2:normalvariate(2,1) ''' - return GiacMethods['normalvariate'](self,*args) + return GiacMethods['normalvariate'](self, *args) - def nprimes(self,*args): + def nprimes(self, *args): r'''From Giac's documentation: Help for nprimes: nprimes(Intg(n)) @@ -10712,9 +10712,9 @@ cdef class GiacMethods_base: See also: 1/ ithprime 2/ prevprime 3/ nextprime 4/ isprime Ex1:nprimes(20) ''' - return GiacMethods['nprimes'](self,*args) + return GiacMethods['nprimes'](self, *args) - def nrows(self,*args): + def nrows(self, *args): r'''From Giac's documentation: Help for nrows: nrows(Mtrx) @@ -10723,9 +10723,9 @@ cdef class GiacMethods_base: Ex1:nrows([[1,2,3],[4,5,6]]) Ex2:nrows([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['nrows'](self,*args) + return GiacMethods['nrows'](self, *args) - def nuage_points(self,*args): + def nuage_points(self, *args): r'''From Giac's documentation: Help for nuage_points: nuage_points(Mtrx) @@ -10733,9 +10733,9 @@ cdef class GiacMethods_base: See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot Ex1:nuage_points([[1,2,3],[2,0,1],[-1,2,3]]) ''' - return GiacMethods['nuage_points'](self,*args) + return GiacMethods['nuage_points'](self, *args) - def nullspace(self,*args): + def nullspace(self, *args): r'''From Giac's documentation: Help for nullspace: nullspace(Mtrx) @@ -10744,9 +10744,9 @@ cdef class GiacMethods_base: Ex1:nullspace([[1,2],[3,6]]) Ex2:nullspace([[1,2,3],[1,3,6],[2,5,9]]) ''' - return GiacMethods['nullspace'](self,*args) + return GiacMethods['nullspace'](self, *args) - def number_of_edges(self,*args): + def number_of_edges(self, *args): r'''From Giac's documentation: Help for number_of_edges: number_of_edges(Graph(G)) @@ -10754,9 +10754,9 @@ cdef class GiacMethods_base: See also: 1/ edges 2/ number_of_vertices Ex1:number_of_edges(complete_graph(5)) ''' - return GiacMethods['number_of_edges'](self,*args) + return GiacMethods['number_of_edges'](self, *args) - def number_of_spanning_trees(self,*args): + def number_of_spanning_trees(self, *args): r'''From Giac's documentation: Help for number_of_spanning_trees: number_of_spanning_trees(Graph(G)) @@ -10765,9 +10765,9 @@ cdef class GiacMethods_base: Ex1:number_of_spanning_trees(complete_graph(4)) Ex2:number_of_spanning_trees(graph(trail(1,2,3,4,1,3))) ''' - return GiacMethods['number_of_spanning_trees'](self,*args) + return GiacMethods['number_of_spanning_trees'](self, *args) - def number_of_triangles(self,*args): + def number_of_triangles(self, *args): r'''From Giac's documentation: Help for number_of_triangles: number_of_triangles(Graph(G)) @@ -10775,9 +10775,9 @@ cdef class GiacMethods_base: See also: 1/ is_clique 2/ maximal_clique Ex1:number_of_triangles(graph("tetrahedron")) ''' - return GiacMethods['number_of_triangles'](self,*args) + return GiacMethods['number_of_triangles'](self, *args) - def number_of_vertices(self,*args): + def number_of_vertices(self, *args): r'''From Giac's documentation: Help for number_of_vertices: number_of_vertices(Graph(G)) @@ -10785,9 +10785,9 @@ cdef class GiacMethods_base: See also: 1/ graph_vertices 2/ number_of_edges Ex1:number_of_vertices(graph("petersen")) ''' - return GiacMethods['number_of_vertices'](self,*args) + return GiacMethods['number_of_vertices'](self, *args) - def numer(self,*args): + def numer(self, *args): r'''From Giac's documentation: Help for numer: numer(Frac(a/b) or RatFrac) @@ -10797,9 +10797,9 @@ cdef class GiacMethods_base: Ex2:numer((x^3-1)/(x^2-1)) Ex3:numer(1+(x^3-1)/x^2) ''' - return GiacMethods['numer'](self,*args) + return GiacMethods['numer'](self, *args) - def octahedron(self,*args): + def octahedron(self, *args): r'''From Giac's documentation: Help for octahedron: octahedron(Pnt(A),Pnt(B),Pnt(C)) @@ -10808,9 +10808,9 @@ cdef class GiacMethods_base: Ex1:octahedron([0,0,0],[0,0,5],[0,5,0]) Ex2:octahedron(evalf([0,0,0],[3,2,4],[1,1,0])) ''' - return GiacMethods['octahedron'](self,*args) + return GiacMethods['octahedron'](self, *args) - def odd(self,*args): + def odd(self, *args): r'''From Giac's documentation: Help for odd: odd(Intg(n)) @@ -10819,9 +10819,9 @@ cdef class GiacMethods_base: Ex1:odd(6) Ex2:odd(1251) ''' - return GiacMethods['odd'](self,*args) + return GiacMethods['odd'](self, *args) - def odd_girth(self,*args): + def odd_girth(self, *args): r'''From Giac's documentation: Help for odd_girth: odd_girth(Graph(G)) @@ -10830,9 +10830,9 @@ cdef class GiacMethods_base: Ex1:odd_girth(graph("petersen")) Ex2:odd_girth(hypercube_graph(3)) ''' - return GiacMethods['odd_girth'](self,*args) + return GiacMethods['odd_girth'](self, *args) - def odd_graph(self,*args): + def odd_graph(self, *args): r'''From Giac's documentation: Help for odd_graph: odd_graph(Intg(n)) @@ -10840,9 +10840,9 @@ cdef class GiacMethods_base: See also: 1/ kneser_graph Ex1:odd_graph(3) ''' - return GiacMethods['odd_graph'](self,*args) + return GiacMethods['odd_graph'](self, *args) - def odeplot(self,*args): + def odeplot(self, *args): r'''From Giac's documentation: Help for odeplot: odeplot(Expr,VectVar,VectInitCond) @@ -10856,9 +10856,9 @@ cdef class GiacMethods_base: Ex6:odeplot([-y+b,-1+(x-a)^2+(y-b)^2],[t=-3..3,x,y],[0,a+1,b+0.5],plan) Ex7:odeplot(5*[-y,x],[t=0..1,x,y],[0,0.3,0.7],tstep=0.05,plan) ''' - return GiacMethods['odeplot'](self,*args) + return GiacMethods['odeplot'](self, *args) - def odesolve(self,*args): + def odesolve(self, *args): r'''From Giac's documentation: Help for odesolve: odesolve(Expr,VectVar,VectInitCond,FinalVal,[tstep=Val,curve]) @@ -10870,9 +10870,9 @@ cdef class GiacMethods_base: Ex4:odesolve(sin(t*y),t=0..2,y,1,tstep=0.5) Ex5:odesolve(sin(t*y),t=0..2,y,1,tstep=0.5,curve) ''' - return GiacMethods['odesolve'](self,*args) + return GiacMethods['odesolve'](self, *args) - def op(self,*args): + def op(self, *args): r'''From Giac's documentation: Help for op: op(Op or Fnc) @@ -10884,9 +10884,9 @@ cdef class GiacMethods_base: Ex4:op([1,2,3]) Ex5:op(set[1,2,3]) ''' - return GiacMethods['op'](self,*args) + return GiacMethods['op'](self, *args) - def open_polygon(self,*args): + def open_polygon(self, *args): r'''From Giac's documentation: Help for open_polygon: open_polygon(LstPnt||LstCplx) @@ -10895,9 +10895,9 @@ cdef class GiacMethods_base: Ex1:open_polygon(i,1+i,2-i,-1,-1+i/2) Ex2:open_polygon(point(0,0,0),point(3,3,3),point(0,0,3),point(3,0,0)) ''' - return GiacMethods['open_polygon'](self,*args) + return GiacMethods['open_polygon'](self, *args) - def ord(self,*args): + def ord(self, *args): r'''From Giac's documentation: Help for ord: ord(Char||LstChar) @@ -10907,9 +10907,9 @@ cdef class GiacMethods_base: Ex2:ord("ABC") Ex3:ord(["a","b","c"]) ''' - return GiacMethods['ord'](self,*args) + return GiacMethods['ord'](self, *args) - def order(self,*args): + def order(self, *args): r'''From Giac's documentation: Help for order: order(g) @@ -10917,9 +10917,9 @@ cdef class GiacMethods_base: Ex1:order(3 % 7) Ex2: GF(3,5,g); order(g^2+g+1); ''' - return GiacMethods['order'](self,*args) + return GiacMethods['order'](self, *args) - def order_size(self,*args): + def order_size(self, *args): r'''From Giac's documentation: Help for order_size: order_size(Expr) @@ -10928,9 +10928,9 @@ cdef class GiacMethods_base: Ex1:order_size(x) Ex2: limit(sqrt(x)*order_size(x),x=0) ''' - return GiacMethods['order_size'](self,*args) + return GiacMethods['order_size'](self, *args) - def ordinate(self,*args): + def ordinate(self, *args): r'''From Giac's documentation: Help for ordinate: ordinate(Pnt or Vect) @@ -10941,9 +10941,9 @@ cdef class GiacMethods_base: Ex3:ordinate(-1-i) Ex4:ordinate(point(1,2,3)) ''' - return GiacMethods['ordinate'](self,*args) + return GiacMethods['ordinate'](self, *args) - def orthocenter(self,*args): + def orthocenter(self, *args): r'''From Giac's documentation: Help for orthocenter: orthocenter((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -10953,9 +10953,9 @@ cdef class GiacMethods_base: Ex2:orthocenter(point(1+i),point(2),point(i)) Ex3:orthocenter(triangle(0,1,1+i)) ''' - return GiacMethods['orthocenter'](self,*args) + return GiacMethods['orthocenter'](self, *args) - def orthogonal(self,*args): + def orthogonal(self, *args): r'''From Giac's documentation: Help for orthogonal: orthogonal((Pnt),(Line or Plan)) @@ -10964,9 +10964,9 @@ cdef class GiacMethods_base: Ex1:orthogonal(point(0,0,0),line(point(1,0,0),point(0,1,0))) Ex2:orthogonal(point(0,0,0),plane(point(1,0,0),point(0,1,0),point(0,0,1))) ''' - return GiacMethods['orthogonal'](self,*args) + return GiacMethods['orthogonal'](self, *args) - def osculating_circle(self,*args): + def osculating_circle(self, *args): r'''From Giac's documentation: Help for osculating_circle: osculating_circle(Curve,Point) @@ -10979,9 +10979,9 @@ cdef class GiacMethods_base: Ex5:osculating_circle([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t) Ex6:osculating_circle([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t,7) ''' - return GiacMethods['osculating_circle'](self,*args) + return GiacMethods['osculating_circle'](self, *args) - def p1oc2(self,*args): + def p1oc2(self, *args): r'''From Giac's documentation: Help for p1oc2: p1oc2(Permut,Cycle) @@ -10989,9 +10989,9 @@ cdef class GiacMethods_base: See also: 1/ c1op2 2/ p1op2 Ex1:p1oc2([0,2,1],[2,1,3]) ''' - return GiacMethods['p1oc2'](self,*args) + return GiacMethods['p1oc2'](self, *args) - def p1op2(self,*args): + def p1op2(self, *args): r'''From Giac's documentation: Help for p1op2: p1op2(Permut,Permut) @@ -10999,9 +10999,9 @@ cdef class GiacMethods_base: See also: 1/ c1op2 2/ p1oc2 Ex1:p1op2([0,2,1],[1,0,3,2]) ''' - return GiacMethods['p1op2'](self,*args) + return GiacMethods['p1op2'](self, *args) - def pa2b2(self,*args): + def pa2b2(self, *args): r'''From Giac's documentation: Help for pa2b2: pa2b2(Intg(n)) @@ -11010,9 +11010,9 @@ cdef class GiacMethods_base: Ex2:pa2b2(209) Ex3:pa2b2(229) ''' - return GiacMethods['pa2b2'](self,*args) + return GiacMethods['pa2b2'](self, *args) - def pade(self,*args): + def pade(self, *args): r'''From Giac's documentation: Help for pade: pade(Expr(Xpr), Var(x), (Intg(n) || Poly(N)), Intg(p)) @@ -11020,9 +11020,9 @@ cdef class GiacMethods_base: See also: 1/ taylor 2/ series Ex1:pade(exp(x),x,10,6) ''' - return GiacMethods['pade'](self,*args) + return GiacMethods['pade'](self, *args) - def parabola(self,*args): + def parabola(self, *args): r'''From Giac's documentation: Help for parabola: parabola(Pnt(F)||Pnt(xA+i*yA),Pnt(A)||Real(c),[Pnt(P)]) @@ -11033,9 +11033,9 @@ cdef class GiacMethods_base: Ex3:parabola(point(0,0,0),point(1,0,0),point(1,1,1)) Ex4:parabola(x-y^2+y-2) ''' - return GiacMethods['parabola'](self,*args) + return GiacMethods['parabola'](self, *args) - def parallel(self,*args): + def parallel(self, *args): r'''From Giac's documentation: Help for parallel: parallel(Pnt or Line,Line or Plan,[Line]) @@ -11049,9 +11049,9 @@ cdef class GiacMethods_base: Ex6:parallel([1,0,0],line(x=0,y=0),line(x=y,y=z)) Ex7:parallel(line(x=y,y=z),line(x=0,y=0)) ''' - return GiacMethods['parallel'](self,*args) + return GiacMethods['parallel'](self, *args) - def parallelepiped(self,*args): + def parallelepiped(self, *args): r'''From Giac's documentation: Help for parallelepiped: parallelepiped(Pnt(A),Pnt(B),Pnt(C),Pnt(D)) @@ -11060,9 +11060,9 @@ cdef class GiacMethods_base: Ex1:parallelepiped([0,0,0],[2,0,0],[0,1,0],[0,0,3]) Ex2: p:=parallelepiped([0,0,0],[5,0,0],[0,3,0],[0,0,2]);c1,c2,c3,c4,c5,c6,c7,c8:=sommets(p); ''' - return GiacMethods['parallelepiped'](self,*args) + return GiacMethods['parallelepiped'](self, *args) - def parallelogram(self,*args): + def parallelogram(self, *args): r'''From Giac's documentation: Help for parallelogram: parallelogram(Pnt(A)||Cplx,Pnt(B)||Cplx,Pnt(C)||Cplx,[Var(D)]) @@ -11073,9 +11073,9 @@ cdef class GiacMethods_base: Ex3:parallelogram(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:parallelogram(point(0,0,0),point(3,3,3),point(0,0,3),D) ''' - return GiacMethods['parallelogram'](self,*args) + return GiacMethods['parallelogram'](self, *args) - def parameq(self,*args): + def parameq(self, *args): r'''From Giac's documentation: Help for parameq: parameq(GeoObj) @@ -11084,18 +11084,18 @@ cdef class GiacMethods_base: Ex1:parameq(circle(0,1)) Ex2:parameq(line(i,1-i)) ''' - return GiacMethods['parameq'](self,*args) + return GiacMethods['parameq'](self, *args) - def parameter(self,*args): + def parameter(self, *args): r'''From Giac's documentation: Help for parameter: parameter() Reserved word. See also: 1/ ''' - return GiacMethods['parameter'](self,*args) + return GiacMethods['parameter'](self, *args) - def paramplot(self,*args): + def paramplot(self, *args): r'''From Giac's documentation: Help for paramplot: paramplot(Cplx||Lst,Var||Lst(Var)) @@ -11110,9 +11110,9 @@ cdef class GiacMethods_base: Ex7:paramplot([v*cos(u),v*sin(u),v],[u,v]) Ex8:paramplot([v*cos(u),v*sin(u),v],[u=0..pi,v=0..3],ustep=0.1,vstep=0.2) ''' - return GiacMethods['paramplot'](self,*args) + return GiacMethods['paramplot'](self, *args) - def parfrac(self,*args): + def parfrac(self, *args): r'''From Giac's documentation: Help for parfrac: parfrac(Opt) @@ -11121,9 +11121,9 @@ cdef class GiacMethods_base: Ex1: convert(1/(x^2-1),parfrac) Ex2: convert(1/(x^2-1),fullparfrac) ''' - return GiacMethods['parfrac'](self,*args) + return GiacMethods['parfrac'](self, *args) - def pari(self,*args): + def pari(self, *args): r'''From Giac's documentation: Help for pari: pari(Str,arguments) @@ -11138,9 +11138,9 @@ cdef class GiacMethods_base: Ex7:pari("isprime",9856989898997789789,1) Ex8:pari("isprime",9856989898997789789,2) ''' - return GiacMethods['pari'](self,*args) + return GiacMethods['pari'](self, *args) - def part(self,*args): + def part(self, *args): r'''From Giac's documentation: Help for part: part(Expr, Intg(n)) @@ -11151,9 +11151,9 @@ cdef class GiacMethods_base: Ex3:part(exp(x)*sin(x),1) Ex4:part(part(exp(x)*sin(x)+cos(x),1),1) ''' - return GiacMethods['part'](self,*args) + return GiacMethods['part'](self, *args) - def partfrac(self,*args): + def partfrac(self, *args): r'''From Giac's documentation: Help for partfrac: partfrac(RatFrac or Opt) @@ -11164,9 +11164,9 @@ cdef class GiacMethods_base: Ex3:partfrac(a/(z*(z-b)),z) Ex4: convert(x/(4-x^2),partfrac) ''' - return GiacMethods['partfrac'](self,*args) + return GiacMethods['partfrac'](self, *args) - def parzen_window(self,*args): + def parzen_window(self, *args): r'''From Giac's documentation: Help for parzen_window: parzen_window(Lst,[Interval(n1..n2)]) @@ -11174,9 +11174,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ bartlett_hann_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(parzen_window(randvector(1000,0..1))) ''' - return GiacMethods['parzen_window'](self,*args) + return GiacMethods['parzen_window'](self, *args) - def pas_de_cote(self,*args): + def pas_de_cote(self, *args): r'''From Giac's documentation: Help for pas_de_cote: pas_de_cote(NULL or Real(n)) @@ -11185,9 +11185,9 @@ cdef class GiacMethods_base: Ex1: pas_de_cote 30 Ex2:pas_de_cote(30) ''' - return GiacMethods['pas_de_cote'](self,*args) + return GiacMethods['pas_de_cote'](self, *args) - def path_graph(self,*args): + def path_graph(self, *args): r'''From Giac's documentation: Help for path_graph: path_graph(Intg(n)||Lst(V)) @@ -11195,9 +11195,9 @@ cdef class GiacMethods_base: See also: 1/ cycle_graph 2/ graph 3/ trail Ex1:path_graph(5) ''' - return GiacMethods['path_graph'](self,*args) + return GiacMethods['path_graph'](self, *args) - def pcar(self,*args): + def pcar(self, *args): r'''From Giac's documentation: Help for pcar: pcar(Mtrx,[Var]) @@ -11208,9 +11208,9 @@ cdef class GiacMethods_base: Ex3:pcar([[1,2,3],[1,3,6],[2,5,7]]) Ex4:pcar([[1,2,3],[1,3,6],[2,5,7]],z) ''' - return GiacMethods['pcar'](self,*args) + return GiacMethods['pcar'](self, *args) - def pcar_hessenberg(self,*args): + def pcar_hessenberg(self, *args): r'''From Giac's documentation: Help for pcar_hessenberg: pcar_hessenberg(Mtrx,[Var]) @@ -11220,9 +11220,9 @@ cdef class GiacMethods_base: Ex2:pcar_hessenberg([[1,2],[3,4]],x) Ex3:pcar_hessenberg([[1,2,3],[1,3,6],[2,5,7]]) ''' - return GiacMethods['pcar_hessenberg'](self,*args) + return GiacMethods['pcar_hessenberg'](self, *args) - def pcoef(self,*args): + def pcoef(self, *args): r'''From Giac's documentation: Help for pcoef: pcoef(Vect) @@ -11231,9 +11231,9 @@ cdef class GiacMethods_base: Ex1:pcoef([1,0,0,0,1]) Ex2:pcoef([1,0,-2]) ''' - return GiacMethods['pcoef'](self,*args) + return GiacMethods['pcoef'](self, *args) - def pcoeff(self,*args): + def pcoeff(self, *args): r'''From Giac's documentation: Help for pcoeff: pcoeff(Vect) @@ -11242,9 +11242,9 @@ cdef class GiacMethods_base: Ex1:pcoeff([1,0,0,0,1]) Ex2:pcoeff([1,0,-2]) ''' - return GiacMethods['pcoeff'](self,*args) + return GiacMethods['pcoeff'](self, *args) - def pencolor(self,*args): + def pencolor(self, *args): r'''From Giac's documentation: Help for pencolor: pencolor(Color) @@ -11255,9 +11255,9 @@ cdef class GiacMethods_base: Ex3:pencolor(5) Ex4:pencolor(gomme) ''' - return GiacMethods['pencolor'](self,*args) + return GiacMethods['pencolor'](self, *args) - def pendown(self,*args): + def pendown(self, *args): r'''From Giac's documentation: Help for pendown: pendown(NULL) @@ -11265,9 +11265,9 @@ cdef class GiacMethods_base: See also: 1/ leve_crayon 2/ crayon Ex1:pendown() ''' - return GiacMethods['pendown'](self,*args) + return GiacMethods['pendown'](self, *args) - def penup(self,*args): + def penup(self, *args): r'''From Giac's documentation: Help for penup: penup(NULL) @@ -11275,9 +11275,9 @@ cdef class GiacMethods_base: See also: 1/ baisse_crayon 2/ crayon Ex1:penup() ''' - return GiacMethods['penup'](self,*args) + return GiacMethods['penup'](self, *args) - def perimeter(self,*args): + def perimeter(self, *args): r'''From Giac's documentation: Help for perimeter: perimeter(Polygone) @@ -11288,9 +11288,9 @@ cdef class GiacMethods_base: Ex3:perimeter(circle(0,2)) Ex4:perimeter(0,1,i) ''' - return GiacMethods['perimeter'](self,*args) + return GiacMethods['perimeter'](self, *args) - def perimeterat(self,*args): + def perimeterat(self, *args): r'''From Giac's documentation: Help for perimeterat: perimeterat(Polygone, Pnt||Cplx(z0)) @@ -11302,9 +11302,9 @@ cdef class GiacMethods_base: Ex4: p:=polygon(0,1,i);perimeterat(p,1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);perimeterat(c,i) ''' - return GiacMethods['perimeterat'](self,*args) + return GiacMethods['perimeterat'](self, *args) - def perimeteratraw(self,*args): + def perimeteratraw(self, *args): r'''From Giac's documentation: Help for perimeteratraw: perimeteratraw(Polygone, Pnt||Cplx(z0)) @@ -11316,18 +11316,18 @@ cdef class GiacMethods_base: Ex4:perimeteratraw(polygon(0,1,i),1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);perimeteratraw(c,i) ''' - return GiacMethods['perimeteratraw'](self,*args) + return GiacMethods['perimeteratraw'](self, *args) - def periodic(self,*args): + def periodic(self, *args): r'''From Giac's documentation: Help for periodic: periodic(Expr,Var,a,b) Makes a periodic expression equal to Expr on a..b, period b-a. Ex1:periodic(x^2,x,-1,1) ''' - return GiacMethods['periodic'](self,*args) + return GiacMethods['periodic'](self, *args) - def perm(self,*args): + def perm(self, *args): r'''From Giac's documentation: Help for perm: perm(Intg(n),Intg(p)) @@ -11335,9 +11335,9 @@ cdef class GiacMethods_base: See also: 1/ comb 2/ factorial Ex1:perm(4,2) ''' - return GiacMethods['perm'](self,*args) + return GiacMethods['perm'](self, *args) - def perminv(self,*args): + def perminv(self, *args): r'''From Giac's documentation: Help for perminv: perminv(Permut(a)) @@ -11345,9 +11345,9 @@ cdef class GiacMethods_base: See also: 1/ cycleinv Ex1:perminv([1,3,2,4,0]) ''' - return GiacMethods['perminv'](self,*args) + return GiacMethods['perminv'](self, *args) - def permu2cycles(self,*args): + def permu2cycles(self, *args): r'''From Giac's documentation: Help for permu2cycles: permu2cycles(Permut) @@ -11356,9 +11356,9 @@ cdef class GiacMethods_base: Ex1:permu2cycles([0,2,1,3,5,4]) Ex2:permu2cycles([0,2,1,4,3,5]) ''' - return GiacMethods['permu2cycles'](self,*args) + return GiacMethods['permu2cycles'](self, *args) - def permu2mat(self,*args): + def permu2mat(self, *args): r'''From Giac's documentation: Help for permu2mat: permu2mat(Permut(p)) @@ -11366,9 +11366,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:permu2mat([1,3,2,4,0]) ''' - return GiacMethods['permu2mat'](self,*args) + return GiacMethods['permu2mat'](self, *args) - def permuorder(self,*args): + def permuorder(self, *args): r'''From Giac's documentation: Help for permuorder: permuorder(Permut(a)) @@ -11376,9 +11376,9 @@ cdef class GiacMethods_base: See also: 1/ cycles2permu Ex1:permuorder([1,3,2,4,0]) ''' - return GiacMethods['permuorder'](self,*args) + return GiacMethods['permuorder'](self, *args) - def permute_vertices(self,*args): + def permute_vertices(self, *args): r'''From Giac's documentation: Help for permute_vertices: permute_vertices(Graph(G),Lst(V)) @@ -11386,9 +11386,9 @@ cdef class GiacMethods_base: See also: 1/ graph_vertices 2/ isomorphic_copy 3/ relabel_vertices Ex1:permute_vertices(graph([a,b,c]),[a,c,b]) ''' - return GiacMethods['permute_vertices'](self,*args) + return GiacMethods['permute_vertices'](self, *args) - def perpen_bisector(self,*args): + def perpen_bisector(self, *args): r'''From Giac's documentation: Help for perpen_bisector: perpen_bisector((Pnt or Cplx),(Pnt or Cplx)) @@ -11397,9 +11397,9 @@ cdef class GiacMethods_base: Ex1:perpen_bisector(1-i,i) Ex2:perpen_bisector([0,0,0],[5,5,0]) ''' - return GiacMethods['perpen_bisector'](self,*args) + return GiacMethods['perpen_bisector'](self, *args) - def perpendicular(self,*args): + def perpendicular(self, *args): r'''From Giac's documentation: Help for perpendicular: perpendicular((Pnt or Line),(Line or Plan)) @@ -11410,9 +11410,9 @@ cdef class GiacMethods_base: Ex3:perpendicular([0,0,0],line(x=y,y=z)) Ex4:perpendicular(line([0,0,0],[1,1,0]),plane(x+y+z=1)) ''' - return GiacMethods['perpendicular'](self,*args) + return GiacMethods['perpendicular'](self, *args) - def petersen_graph(self,*args): + def petersen_graph(self, *args): r'''From Giac's documentation: Help for petersen_graph: petersen_graph(Intg(n),[Intg(k)]) @@ -11422,9 +11422,9 @@ cdef class GiacMethods_base: Ex2:petersen_graph(6,3) Ex3:petersen_graph(10,2) ''' - return GiacMethods['petersen_graph'](self,*args) + return GiacMethods['petersen_graph'](self, *args) - def peval(self,*args): + def peval(self, *args): r'''From Giac's documentation: Help for peval: peval(Vect,Real(x0)) @@ -11433,9 +11433,9 @@ cdef class GiacMethods_base: Ex1:peval([1,0,-2],1) Ex2:peval([1,2,-25,-26,120],8) ''' - return GiacMethods['peval'](self,*args) + return GiacMethods['peval'](self, *args) - def pi(self,*args): + def pi(self, *args): r'''From Giac's documentation: Help for pi: pi() @@ -11446,9 +11446,9 @@ cdef class GiacMethods_base: Ex3: evalf(pi) Ex4: evalf(Pi) ''' - return GiacMethods['pi'](self,*args) + return GiacMethods['pi'](self, *args) - def pie(self,*args): + def pie(self, *args): r'''From Giac's documentation: Help for pie: pie(Mtrx) @@ -11458,9 +11458,9 @@ cdef class GiacMethods_base: Ex2:pie([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:pie([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) ''' - return GiacMethods['pie'](self,*args) + return GiacMethods['pie'](self, *args) - def piecewise(self,*args): + def piecewise(self, *args): r'''From Giac's documentation: Help for piecewise: piecewise(Cond1,Expr1,..,Cond2p,Expr2p,[Expr2p+1]) @@ -11469,9 +11469,9 @@ cdef class GiacMethods_base: Ex1:piecewise(x<=-pi,x+2*pi,x<=pi,x,x+2*pi) Ex2:piecewise(x<-2,-2,x<-1,3x+4,x<0,1,x+1) ''' - return GiacMethods['piecewise'](self,*args) + return GiacMethods['piecewise'](self, *args) - def pivot(self,*args): + def pivot(self, *args): r'''From Giac's documentation: Help for pivot: pivot(Mtrx(A),Intg(nl),Intg(nc)) @@ -11480,9 +11480,9 @@ cdef class GiacMethods_base: Ex1:pivot([[1,2],[3,4],[5,6]],0,1) Ex2:pivot([[1,2],[3,4],[5,6]],1,1) ''' - return GiacMethods['pivot'](self,*args) + return GiacMethods['pivot'](self, *args) - def pixoff(self,*args): + def pixoff(self, *args): r'''From Giac's documentation: Help for pixoff: pixoff(Real(x),Real(y)) @@ -11490,9 +11490,9 @@ cdef class GiacMethods_base: See also: 1/ set_pixel 2/ pixon Ex1:pixoff(1,2) ''' - return GiacMethods['pixoff'](self,*args) + return GiacMethods['pixoff'](self, *args) - def pixon(self,*args): + def pixon(self, *args): r'''From Giac's documentation: Help for pixon: pixon(Real(x),Real(y)) @@ -11500,18 +11500,18 @@ cdef class GiacMethods_base: See also: 1/ set_pixel 2/ pixoff Ex1:pixon(1,2) ''' - return GiacMethods['pixon'](self,*args) + return GiacMethods['pixon'](self, *args) - def planar(self,*args): + def planar(self, *args): r'''From Giac's documentation: Help for planar: planar(Opt) Option for the draw_graph command. See also: 1/ spring 2/ tree 3/ draw_graph ''' - return GiacMethods['planar'](self,*args) + return GiacMethods['planar'](self, *args) - def plane(self,*args): + def plane(self, *args): r'''From Giac's documentation: Help for plane: plane(Pnt or Eq, [Pnt or Line],[Pnt]) @@ -11522,9 +11522,9 @@ cdef class GiacMethods_base: Ex3:plane(x+y+z=0) Ex4:plane(2*x+y-2*z-1) ''' - return GiacMethods['plane'](self,*args) + return GiacMethods['plane'](self, *args) - def plane_dual(self,*args): + def plane_dual(self, *args): r'''From Giac's documentation: Help for plane_dual: plane_dual(Graph(G)||Lst(F)) @@ -11532,9 +11532,9 @@ cdef class GiacMethods_base: See also: 1/ is_planar Ex1:plane_dual(hypercube_graph(3)) ''' - return GiacMethods['plane_dual'](self,*args) + return GiacMethods['plane_dual'](self, *args) - def playsnd(self,*args): + def playsnd(self, *args): r'''From Giac's documentation: Help for playsnd: playsnd(Vect) @@ -11542,18 +11542,18 @@ cdef class GiacMethods_base: See also: 1/ readwav 2/ writewav 3/ soundsec Ex1:playsnd(2^14*(sin(2*pi*440*soundsec(1))) ''' - return GiacMethods['playsnd'](self,*args) + return GiacMethods['playsnd'](self, *args) - def plex(self,*args): + def plex(self, *args): r'''From Giac's documentation: Help for plex: plex(Opt) Option of the gbasis or greduce command to specify an order for monomials (=default order=pure lexicographic). See also: 1/ gbasis 2/ greduce ''' - return GiacMethods['plex'](self,*args) + return GiacMethods['plex'](self, *args) - def plot(self,*args): + def plot(self, *args): r'''From Giac's documentation: Help for plot: plot((Expr or LstExpr),Var[=VarMin..VarMax],[color=LstColor]) @@ -11567,9 +11567,9 @@ cdef class GiacMethods_base: Ex6:plot(normald) Ex7:plot(normald(-1,2)) ''' - return GiacMethods['plot'](self,*args) + return GiacMethods['plot'](self, *args) - def plot3d(self,*args): + def plot3d(self, *args): r'''From Giac's documentation: Help for plot3d: plot3d(Expr||Lst(3*Expr),Var,Var) @@ -11581,9 +11581,9 @@ cdef class GiacMethods_base: Ex4:plot3d(f,-1..1,-2..2) Ex5:plot3d([f,g,h],-1..1,-2..2) ''' - return GiacMethods['plot3d'](self,*args) + return GiacMethods['plot3d'](self, *args) - def plotarea(self,*args): + def plotarea(self, *args): r'''From Giac's documentation: Help for plotarea: plotarea(Expr,x=a..b,[n],[Method]) @@ -11593,9 +11593,9 @@ cdef class GiacMethods_base: Ex2:plotarea(x^2,x=0..1,5,trapezoid) Ex3:plotarea(x^2,x=0..1,5,middle_point) ''' - return GiacMethods['plotarea'](self,*args) + return GiacMethods['plotarea'](self, *args) - def plotcdf(self,*args): + def plotcdf(self, *args): r'''From Giac's documentation: Help for plotcdf: plotcdf(Func,FuncParams) @@ -11605,9 +11605,9 @@ cdef class GiacMethods_base: Ex2:plotcdf(normald,0.0,1.0) Ex3:plotcdf([1,3,4,3,5,6]) ''' - return GiacMethods['plotcdf'](self,*args) + return GiacMethods['plotcdf'](self, *args) - def plotcontour(self,*args): + def plotcontour(self, *args): r'''From Giac's documentation: Help for plotcontour: plotcontour(Expr(Xpr),[LstVar],[LstVal]) @@ -11618,9 +11618,9 @@ cdef class GiacMethods_base: Ex3:plotcontour(x^2+2*y^2-2,[x,y],[1.0,2.0,3.0]) Ex4:plotcontour(x^2-y^2,[x=-4..4,y=-4..4],seq(k,k,-11,11,3),xstep=0.1,ystep=0.1) ''' - return GiacMethods['plotcontour'](self,*args) + return GiacMethods['plotcontour'](self, *args) - def plotdensity(self,*args): + def plotdensity(self, *args): r'''From Giac's documentation: Help for plotdensity: plotdensity(Expr,[x=xrange,y=yrange],[z],[xstep],[ystep]) @@ -11629,9 +11629,9 @@ cdef class GiacMethods_base: Ex1:plotdensity(x^2-y^2,[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex2:plotdensity(x^2-y^2,[x=-2..2,y=-2..2],z=-2..2,xstep=0.1,ystep=0.1) ''' - return GiacMethods['plotdensity'](self,*args) + return GiacMethods['plotdensity'](self, *args) - def plotfield(self,*args): + def plotfield(self, *args): r'''From Giac's documentation: Help for plotfield: plotfield(Expr,VectVar,[Opt]) @@ -11643,9 +11643,9 @@ cdef class GiacMethods_base: Ex4:plotfield(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) Ex5:plotfield(-t*y,[t=-6.868..6.868,y=-6.868..6.868],normalize) ''' - return GiacMethods['plotfield'](self,*args) + return GiacMethods['plotfield'](self, *args) - def plotfunc(self,*args): + def plotfunc(self, *args): r'''From Giac's documentation: Help for plotfunc: plotfunc(Expr,[Var(x) or VectVar] ,[Intg(color)]) @@ -11657,9 +11657,9 @@ cdef class GiacMethods_base: Ex4:plotfunc(x^2+y^2,[x=-1..1,y=-2..2],nstep=900) Ex5:plotfunc((x+i*y)^2,[x=-1..1,y=-2..2],nstep=900,affichage=rempli) ''' - return GiacMethods['plotfunc'](self,*args) + return GiacMethods['plotfunc'](self, *args) - def plotimplicit(self,*args): + def plotimplicit(self, *args): r'''From Giac's documentation: Help for plotimplicit: plotimplicit(Expr,Var1,Var2) @@ -11675,9 +11675,9 @@ cdef class GiacMethods_base: Ex8:plotimplicit((x+5)^2+(y+4)^2-1,x=-6..-4,y=-5..-3) Ex9:plotimplicit((x+5)^2+(y+4)^2-1,[x=-6..-4,y=-5..-3]) ''' - return GiacMethods['plotimplicit'](self,*args) + return GiacMethods['plotimplicit'](self, *args) - def plotinequation(self,*args): + def plotinequation(self, *args): r'''From Giac's documentation: Help for plotinequation: plotinequation(Expr,[x=xrange,y=yrange],[xstep],[ystep]) @@ -11688,9 +11688,9 @@ cdef class GiacMethods_base: Ex3:plotinequation(3-(x^2-y^2),[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex4:plotinequation([x+y>3,x^2x>=5,[1,2,6,7]) Ex2:remove(5,[1,2,5,6,7,5]) ''' - return GiacMethods['remove'](self,*args) + return GiacMethods['remove'](self, *args) - def reorder(self,*args): + def reorder(self, *args): r'''From Giac's documentation: Help for reorder: reorder(Expr, LstVar) @@ -13475,9 +13475,9 @@ cdef class GiacMethods_base: Ex1:reorder(-2) Ex2:reorder(x^2+2*x+y^2,[y,x]) ''' - return GiacMethods['reorder'](self,*args) + return GiacMethods['reorder'](self, *args) - def resample(self,*args): + def resample(self, *args): r'''From Giac's documentation: Help for resample: resample(Lst(clip),[Intg(s),[Intg(q)]]) @@ -13486,9 +13486,9 @@ cdef class GiacMethods_base: Ex1:resample(readwav("/some/file"),48000) Ex2:resample(readwav("/some/file"),48000,3) ''' - return GiacMethods['resample'](self,*args) + return GiacMethods['resample'](self, *args) - def residue(self,*args): + def residue(self, *args): r'''From Giac's documentation: Help for residue: residue(Expr,Var(v),Cplx(a)) @@ -13499,9 +13499,9 @@ cdef class GiacMethods_base: Ex3:residue(cos(z)/(z*(z-b)),z,0) Ex4:residue(c/(z*(z-b)),z=b) ''' - return GiacMethods['residue'](self,*args) + return GiacMethods['residue'](self, *args) - def resoudre(self,*args): + def resoudre(self, *args): r'''From Giac's documentation: Help for resoudre: resoudre(Expr,[Var]) @@ -13512,9 +13512,9 @@ cdef class GiacMethods_base: Ex3:resoudre([y-z=0,z-x=0,x-y=0,x-1+y+z=0],[x,y,z]) Ex4:resoudre([x^2-y^2=0,x^2-z^2=0],[x,y,z]) ''' - return GiacMethods['resoudre'](self,*args) + return GiacMethods['resoudre'](self, *args) - def resoudre_dans_C(self,*args): + def resoudre_dans_C(self, *args): r'''From Giac's documentation: Help for resoudre_dans_C: resoudre_dans_C(LstEq,LstVar) @@ -13525,9 +13525,9 @@ cdef class GiacMethods_base: Ex3:resoudre_dans_C(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:resoudre_dans_C(u*v-u=v and v^2=u,[u,v]) ''' - return GiacMethods['resoudre_dans_C'](self,*args) + return GiacMethods['resoudre_dans_C'](self, *args) - def resoudre_systeme_lineaire(self,*args): + def resoudre_systeme_lineaire(self, *args): r'''From Giac's documentation: Help for resoudre_systeme_lineaire: resoudre_systeme_lineaire(LstLinEq,LstVar) @@ -13543,9 +13543,9 @@ cdef class GiacMethods_base: Ex8: p,l,u:=lu([[2,1,1],[1,1,2],[1,2,1]]);linsolve(p,l,u,[1,1,4]) Ex9: a:=[[100,2],[2,100]];linsolve(evalf(a),[0,1]); ''' - return GiacMethods['resoudre_systeme_lineaire'](self,*args) + return GiacMethods['resoudre_systeme_lineaire'](self, *args) - def resultant(self,*args): + def resultant(self, *args): r'''From Giac's documentation: Help for resultant: resultant(Poly,Poly,Var) @@ -13554,9 +13554,9 @@ cdef class GiacMethods_base: Ex1:resultant(x^2-1,x^3-1,x) Ex2:resultant(x^3-p*x+q,3*x^2-p,x) ''' - return GiacMethods['resultant'](self,*args) + return GiacMethods['resultant'](self, *args) - def reverse(self,*args): + def reverse(self, *args): r'''From Giac's documentation: Help for reverse: reverse(Lst(L)) @@ -13566,9 +13566,9 @@ cdef class GiacMethods_base: Ex3: L:=[1,2,3,4];L.revlist() Ex4: L:=[1,2,3,4];L.reverse() ''' - return GiacMethods['reverse'](self,*args) + return GiacMethods['reverse'](self, *args) - def reverse_graph(self,*args): + def reverse_graph(self, *args): r'''From Giac's documentation: Help for reverse_graph: reverse_graph(Graph(G)) @@ -13576,9 +13576,9 @@ cdef class GiacMethods_base: See also: 1/ digraph Ex1:reverse_graph(digraph(%{[1,2],[1,3],[2,3]%})) ''' - return GiacMethods['reverse_graph'](self,*args) + return GiacMethods['reverse_graph'](self, *args) - def reverse_rsolve(self,*args): + def reverse_rsolve(self, *args): r'''From Giac's documentation: Help for reverse_rsolve: reverse_rsolve(Vect(v)) @@ -13586,9 +13586,9 @@ cdef class GiacMethods_base: See also: 1/ rsolve Ex1:reverse_rsolve([1,-1,3,3]) ''' - return GiacMethods['reverse_rsolve'](self,*args) + return GiacMethods['reverse_rsolve'](self, *args) - def revert(self,*args): + def revert(self, *args): r'''From Giac's documentation: Help for revert: revert(Expr) @@ -13596,18 +13596,18 @@ cdef class GiacMethods_base: See also: 1/ series Ex1:revert(x+x^2+x^4) ''' - return GiacMethods['revert'](self,*args) + return GiacMethods['revert'](self, *args) - def revlex(self,*args): + def revlex(self, *args): r'''From Giac's documentation: Help for revlex: revlex(Opt) Option of the gbasis or greduce command to specify an order for monomials (complete degree then inverse lexicographic order). See also: 1/ gbasis 2/ greduce ''' - return GiacMethods['revlex'](self,*args) + return GiacMethods['revlex'](self, *args) - def revlist(self,*args): + def revlist(self, *args): r'''From Giac's documentation: Help for revlist: revlist(Lst(L)) @@ -13617,9 +13617,9 @@ cdef class GiacMethods_base: Ex3: L:=[1,2,3,4];L.revlist() Ex4: L:=[1,2,3,4];L.reverse() ''' - return GiacMethods['revlist'](self,*args) + return GiacMethods['revlist'](self, *args) - def rgb(self,*args): + def rgb(self, *args): r'''From Giac's documentation: Help for rgb: rgb(Opt) @@ -13632,9 +13632,9 @@ cdef class GiacMethods_base: Ex5: F:=display(square(0,2+i),filled+rgb(rand(),rand(),rand())) Ex6: L:=rand(),rand(),rand();affichage(square(0,2+i),rgb(L)+rempli);legend(0.2,[L]) ''' - return GiacMethods['rgb'](self,*args) + return GiacMethods['rgb'](self, *args) - def rhombus(self,*args): + def rhombus(self, *args): r'''From Giac's documentation: Help for rhombus: rhombus(Pnt(A)||Cplx,Pnt(B)||Cplx,Angle(a)||Pnt(P)||Lst(P,a)),[Var(C)],[Var(D)]) @@ -13646,9 +13646,9 @@ cdef class GiacMethods_base: Ex4:rhombus(point(0,0,0),point(3,3,3),point(0,0,3),C,D) Ex5:rhombus(point(0,0,0),point(3,3,3),[point(0,0,3),pi/4],C,D) ''' - return GiacMethods['rhombus'](self,*args) + return GiacMethods['rhombus'](self, *args) - def rhombus_point(self,*args): + def rhombus_point(self, *args): r'''From Giac's documentation: Help for rhombus_point: rhombus_point(Opt) @@ -13657,9 +13657,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) ''' - return GiacMethods['rhombus_point'](self,*args) + return GiacMethods['rhombus_point'](self, *args) - def rhs(self,*args): + def rhs(self, *args): r'''From Giac's documentation: Help for rhs: rhs(Equal(a=b) or Interval(a..b) or Str,Intg) @@ -13670,9 +13670,9 @@ cdef class GiacMethods_base: Ex3:rhs(1..5) Ex4:rhs("abcdefg",3) ''' - return GiacMethods['rhs'](self,*args) + return GiacMethods['rhs'](self, *args) - def riemann_window(self,*args): + def riemann_window(self, *args): r'''From Giac's documentation: Help for riemann_window: riemann_window(Lst,[Interval(n1..n2)]) @@ -13680,9 +13680,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ bartlett_hann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(riemann_window(randvector(1000,0..1))) ''' - return GiacMethods['riemann_window'](self,*args) + return GiacMethods['riemann_window'](self, *args) - def right(self,*args): + def right(self, *args): r'''From Giac's documentation: Help for right: right(Equal(a=b) or Interval(a..b) or Str,Intg) @@ -13693,9 +13693,9 @@ cdef class GiacMethods_base: Ex3:right(1..5) Ex4:right("abcdefg",3) ''' - return GiacMethods['right'](self,*args) + return GiacMethods['right'](self, *args) - def right_rectangle(self,*args): + def right_rectangle(self, *args): r'''From Giac's documentation: Help for right_rectangle: right_rectangle(Opt) @@ -13708,9 +13708,9 @@ cdef class GiacMethods_base: Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) ''' - return GiacMethods['right_rectangle'](self,*args) + return GiacMethods['right_rectangle'](self, *args) - def right_triangle(self,*args): + def right_triangle(self, *args): r'''From Giac's documentation: Help for right_triangle: right_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Real(k) or Pnt(P) or Lst(P,k)),[Var(C)]) @@ -13722,9 +13722,9 @@ cdef class GiacMethods_base: Ex4:right_triangle(point(0,0,0),point(3,3,3),[point(0,0,3),1/2],C) Ex5:right_triangle(point(0,0,0),point(3,3,3),[point(0,0,3),1/2],C) ''' - return GiacMethods['right_triangle'](self,*args) + return GiacMethods['right_triangle'](self, *args) - def risch(self,*args): + def risch(self, *args): r'''From Giac's documentation: Help for risch: risch(Expr,[Var]) @@ -13734,9 +13734,9 @@ cdef class GiacMethods_base: Ex2:risch(ln(x)) Ex3:risch(exp(x^2),x) ''' - return GiacMethods['risch'](self,*args) + return GiacMethods['risch'](self, *args) - def rm_a_z(self,*args): + def rm_a_z(self, *args): r'''From Giac's documentation: Help for rm_a_z: rm_a_z(NULL) @@ -13744,9 +13744,9 @@ cdef class GiacMethods_base: See also: 1/ rm_all_vars Ex1:rm_a_z() ''' - return GiacMethods['rm_a_z'](self,*args) + return GiacMethods['rm_a_z'](self, *args) - def rm_all_vars(self,*args): + def rm_all_vars(self, *args): r'''From Giac's documentation: Help for rm_all_vars: rm_all_vars(NULL) @@ -13754,9 +13754,9 @@ cdef class GiacMethods_base: See also: 1/ rm_a_z Ex1:rm_all_vars() ''' - return GiacMethods['rm_all_vars'](self,*args) + return GiacMethods['rm_all_vars'](self, *args) - def rmbreakpoint(self,*args): + def rmbreakpoint(self, *args): r'''From Giac's documentation: Help for rmbreakpoint: rmbreakpoint(Intg) @@ -13764,9 +13764,9 @@ cdef class GiacMethods_base: See also: 1/ breakpoint Ex1:rmbreakpoint(1) ''' - return GiacMethods['rmbreakpoint'](self,*args) + return GiacMethods['rmbreakpoint'](self, *args) - def rmmod(self,*args): + def rmmod(self, *args): r'''From Giac's documentation: Help for rmmod: rmmod(Str(pwd)) @@ -13774,9 +13774,9 @@ cdef class GiacMethods_base: See also: 1/ lsmod 2/ insmod Ex1:rmmod("/home/parisse/giac/src/libprogfr.so") ''' - return GiacMethods['rmmod'](self,*args) + return GiacMethods['rmmod'](self, *args) - def rmwatch(self,*args): + def rmwatch(self, *args): r'''From Giac's documentation: Help for rmwatch: rmwatch(Var) @@ -13784,9 +13784,9 @@ cdef class GiacMethods_base: See also: 1/ watch Ex1:rmwatch(a) ''' - return GiacMethods['rmwatch'](self,*args) + return GiacMethods['rmwatch'](self, *args) - def romberg(self,*args): + def romberg(self, *args): r'''From Giac's documentation: Help for romberg: romberg(Expr(f(x)),Var(x),Real(a),Real(b)) @@ -13796,9 +13796,9 @@ cdef class GiacMethods_base: Ex2:romberg(x^2,x,0,1) Ex3:romberg(exp(-x^2),x,-1,1) ''' - return GiacMethods['romberg'](self,*args) + return GiacMethods['romberg'](self, *args) - def rombergm(self,*args): + def rombergm(self, *args): r'''From Giac's documentation: Help for rombergm: rombergm(Opt) @@ -13809,9 +13809,9 @@ cdef class GiacMethods_base: Ex3: area(x^2,x=0..1,5,rombergm) Ex4:rombergm(area(x^2,x=0..1,5,gauss15)) ''' - return GiacMethods['rombergm'](self,*args) + return GiacMethods['rombergm'](self, *args) - def rombergt(self,*args): + def rombergt(self, *args): r'''From Giac's documentation: Help for rombergt: rombergt(Opt) @@ -13822,9 +13822,9 @@ cdef class GiacMethods_base: Ex3: area(x^2,x=0..1,5,rombergm) Ex4:rombergt(area(x^2,x=0..1,5,gauss15)) ''' - return GiacMethods['rombergt'](self,*args) + return GiacMethods['rombergt'](self, *args) - def rond(self,*args): + def rond(self, *args): r'''From Giac's documentation: Help for rond: rond(Real(r),[Real(a)],[Real(b)]) @@ -13835,9 +13835,9 @@ cdef class GiacMethods_base: Ex3:rond(40,90) Ex4:rond(40,10,100) ''' - return GiacMethods['rond'](self,*args) + return GiacMethods['rond'](self, *args) - def root(self,*args): + def root(self, *args): r'''From Giac's documentation: Help for root: root(Expr(a),Expr(b)) @@ -13848,9 +13848,9 @@ cdef class GiacMethods_base: Ex3:root(3,1.2) Ex4:root(3.2,1.2) ''' - return GiacMethods['root'](self,*args) + return GiacMethods['root'](self, *args) - def rootof(self,*args): + def rootof(self, *args): r'''From Giac's documentation: Help for rootof: rootof(LstPoly(P),LstPoly(Q)) @@ -13860,9 +13860,9 @@ cdef class GiacMethods_base: Ex2: normal(1/rootof([1,0,0],[1,1,0,-1])) Ex3: rootof(x^4+x+1):='j'; normal(j^5); ''' - return GiacMethods['rootof'](self,*args) + return GiacMethods['rootof'](self, *args) - def roots(self,*args): + def roots(self, *args): r'''From Giac's documentation: Help for roots: roots(Poly,[Var]) @@ -13871,9 +13871,9 @@ cdef class GiacMethods_base: Ex1:roots(t^3-1,t) Ex2:roots(x^5-2*x^4+x^3) ''' - return GiacMethods['roots'](self,*args) + return GiacMethods['roots'](self, *args) - def rotate(self,*args): + def rotate(self, *args): r'''From Giac's documentation: Help for rotate: rotate(Lst||Str(L),[Intg(n)]) @@ -13888,9 +13888,9 @@ cdef class GiacMethods_base: Ex7: L:=[0,1,2,3];L:=rotate([0,1,2,3],2) Ex8: L:=[0,1,2,3];L.rotate(2) ''' - return GiacMethods['rotate'](self,*args) + return GiacMethods['rotate'](self, *args) - def rotation(self,*args): + def rotation(self, *args): r'''From Giac's documentation: Help for rotation: rotation((Pnt(B) or Cplx or Dr3),Angle(a1),(Pnt(A) or Curve)) @@ -13902,9 +13902,9 @@ cdef class GiacMethods_base: Ex4: r:=rotation(1+i,pi/2);r(i) Ex5: r:=rotation(line(x=y,y=z),pi/2);r(point(1,-1,2)) ''' - return GiacMethods['rotation'](self,*args) + return GiacMethods['rotation'](self, *args) - def round(self,*args): + def round(self, *args): r'''From Giac's documentation: Help for round: round(Real or Cplx,[Intg(n)]) @@ -13916,9 +13916,9 @@ cdef class GiacMethods_base: Ex4:round(1.237,2) Ex5:round(sqrt(2)+i*sqrt(5),4) ''' - return GiacMethods['round'](self,*args) + return GiacMethods['round'](self, *args) - def row(self,*args): + def row(self, *args): r'''From Giac's documentation: Help for row: row(Mtrx(A),Intg(n)||Interval(n1..n2)) @@ -13928,9 +13928,9 @@ cdef class GiacMethods_base: Ex2:row([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3: count_eq(3,[[1,2,3],[4,3,2],[3,2,1]],row) ''' - return GiacMethods['row'](self,*args) + return GiacMethods['row'](self, *args) - def rowAdd(self,*args): + def rowAdd(self, *args): r'''From Giac's documentation: Help for rowAdd: rowAdd(Mtrx(A),Intg(n1),Intg(n2)) @@ -13938,9 +13938,9 @@ cdef class GiacMethods_base: See also: 1/ rowSwap Ex1:rowAdd([[1,2],[3,4],[5,6]],1,2) ''' - return GiacMethods['rowAdd'](self,*args) + return GiacMethods['rowAdd'](self, *args) - def rowDim(self,*args): + def rowDim(self, *args): r'''From Giac's documentation: Help for rowDim: rowDim(Mtrx) @@ -13949,9 +13949,9 @@ cdef class GiacMethods_base: Ex1:rowDim([[1,2,3],[4,5,6]]) Ex2:rowDim([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['rowDim'](self,*args) + return GiacMethods['rowDim'](self, *args) - def rowNorm(self,*args): + def rowNorm(self, *args): r'''From Giac's documentation: Help for rowNorm: rowNorm(Vect or Mtrx) @@ -13960,9 +13960,9 @@ cdef class GiacMethods_base: Ex1:rowNorm([[1,2],[3,-4]]) Ex2:rowNorm([[1,2,3,-4],[-5,3,2,1]]) ''' - return GiacMethods['rowNorm'](self,*args) + return GiacMethods['rowNorm'](self, *args) - def rowSwap(self,*args): + def rowSwap(self, *args): r'''From Giac's documentation: Help for rowSwap: rowSwap(Mtrx(A),Intg(n1),Intg(n2)) @@ -13970,9 +13970,9 @@ cdef class GiacMethods_base: See also: 1/ rowAdd 2/ colSwap Ex1:rowSwap([[1,2],[3,4],[5,6]],1,2) ''' - return GiacMethods['rowSwap'](self,*args) + return GiacMethods['rowSwap'](self, *args) - def rowdim(self,*args): + def rowdim(self, *args): r'''From Giac's documentation: Help for rowdim: rowdim(Mtrx) @@ -13981,9 +13981,9 @@ cdef class GiacMethods_base: Ex1:rowdim([[1,2,3],[4,5,6]]) Ex2:rowdim([[1,2],[3,4],[5,6]]) ''' - return GiacMethods['rowdim'](self,*args) + return GiacMethods['rowdim'](self, *args) - def rownorm(self,*args): + def rownorm(self, *args): r'''From Giac's documentation: Help for rownorm: rownorm(Vect or Mtrx) @@ -13992,9 +13992,9 @@ cdef class GiacMethods_base: Ex1:rownorm([[1,2],[3,-4]]) Ex2:rownorm([[1,2,3,-4],[-5,3,2,1]]) ''' - return GiacMethods['rownorm'](self,*args) + return GiacMethods['rownorm'](self, *args) - def rowspace(self,*args): + def rowspace(self, *args): r'''From Giac's documentation: Help for rowspace: rowspace(Mtrx(A), [Var(d)]) @@ -14003,9 +14003,9 @@ cdef class GiacMethods_base: Ex1:rowspace([[1,2,3],[1,2,3],[1,2,4],[1,2,5]]) Ex2:rowspace([[1,2,3],[1,3,6],[2,5,9]],d) ''' - return GiacMethods['rowspace'](self,*args) + return GiacMethods['rowspace'](self, *args) - def rowswap(self,*args): + def rowswap(self, *args): r'''From Giac's documentation: Help for rowswap: rowswap(Mtrx(A),Intg(n1),Intg(n2)) @@ -14013,9 +14013,9 @@ cdef class GiacMethods_base: See also: 1/ rowAdd 2/ colSwap Ex1:rowswap([[1,2],[3,4],[5,6]],1,2) ''' - return GiacMethods['rowswap'](self,*args) + return GiacMethods['rowswap'](self, *args) - def rref(self,*args): + def rref(self, *args): r'''From Giac's documentation: Help for rref: rref(Mtrx(M),[Intg(k)]||Opt) @@ -14026,9 +14026,9 @@ cdef class GiacMethods_base: Ex3:rref([[2,1,1,-1],[1,1,2,-1],[1,2,1,-4]],2) Ex4:rref([[1,1,0,0,-a1],[0,1,1,0,-a2],[0,0,1,1,-a3],[1,0,0,1,-a4]],keep_pivot) ''' - return GiacMethods['rref'](self,*args) + return GiacMethods['rref'](self, *args) - def rsolve(self,*args): + def rsolve(self, *args): r'''From Giac's documentation: Help for rsolve: rsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal)) @@ -14040,9 +14040,9 @@ cdef class GiacMethods_base: Ex4:rsolve(u(n+2)=u(n)+2*u(n+1)+n+1,u(n),[u(0)=0,u(1)=1]) Ex5:rsolve([u(n+1)=3*v(n)+u(n),v(n+1)=v(n)+u(n)],[u(n),v(n)],[u(0)=1,v(0)=2]) ''' - return GiacMethods['rsolve'](self,*args) + return GiacMethods['rsolve'](self, *args) - def same(self,*args): + def same(self, *args): r'''From Giac's documentation: Help for same: same(Expr,Expr) @@ -14051,9 +14051,9 @@ cdef class GiacMethods_base: Ex1:same(a,b) Ex2:same((2-1)^2,2^2-2*2+1) ''' - return GiacMethods['same'](self,*args) + return GiacMethods['same'](self, *args) - def sample(self,*args): + def sample(self, *args): r'''From Giac's documentation: Help for sample: sample(Lst(L),Intg(n)) @@ -14066,9 +14066,9 @@ cdef class GiacMethods_base: Ex5: L:=[1,2,3,4,5,6];L.sample(3) Ex6: ''' - return GiacMethods['sample'](self,*args) + return GiacMethods['sample'](self, *args) - def samplerate(self,*args): + def samplerate(self, *args): r'''From Giac's documentation: Help for samplerate: samplerate(Lst(clip)) @@ -14076,9 +14076,9 @@ cdef class GiacMethods_base: See also: 1/ bit_depth 2/ channels 3/ channel_data 4/ duration Ex1:samplerate(readwav("/some/file")) ''' - return GiacMethods['samplerate'](self,*args) + return GiacMethods['samplerate'](self, *args) - def sans_factoriser(self,*args): + def sans_factoriser(self, *args): r'''From Giac's documentation: Help for sans_factoriser: sans_factoriser(Opt.) @@ -14090,9 +14090,9 @@ cdef class GiacMethods_base: Ex4: plotimplicit(x^2+y^2+z^2-1,[x,y,z],xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex5: plotimplicit(x^2+y^2+z^2-1,x=0..1,y=0..1,z=0..1,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) ''' - return GiacMethods['sans_factoriser'](self,*args) + return GiacMethods['sans_factoriser'](self, *args) - def saute(self,*args): + def saute(self, *args): r'''From Giac's documentation: Help for saute: saute(NULL or Real(n)) @@ -14101,9 +14101,9 @@ cdef class GiacMethods_base: Ex1: saute 30 Ex2:saute(30) ''' - return GiacMethods['saute'](self,*args) + return GiacMethods['saute'](self, *args) - def scalarProduct(self,*args): + def scalarProduct(self, *args): r'''From Giac's documentation: Help for scalarProduct: scalarProduct(Vect(v1),Vect(v2)) @@ -14113,9 +14113,9 @@ cdef class GiacMethods_base: Ex2:scalarProduct([3,2,4],[3,2,4]) Ex3:scalarProduct([[1,2],[3,4]],[[3,2],[4,5]]) ''' - return GiacMethods['scalarProduct'](self,*args) + return GiacMethods['scalarProduct'](self, *args) - def scalar_product(self,*args): + def scalar_product(self, *args): r'''From Giac's documentation: Help for scalar_product: scalar_product(Vect(v1),Vect(v2)) @@ -14125,9 +14125,9 @@ cdef class GiacMethods_base: Ex2:scalar_product([3,2,4],[3,2,4]) Ex3:scalar_product([[1,2],[3,4]],[[3,2],[4,5]]) ''' - return GiacMethods['scalar_product'](self,*args) + return GiacMethods['scalar_product'](self, *args) - def scatterplot(self,*args): + def scatterplot(self, *args): r'''From Giac's documentation: Help for scatterplot: scatterplot(Mtrx) @@ -14135,9 +14135,9 @@ cdef class GiacMethods_base: See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot Ex1:scatterplot([[1,2,3],[2,0,1],[-1,2,3]]) ''' - return GiacMethods['scatterplot'](self,*args) + return GiacMethods['scatterplot'](self, *args) - def schur(self,*args): + def schur(self, *args): r'''From Giac's documentation: Help for schur: schur(Mtrx(A)) @@ -14146,9 +14146,9 @@ cdef class GiacMethods_base: Ex1:schur([[1,2,3],[4,5,6],[7,8,1]]) Ex2:schur([[1,2,3,4],[4,5,6,7],[7,8,9,0],[0,1,2,3]]) ''' - return GiacMethods['schur'](self,*args) + return GiacMethods['schur'](self, *args) - def sec(self,*args): + def sec(self, *args): r'''From Giac's documentation: Help for sec: sec(Expr) @@ -14156,9 +14156,9 @@ cdef class GiacMethods_base: See also: 1/ cos 2/ asec Ex1:sec(pi/3) ''' - return GiacMethods['sec'](self,*args) + return GiacMethods['sec'](self, *args) - def secant_solver(self,*args): + def secant_solver(self, *args): r'''From Giac's documentation: Help for secant_solver: secant_solver(Opt) @@ -14171,9 +14171,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['secant_solver'](self,*args) + return GiacMethods['secant_solver'](self, *args) - def segment(self,*args): + def segment(self, *args): r'''From Giac's documentation: Help for segment: segment((Pnt or Cplx or Lst([xM,yM])),(Pnt or Cplx or Lst([xN,yN]),[Var],[Var] or Opt) @@ -14187,9 +14187,9 @@ cdef class GiacMethods_base: Ex6: arc(i,1,pi/4,segment) Ex7: affichage( arc(i,1,pi/4,segment),1+rempli) ''' - return GiacMethods['segment'](self,*args) + return GiacMethods['segment'](self, *args) - def seidel_spectrum(self,*args): + def seidel_spectrum(self, *args): r'''From Giac's documentation: Help for seidel_spectrum: seidel_spectrum(Graph(G)) @@ -14197,9 +14197,9 @@ cdef class GiacMethods_base: See also: 1/ graph_spectrum Ex1:seidel_spectrum(graph("clebsch")) ''' - return GiacMethods['seidel_spectrum'](self,*args) + return GiacMethods['seidel_spectrum'](self, *args) - def seidel_switch(self,*args): + def seidel_switch(self, *args): r'''From Giac's documentation: Help for seidel_switch: seidel_switch(Graph(G),Lst(V)) @@ -14207,9 +14207,9 @@ cdef class GiacMethods_base: See also: 1/ neighbors 2/ graph_complement Ex1:seidel_switch(cycle_graph(5),[1,2]) ''' - return GiacMethods['seidel_switch'](self,*args) + return GiacMethods['seidel_switch'](self, *args) - def select(self,*args): + def select(self, *args): r'''From Giac's documentation: Help for select: select(FncBool(f),Lst(l)) @@ -14218,9 +14218,9 @@ cdef class GiacMethods_base: Ex1:select(x->x>=5,[1,2,6,7]) Ex2:select(x->isprime(x),range(20)).^2 ''' - return GiacMethods['select'](self,*args) + return GiacMethods['select'](self, *args) - def semi_augment(self,*args): + def semi_augment(self, *args): r'''From Giac's documentation: Help for semi_augment: semi_augment(Mtrx(A),Mtrx(B)) @@ -14228,9 +14228,9 @@ cdef class GiacMethods_base: See also: 1/ augment Ex1:semi_augment([[68,-21],[56,59],[1,2]],[[68,-21],[56,59]]) ''' - return GiacMethods['semi_augment'](self,*args) + return GiacMethods['semi_augment'](self, *args) - def seq(self,*args): + def seq(self, *args): r'''From Giac's documentation: Help for seq: seq(Expr(Xpr),Var(Var)=Int(a..b),[Real(p)]||Expr(Xpr),Var(Var),Real(a),Real(b),[Real(p)]) @@ -14248,9 +14248,9 @@ cdef class GiacMethods_base: Ex10: [seq(0.3..2,0.2)] Ex11: a:=(1,2,3);eval(seq(a,4)) ''' - return GiacMethods['seq'](self,*args) + return GiacMethods['seq'](self, *args) - def seqplot(self,*args): + def seqplot(self, *args): r'''From Giac's documentation: Help for seqplot: seqplot(Expr(f(Var)),Var=[a,xm,xM],Intg(p)) @@ -14260,9 +14260,9 @@ cdef class GiacMethods_base: Ex2:seqplot(sqrt(2+t),t=6,5) Ex3:seqplot(sqrt(2+x),x=[6,1,7],5,affichage=epaisseur_ligne_2) ''' - return GiacMethods['seqplot'](self,*args) + return GiacMethods['seqplot'](self, *args) - def seqsolve(self,*args): + def seqsolve(self, *args): r'''From Giac's documentation: Help for seqsolve: seqsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal)) @@ -14275,9 +14275,9 @@ cdef class GiacMethods_base: Ex5:seqsolve([x+2*y,n+1+x],[x,y,n],[0,1]) Ex6:seqsolve([x+2*y+n+1,x],[x,y,n],[0,1]) ''' - return GiacMethods['seqsolve'](self,*args) + return GiacMethods['seqsolve'](self, *args) - def sequence_graph(self,*args): + def sequence_graph(self, *args): r'''From Giac's documentation: Help for sequence_graph: sequence_graph(Lst(L)) @@ -14285,9 +14285,9 @@ cdef class GiacMethods_base: See also: 1/ degree_sequence 2/ is_graphic_sequence Ex1:sequence_graph(degree_sequence(sequence_graph([3,2,4,2,3,4,5,7]))) ''' - return GiacMethods['sequence_graph'](self,*args) + return GiacMethods['sequence_graph'](self, *args) - def series(self,*args): + def series(self, *args): r'''From Giac's documentation: Help for series: series(Expr,Equal(var=limit_point),[Order],[Dir(1,0,-1)]) @@ -14307,9 +14307,9 @@ cdef class GiacMethods_base: Ex12:series(subst(sin(x+y)+cos(y*x),[x,y],h*[x,y]),h=0,6,polynom)(h=1) Ex13: truncate(series(sin(x),x=0,6),6) ''' - return GiacMethods['series'](self,*args) + return GiacMethods['series'](self, *args) - def set_edge_attribute(self,*args): + def set_edge_attribute(self, *args): r'''From Giac's documentation: Help for set_edge_attribute: set_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) @@ -14317,9 +14317,9 @@ cdef class GiacMethods_base: See also: 1/ discard_edge_attribute 2/ get_edge_attribute 3/ list_edge_attributes Ex1:set_edge_attribute(cycle_graph(3),[1,2],"cost"=12.4) ''' - return GiacMethods['set_edge_attribute'](self,*args) + return GiacMethods['set_edge_attribute'](self, *args) - def set_edge_weight(self,*args): + def set_edge_weight(self, *args): r'''From Giac's documentation: Help for set_edge_weight: set_edge_weight(Graph(G),Edge(e),Real(w)) @@ -14327,9 +14327,9 @@ cdef class GiacMethods_base: See also: 1/ is_weighted 2/ get_edge_weight 3/ make_weighted 4/ weight_matrix Ex1:set_edge_weight(graph(%{[1,2],[2,3]%}),[1,2],5) ''' - return GiacMethods['set_edge_weight'](self,*args) + return GiacMethods['set_edge_weight'](self, *args) - def set_graph_attribute(self,*args): + def set_graph_attribute(self, *args): r'''From Giac's documentation: Help for set_graph_attribute: set_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) @@ -14337,9 +14337,9 @@ cdef class GiacMethods_base: See also: 1/ discard_graph_attribute 2/ get_graph_attribute 3/ list_graph_attributes Ex1:set_graph_attribute(cycle_graph(3),"name"="cycle graph") ''' - return GiacMethods['set_graph_attribute'](self,*args) + return GiacMethods['set_graph_attribute'](self, *args) - def set_pixel(self,*args): + def set_pixel(self, *args): r'''From Giac's documentation: Help for set_pixel: set_pixel(Intg(x),Intg(y),Intg(col)) @@ -14347,9 +14347,9 @@ cdef class GiacMethods_base: See also: 1/ clear 2/ show_pixels 3/ draw_line 4/ draw_rectangle 5/ draw_polygon Ex1: clear(); set_pixel(4); draw_pixel(1,2,red); show_pixels(); ''' - return GiacMethods['set_pixel'](self,*args) + return GiacMethods['set_pixel'](self, *args) - def set_vertex_attribute(self,*args): + def set_vertex_attribute(self, *args): r'''From Giac's documentation: Help for set_vertex_attribute: set_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) @@ -14357,9 +14357,9 @@ cdef class GiacMethods_base: See also: 1/ discard_vertex_attribute 2/ get_vertex_attribute 3/ list_vertex_attributes Ex1:set_vertex_attribute(cycle_graph(3),1,"supply"=27) ''' - return GiacMethods['set_vertex_attribute'](self,*args) + return GiacMethods['set_vertex_attribute'](self, *args) - def set_vertex_positions(self,*args): + def set_vertex_positions(self, *args): r'''From Giac's documentation: Help for set_vertex_positions: set_vertex_positions(Graph(G),Lst(vp)) @@ -14367,9 +14367,9 @@ cdef class GiacMethods_base: See also: 1/ draw_graph Ex1: G:=graph([1,2,3,4,5,6],%{[1,2],[1,4],[4,5],[2,5],[2,3],[3,6],[5,6]%}); G:=set_vertex_positions(G,[[0,0],[0.5,0],[1,0],[0,0.5],[0.5,0.5],[1,0.5]]) ''' - return GiacMethods['set_vertex_positions'](self,*args) + return GiacMethods['set_vertex_positions'](self, *args) - def shift(self,*args): + def shift(self, *args): r'''From Giac's documentation: Help for shift: shift(Lst,[Intg(n)]) @@ -14381,9 +14381,9 @@ cdef class GiacMethods_base: Ex4: L:=[0,1,2,3];L:=shift(L,2) Ex5: L:=[0,1,2,3];L.shift(2) ''' - return GiacMethods['shift'](self,*args) + return GiacMethods['shift'](self, *args) - def shift_phase(self,*args): + def shift_phase(self, *args): r'''From Giac's documentation: Help for shift_phase: shift_phase(Expr) @@ -14396,9 +14396,9 @@ cdef class GiacMethods_base: Ex5:shift_phase(cos(t)) Ex6:shift_phase(tan(u)) ''' - return GiacMethods['shift_phase'](self,*args) + return GiacMethods['shift_phase'](self, *args) - def shortest_path(self,*args): + def shortest_path(self, *args): r'''From Giac's documentation: Help for shortest_path: shortest_path(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) @@ -14406,9 +14406,9 @@ cdef class GiacMethods_base: See also: 1/ dijkstra 2/ vertex_distance Ex1:shortest_path(cycle_graph(6),1,5) ''' - return GiacMethods['shortest_path'](self,*args) + return GiacMethods['shortest_path'](self, *args) - def show_pixels(self,*args): + def show_pixels(self, *args): r'''From Giac's documentation: Help for show_pixels: show_pixels(NULL) @@ -14416,9 +14416,9 @@ cdef class GiacMethods_base: See also: 1/ set_pixel 2/ clear Ex1:show_pixels() ''' - return GiacMethods['show_pixels'](self,*args) + return GiacMethods['show_pixels'](self, *args) - def shuffle(self,*args): + def shuffle(self, *args): r'''From Giac's documentation: Help for shuffle: shuffle(Intg(n)||Lst(L)) @@ -14430,9 +14430,9 @@ cdef class GiacMethods_base: Ex4: L:=[1,3,5,7,9];L:=randperm(L) Ex5: L:=[1,3,5,7,9];L.randperm() ''' - return GiacMethods['shuffle'](self,*args) + return GiacMethods['shuffle'](self, *args) - def sierpinski_graph(self,*args): + def sierpinski_graph(self, *args): r'''From Giac's documentation: Help for sierpinski_graph: sierpinski_graph(Intg(n),Intg(k),[triangle]) @@ -14444,9 +14444,9 @@ cdef class GiacMethods_base: Ex4:sierpinski_graph(3,2) Ex5:sierpinski_graph(3,3,at_triangle) ''' - return GiacMethods['sierpinski_graph'](self,*args) + return GiacMethods['sierpinski_graph'](self, *args) - def sign(self,*args): + def sign(self, *args): r'''From Giac's documentation: Help for sign: sign(Expr) @@ -14455,9 +14455,9 @@ cdef class GiacMethods_base: Ex1:sign(-4) Ex2:sign(4-5) ''' - return GiacMethods['sign'](self,*args) + return GiacMethods['sign'](self, *args) - def signature(self,*args): + def signature(self, *args): r'''From Giac's documentation: Help for signature: signature(Permut) @@ -14465,9 +14465,9 @@ cdef class GiacMethods_base: See also: 1/ permu2cycles 2/ is_permu Ex1:signature([1,0,3,4,2]) ''' - return GiacMethods['signature'](self,*args) + return GiacMethods['signature'](self, *args) - def signe(self,*args): + def signe(self, *args): r'''From Giac's documentation: Help for signe: signe(Str(s)) @@ -14476,9 +14476,9 @@ cdef class GiacMethods_base: Ex1:signe("Thomas") Ex2:signe(Thomas) ''' - return GiacMethods['signe'](self,*args) + return GiacMethods['signe'](self, *args) - def similarity(self,*args): + def similarity(self, *args): r'''From Giac's documentation: Help for similarity: similarity(Pnt or Dr3,Real,Angle,Pnt) @@ -14489,9 +14489,9 @@ cdef class GiacMethods_base: Ex3: s:=similarity(1+i,2,pi/3);s(i) Ex4: s:=similarity(line(x=y,y=z),2,pi/3),s(point(-1,2,1)) ''' - return GiacMethods['similarity'](self,*args) + return GiacMethods['similarity'](self, *args) - def simp2(self,*args): + def simp2(self, *args): r'''From Giac's documentation: Help for simp2: simp2(Intg(A) or Poly(A),Intg(B) or Poly(B)) @@ -14500,9 +14500,9 @@ cdef class GiacMethods_base: Ex1:simp2(12,18) Ex2:simp2(x^3-1,x^2-1) ''' - return GiacMethods['simp2'](self,*args) + return GiacMethods['simp2'](self, *args) - def simplex_reduce(self,*args): + def simplex_reduce(self, *args): r'''From Giac's documentation: Help for simplex_reduce: simplex_reduce(Mtrx(A), Vect(b), Vect(c)) @@ -14513,9 +14513,9 @@ cdef class GiacMethods_base: Ex4:simplex_reduce([[-3,2,1,0,3],[1,1,0,1,4],[-1,-2,0,0,0]]) Ex5:simplex_reduce([[2,1,1,1,0,0,2],[1,2,3,0,1,0,5],[2,2,1,0,0,1,6],[-3,-1,-3,1,-1,2,0]]) ''' - return GiacMethods['simplex_reduce'](self,*args) + return GiacMethods['simplex_reduce'](self, *args) - def simplifier(self,*args): + def simplifier(self, *args): r'''From Giac's documentation: Help for simplifier: simplifier(Expr) @@ -14525,9 +14525,9 @@ cdef class GiacMethods_base: Ex2:simplifier(texpand((sin(3*x)+sin(7*x))/sin(5*x))) Ex3:simplifier(texpand((cos(3*x)+cos(7*x))/cos(5*x))) ''' - return GiacMethods['simplifier'](self,*args) + return GiacMethods['simplifier'](self, *args) - def simplify(self,*args): + def simplify(self, *args): r'''From Giac's documentation: Help for simplify: simplify(Expr) @@ -14537,9 +14537,9 @@ cdef class GiacMethods_base: Ex2:simplify(texpand((sin(3*x)+sin(7*x))/sin(5*x))) Ex3:simplify(texpand((cos(3*x)+cos(7*x))/cos(5*x))) ''' - return GiacMethods['simplify'](self,*args) + return GiacMethods['simplify'](self, *args) - def simpson(self,*args): + def simpson(self, *args): r'''From Giac's documentation: Help for simpson: simpson(Opt) @@ -14550,9 +14550,9 @@ cdef class GiacMethods_base: Ex3: area(x^2,x=0..1,5,rombergm) Ex4:simpson(area(x^2,x=0..1,5,gauss15)) ''' - return GiacMethods['simpson'](self,*args) + return GiacMethods['simpson'](self, *args) - def simult(self,*args): + def simult(self, *args): r'''From Giac's documentation: Help for simult: simult(Mtrx(A),Mtrx(B)) @@ -14561,9 +14561,9 @@ cdef class GiacMethods_base: Ex1:simult([[3,1],[3,2]],[[-2],[2]]) Ex2:simult([[3,1],[3,2]],[[-2,1],[2,-1]]) ''' - return GiacMethods['simult'](self,*args) + return GiacMethods['simult'](self, *args) - def sin(self,*args): + def sin(self, *args): r'''From Giac's documentation: Help for sin: sin(Expr or Opt) @@ -14572,9 +14572,9 @@ cdef class GiacMethods_base: Ex1:sin(0) Ex2: convert(cos(x)^4+sin(x)^2,sin) ''' - return GiacMethods['sin'](self,*args) + return GiacMethods['sin'](self, *args) - def sin2costan(self,*args): + def sin2costan(self, *args): r'''From Giac's documentation: Help for sin2costan: sin2costan(Expr) @@ -14582,9 +14582,9 @@ cdef class GiacMethods_base: See also: 1/ tan2sincos 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 Ex1:sin2costan(sin(x)) ''' - return GiacMethods['sin2costan'](self,*args) + return GiacMethods['sin2costan'](self, *args) - def sinc(self,*args): + def sinc(self, *args): r'''From Giac's documentation: Help for sinc: sinc(Expr(x)) @@ -14592,9 +14592,9 @@ cdef class GiacMethods_base: See also: 1/ sin Ex1:sinc(pi*x) ''' - return GiacMethods['sinc'](self,*args) + return GiacMethods['sinc'](self, *args) - def sincos(self,*args): + def sincos(self, *args): r'''From Giac's documentation: Help for sincos: sincos(Expr or Opt) @@ -14604,9 +14604,9 @@ cdef class GiacMethods_base: Ex2:sincos(exp(-i*x)) Ex3: convert(exp(i*x),sincos) ''' - return GiacMethods['sincos'](self,*args) + return GiacMethods['sincos'](self, *args) - def single_inter(self,*args): + def single_inter(self, *args): r'''From Giac's documentation: Help for single_inter: single_inter(Curve,Curve,[Pnt(A)||LstPnt(L)]) @@ -14620,9 +14620,9 @@ cdef class GiacMethods_base: Ex6:single_inter(plane(x=y),plane(y=z)) Ex7:single_inter(line(x=y+1,y=2*z),plane(y=z)) ''' - return GiacMethods['single_inter'](self,*args) + return GiacMethods['single_inter'](self, *args) - def sinh(self,*args): + def sinh(self, *args): r'''From Giac's documentation: Help for sinh: sinh(Expr) @@ -14630,9 +14630,9 @@ cdef class GiacMethods_base: See also: 1/ asinh Ex1:sinh(0) ''' - return GiacMethods['sinh'](self,*args) + return GiacMethods['sinh'](self, *args) - def sizes(self,*args): + def sizes(self, *args): r'''From Giac's documentation: Help for sizes: sizes(Lst or Str or Seq) @@ -14640,9 +14640,9 @@ cdef class GiacMethods_base: See also: 1/ size 2/ dim Ex1:sizes([[1,2,3],[1,2],[1]]) ''' - return GiacMethods['sizes'](self,*args) + return GiacMethods['sizes'](self, *args) - def slope(self,*args): + def slope(self, *args): r'''From Giac's documentation: Help for slope: slope(Line||Pnt||Cplx,[Pnt||Cplx]) @@ -14657,9 +14657,9 @@ cdef class GiacMethods_base: Ex7:slope(LineTan(sin(x),pi/4)) Ex8: line(point(1,2),slope=-1) ''' - return GiacMethods['slope'](self,*args) + return GiacMethods['slope'](self, *args) - def slopeat(self,*args): + def slopeat(self, *args): r'''From Giac's documentation: Help for slopeat: slopeat(Line, Pnt||Cplx(z0)) @@ -14669,9 +14669,9 @@ cdef class GiacMethods_base: Ex2: s:=segment(1-i,i);slopeat(s,point(0.4)) Ex3: t:=tangent(plotfunc(sin(x)),pi/4);slopeat(t,0) ''' - return GiacMethods['slopeat'](self,*args) + return GiacMethods['slopeat'](self, *args) - def slopeatraw(self,*args): + def slopeatraw(self, *args): r'''From Giac's documentation: Help for slopeatraw: slopeatraw(Line, Pnt||Cplx(z0)) @@ -14682,9 +14682,9 @@ cdef class GiacMethods_base: Ex3:slopeatraw(tangent(plotfunc(sin(x)),pi/4),0) Ex4:slopeatraw((LineTan sin(x),pi/4),i) ''' - return GiacMethods['slopeatraw'](self,*args) + return GiacMethods['slopeatraw'](self, *args) - def smith(self,*args): + def smith(self, *args): r'''From Giac's documentation: Help for smith: smith(Mtrx(A)) @@ -14693,9 +14693,9 @@ cdef class GiacMethods_base: Ex1: n:=10; A:=ranm(n,n) % 17; U,D,V:=smith(x*idn(n)-A);normal(U*(x*idn(n)-A)*V-D); diag(D); Ex2: GF(3,5,g); n:=3; A:=ranm(n,n,g); U,D,V:=smith(x*idn(n)-A);normal(U*(x*idn(n)-A)*V-D); diag(D); ''' - return GiacMethods['smith'](self,*args) + return GiacMethods['smith'](self, *args) - def smod(self,*args): + def smod(self, *args): r'''From Giac's documentation: Help for smod: smod(Intg,Intg) @@ -14705,9 +14705,9 @@ cdef class GiacMethods_base: Ex2:smod(10,4) Ex3:smod(11,7) ''' - return GiacMethods['smod'](self,*args) + return GiacMethods['smod'](self, *args) - def snedecor(self,*args): + def snedecor(self, *args): r'''From Giac's documentation: Help for snedecor: snedecor(Intg(n),Intg(m),Real(x0)) @@ -14718,9 +14718,9 @@ cdef class GiacMethods_base: Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) ''' - return GiacMethods['snedecor'](self,*args) + return GiacMethods['snedecor'](self, *args) - def snedecor_cdf(self,*args): + def snedecor_cdf(self, *args): r'''From Giac's documentation: Help for snedecor_cdf: snedecor_cdf(Intg(n),Intg(m),Real(x0)) @@ -14729,9 +14729,9 @@ cdef class GiacMethods_base: Ex1:snedecor_cdf(4,4,2.1) Ex2:snedecor_cdf(4,10,3.5) ''' - return GiacMethods['snedecor_cdf'](self,*args) + return GiacMethods['snedecor_cdf'](self, *args) - def snedecor_icdf(self,*args): + def snedecor_icdf(self, *args): r'''From Giac's documentation: Help for snedecor_icdf: snedecor_icdf(Intg(n),Intg(m),Real(p)) @@ -14740,9 +14740,9 @@ cdef class GiacMethods_base: Ex1:snedecor_icdf(4,10,0.95) Ex2:snedecor_icdf(4,10,0.05) ''' - return GiacMethods['snedecor_icdf'](self,*args) + return GiacMethods['snedecor_icdf'](self, *args) - def snedecord(self,*args): + def snedecord(self, *args): r'''From Giac's documentation: Help for snedecord: snedecord(Intg(n),Intg(m),Real(x0)) @@ -14753,9 +14753,9 @@ cdef class GiacMethods_base: Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) ''' - return GiacMethods['snedecord'](self,*args) + return GiacMethods['snedecord'](self, *args) - def snedecord_cdf(self,*args): + def snedecord_cdf(self, *args): r'''From Giac's documentation: Help for snedecord_cdf: snedecord_cdf(Intg(n),Intg(m),Real(x0)) @@ -14764,9 +14764,9 @@ cdef class GiacMethods_base: Ex1:snedecord_cdf(4,4,2.1) Ex2:snedecord_cdf(4,10,3.5) ''' - return GiacMethods['snedecord_cdf'](self,*args) + return GiacMethods['snedecord_cdf'](self, *args) - def snedecord_icdf(self,*args): + def snedecord_icdf(self, *args): r'''From Giac's documentation: Help for snedecord_icdf: snedecord_icdf(Intg(n),Intg(m),Real(p)) @@ -14775,9 +14775,9 @@ cdef class GiacMethods_base: Ex1:snedecord_icdf(4,10,0.95) Ex2:snedecord_icdf(4,10,0.05) ''' - return GiacMethods['snedecord_icdf'](self,*args) + return GiacMethods['snedecord_icdf'](self, *args) - def solid_line(self,*args): + def solid_line(self, *args): r'''From Giac's documentation: Help for solid_line: solid_line(Opt) @@ -14786,9 +14786,9 @@ cdef class GiacMethods_base: Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) ''' - return GiacMethods['solid_line'](self,*args) + return GiacMethods['solid_line'](self, *args) - def solve(self,*args): + def solve(self, *args): r'''From Giac's documentation: Help for solve: solve(Expr,[Var]) @@ -14799,9 +14799,9 @@ cdef class GiacMethods_base: Ex3:solve([y-z=0,z-x=0,x-y=0,x-1+y+z=0],[x,y,z]) Ex4:solve([x^2-y^2=0,x^2-z^2=0],[x,y,z]) ''' - return GiacMethods['solve'](self,*args) + return GiacMethods['solve'](self, *args) - def somme(self,*args): + def somme(self, *args): r'''From Giac's documentation: Help for somme: somme(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) @@ -14818,9 +14818,9 @@ cdef class GiacMethods_base: Ex9:somme(1/(x*(x+1)),x) Ex10:somme(cos(n*x),n) ''' - return GiacMethods['somme'](self,*args) + return GiacMethods['somme'](self, *args) - def sommet(self,*args): + def sommet(self, *args): r'''From Giac's documentation: Help for sommet: sommet(Op or Fnct) @@ -14829,9 +14829,9 @@ cdef class GiacMethods_base: Ex1:sommet(quote(gcd(45,123))) Ex2:sommet('gcd(45,123)') ''' - return GiacMethods['sommet'](self,*args) + return GiacMethods['sommet'](self, *args) - def sort(self,*args): + def sort(self, *args): r'''From Giac's documentation: Help for sort: sort(LstReal or Seq [Fnc]) @@ -14843,9 +14843,9 @@ cdef class GiacMethods_base: Ex4:sort([[1,2],[2,3],[4,3]],(x,y)->when(x[1]==y[1],x[0]>y[0],x[1]>y[1])) Ex5:sort(y*x*2+x*y) ''' - return GiacMethods['sort'](self,*args) + return GiacMethods['sort'](self, *args) - def sorta(self,*args): + def sorta(self, *args): r'''From Giac's documentation: Help for sorta: sorta(LstReal||Seq×||Mtrx) @@ -14855,9 +14855,9 @@ cdef class GiacMethods_base: Ex2:sorta([3,4,2]) Ex3:sorta([[3,4,2],[6,4,5]]) ''' - return GiacMethods['sorta'](self,*args) + return GiacMethods['sorta'](self, *args) - def sortd(self,*args): + def sortd(self, *args): r'''From Giac's documentation: Help for sortd: sortd(LstReal||Seq||Mtrx) @@ -14867,9 +14867,9 @@ cdef class GiacMethods_base: Ex2:sortd([3,4,2]) Ex3:sortd([[3,4,2],[6,4,5]]) ''' - return GiacMethods['sortd'](self,*args) + return GiacMethods['sortd'](self, *args) - def sorted(self,*args): + def sorted(self, *args): r'''From Giac's documentation: Help for sorted: sorted(LstReal or Seq [Fnc]) @@ -14881,9 +14881,9 @@ cdef class GiacMethods_base: Ex4:sorted([[1,2],[2,3],[4,3]],(x,y)->when(x[1]==y[1],x[0]>y[0],x[1]>y[1])) Ex5:sorted(y*x*2+x*y) ''' - return GiacMethods['sorted'](self,*args) + return GiacMethods['sorted'](self, *args) - def soundsec(self,*args): + def soundsec(self, *args): r'''From Giac's documentation: Help for soundsec: soundsec(Intg(n),[Intg(N)]) @@ -14892,9 +14892,9 @@ cdef class GiacMethods_base: Ex1:soundsec(1) Ex2:soundsec(1,22100) ''' - return GiacMethods['soundsec'](self,*args) + return GiacMethods['soundsec'](self, *args) - def spanning_tree(self,*args): + def spanning_tree(self, *args): r'''From Giac's documentation: Help for spanning_tree: spanning_tree(Graph(G),[Vrtx(r)]) @@ -14903,9 +14903,9 @@ cdef class GiacMethods_base: Ex1:spanning_tree(graph("petersen")) Ex2:spanning_tree(graph("petersen"),5) ''' - return GiacMethods['spanning_tree'](self,*args) + return GiacMethods['spanning_tree'](self, *args) - def sphere(self,*args): + def sphere(self, *args): r'''From Giac's documentation: Help for sphere: sphere((Pnt or Vect),(Pnt or Real)) @@ -14914,9 +14914,9 @@ cdef class GiacMethods_base: Ex1:sphere([0,0,0],[2,2,2]) Ex2:sphere([1,1,1],1) ''' - return GiacMethods['sphere'](self,*args) + return GiacMethods['sphere'](self, *args) - def spline(self,*args): + def spline(self, *args): r'''From Giac's documentation: Help for spline: spline(Lst(lx),Lst(ly),Var(x),Intg(d)) @@ -14924,9 +14924,9 @@ cdef class GiacMethods_base: See also: 1/ lagrange Ex1:spline([0,1,2],[1,3,0],x,3) ''' - return GiacMethods['spline'](self,*args) + return GiacMethods['spline'](self, *args) - def split(self,*args): + def split(self, *args): r'''From Giac's documentation: Help for split: split(Expr(Xpr),Lst(var1,var2)) @@ -14935,18 +14935,18 @@ cdef class GiacMethods_base: Ex1:split(x^3*y^2-y^2+x^3-1,[x,y]) Ex2:split(x^3*y^2-y^2+x^3+1,[x,y]) ''' - return GiacMethods['split'](self,*args) + return GiacMethods['split'](self, *args) - def spring(self,*args): + def spring(self, *args): r'''From Giac's documentation: Help for spring: spring(Opt) Option for the draw_graph command. See also: 1/ planar 2/ tree 3/ draw_graph ''' - return GiacMethods['spring'](self,*args) + return GiacMethods['spring'](self, *args) - def sq(self,*args): + def sq(self, *args): r'''From Giac's documentation: Help for sq: sq(Seq) @@ -14955,9 +14955,9 @@ cdef class GiacMethods_base: Ex1:sq(5) Ex2:sq(1,2,3) ''' - return GiacMethods['sq'](self,*args) + return GiacMethods['sq'](self, *args) - def sqrfree(self,*args): + def sqrfree(self, *args): r'''From Giac's documentation: Help for sqrfree: sqrfree(Expr) @@ -14966,9 +14966,9 @@ cdef class GiacMethods_base: Ex1:sqrfree(x^4-2*x^2+1) Ex2:sqrfree((x-2)^7*(x+2)^7*(x^4-2*x^2+1)) ''' - return GiacMethods['sqrfree'](self,*args) + return GiacMethods['sqrfree'](self, *args) - def sqrt(self,*args): + def sqrt(self, *args): r'''From Giac's documentation: Help for sqrt: sqrt(Expr) @@ -14977,9 +14977,9 @@ cdef class GiacMethods_base: Ex1:sqrt(50) Ex2:sqrt(x^2) ''' - return GiacMethods['sqrt'](self,*args) + return GiacMethods['sqrt'](self, *args) - def square(self,*args): + def square(self, *args): r'''From Giac's documentation: Help for square: square((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P),Var(C),Var(D)]) @@ -14990,9 +14990,9 @@ cdef class GiacMethods_base: Ex3:square(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:square(point(0,0,0),point(3,3,3),point(0,0,3),C,D) ''' - return GiacMethods['square'](self,*args) + return GiacMethods['square'](self, *args) - def square_point(self,*args): + def square_point(self, *args): r'''From Giac's documentation: Help for square_point: square_point(Opt) @@ -15001,9 +15001,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) ''' - return GiacMethods['square_point'](self,*args) + return GiacMethods['square_point'](self, *args) - def srand(self,*args): + def srand(self, *args): r'''From Giac's documentation: Help for srand: srand() @@ -15012,9 +15012,9 @@ cdef class GiacMethods_base: Ex1:srand(12) Ex2: srand ''' - return GiacMethods['srand'](self,*args) + return GiacMethods['srand'](self, *args) - def sst(self,*args): + def sst(self, *args): r'''From Giac's documentation: Help for sst: sst(NULL) @@ -15022,9 +15022,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:sst() ''' - return GiacMethods['sst'](self,*args) + return GiacMethods['sst'](self, *args) - def sst_in(self,*args): + def sst_in(self, *args): r'''From Giac's documentation: Help for sst_in: sst_in(NULL) @@ -15032,9 +15032,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:sst_in() ''' - return GiacMethods['sst_in'](self,*args) + return GiacMethods['sst_in'](self, *args) - def st_ordering(self,*args): + def st_ordering(self, *args): r'''From Giac's documentation: Help for st_ordering: st_ordering(Graph(G),Vrtx(s),Vrtx(t)) @@ -15042,9 +15042,9 @@ cdef class GiacMethods_base: See also: 1/ is_biconnected Ex1:st_ordering(graph("petersen"),1,2) ''' - return GiacMethods['st_ordering'](self,*args) + return GiacMethods['st_ordering'](self, *args) - def star_graph(self,*args): + def star_graph(self, *args): r'''From Giac's documentation: Help for star_graph: star_graph(Intg(n)) @@ -15052,9 +15052,9 @@ cdef class GiacMethods_base: See also: 1/ complete_graph 2/ wheel_graph Ex1:star_graph(5) ''' - return GiacMethods['star_graph'](self,*args) + return GiacMethods['star_graph'](self, *args) - def star_point(self,*args): + def star_point(self, *args): r'''From Giac's documentation: Help for star_point: star_point(Opt) @@ -15063,9 +15063,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) ''' - return GiacMethods['star_point'](self,*args) + return GiacMethods['star_point'](self, *args) - def stdDev(self,*args): + def stdDev(self, *args): r'''From Giac's documentation: Help for stdDev: stdDev(Lst||Mtrx,[Lst]) @@ -15075,9 +15075,9 @@ cdef class GiacMethods_base: Ex2:stdDev([1,2,3],[1,2,1]) Ex3:stdDev([[1,2,3],[5,6,7]]) ''' - return GiacMethods['stdDev'](self,*args) + return GiacMethods['stdDev'](self, *args) - def stddev(self,*args): + def stddev(self, *args): r'''From Giac's documentation: Help for stddev: stddev(Lst||Mtrx,[Lst]) @@ -15087,9 +15087,9 @@ cdef class GiacMethods_base: Ex2:stddev([1,2,3],[1,2,1]) Ex3:stddev([[1,2,3],[5,6,7]]) ''' - return GiacMethods['stddev'](self,*args) + return GiacMethods['stddev'](self, *args) - def stddevp(self,*args): + def stddevp(self, *args): r'''From Giac's documentation: Help for stddevp: stddevp(Lst||Mtrx,[Lst]) @@ -15099,9 +15099,9 @@ cdef class GiacMethods_base: Ex2:stddevp([1,2,3],[1,2,1]) Ex3:stddevp([[1,2,3],[5,6,7]]) ''' - return GiacMethods['stddevp'](self,*args) + return GiacMethods['stddevp'](self, *args) - def steffenson_solver(self,*args): + def steffenson_solver(self, *args): r'''From Giac's documentation: Help for steffenson_solver: steffenson_solver(Opt) @@ -15114,9 +15114,9 @@ cdef class GiacMethods_base: Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) ''' - return GiacMethods['steffenson_solver'](self,*args) + return GiacMethods['steffenson_solver'](self, *args) - def stereo2mono(self,*args): + def stereo2mono(self, *args): r'''From Giac's documentation: Help for stereo2mono: stereo2mono(Lst(clip)) @@ -15124,9 +15124,9 @@ cdef class GiacMethods_base: See also: 1/ channel_data 2/ mean 3/ createwav Ex1:stereo2mono(readwav("/some/file")) ''' - return GiacMethods['stereo2mono'](self,*args) + return GiacMethods['stereo2mono'](self, *args) - def str(self,*args): + def str(self, *args): r'''From Giac's documentation: Help for str: str(Expr or Opt) @@ -15137,9 +15137,9 @@ cdef class GiacMethods_base: Ex3:str(quote(a:=12)) Ex4: convert(quote(a:=12),string) ''' - return GiacMethods['str'](self,*args) + return GiacMethods['str'](self, *args) - def strongly_connected_components(self,*args): + def strongly_connected_components(self, *args): r'''From Giac's documentation: Help for strongly_connected_components: strongly_connected_components(Graph(G)) @@ -15147,9 +15147,9 @@ cdef class GiacMethods_base: See also: 1/ connected_components 2/ is_connected 3/ is_strongly_connected Ex1:strongly_connected_components(digraph([1,2,3],%{[1,2],[1,3],[2,3],[3,2]%})) ''' - return GiacMethods['strongly_connected_components'](self,*args) + return GiacMethods['strongly_connected_components'](self, *args) - def student(self,*args): + def student(self, *args): r'''From Giac's documentation: Help for student: student(Intg(n),Real(x0)) @@ -15158,9 +15158,9 @@ cdef class GiacMethods_base: Ex1:student(3,5.2) Ex2:student(1,5.2) ''' - return GiacMethods['student'](self,*args) + return GiacMethods['student'](self, *args) - def student_cdf(self,*args): + def student_cdf(self, *args): r'''From Giac's documentation: Help for student_cdf: student_cdf(Intg(n),Real(x0)) @@ -15169,9 +15169,9 @@ cdef class GiacMethods_base: Ex1:student_cdf(3,2.35) Ex2:student_cdf(3,-3.2) ''' - return GiacMethods['student_cdf'](self,*args) + return GiacMethods['student_cdf'](self, *args) - def student_icdf(self,*args): + def student_icdf(self, *args): r'''From Giac's documentation: Help for student_icdf: student_icdf(Intg(n),Real(p)) @@ -15180,9 +15180,9 @@ cdef class GiacMethods_base: Ex1:student_icdf(3,0.95) Ex2:student_icdf(3,0.05) ''' - return GiacMethods['student_icdf'](self,*args) + return GiacMethods['student_icdf'](self, *args) - def studentd(self,*args): + def studentd(self, *args): r'''From Giac's documentation: Help for studentd: studentd(Intg(n),Real(x0)) @@ -15191,9 +15191,9 @@ cdef class GiacMethods_base: Ex1:studentd(3,5.2) Ex2:studentd(1,5.2) ''' - return GiacMethods['studentd'](self,*args) + return GiacMethods['studentd'](self, *args) - def studentt(self,*args): + def studentt(self, *args): r'''From Giac's documentation: Help for studentt: studentt(Lst,Real,[Real],Fnc,[Real]) @@ -15202,9 +15202,9 @@ cdef class GiacMethods_base: Ex1:studentt([10,20],.5,.02,'!=',0.1) Ex2:studentt([0.48,20],0.5,0.1,'<') ''' - return GiacMethods['studentt'](self,*args) + return GiacMethods['studentt'](self, *args) - def sturm(self,*args): + def sturm(self, *args): r'''From Giac's documentation: Help for sturm: sturm(Poly,[Var],[Cplx(a)],[Cplx(b)]) @@ -15216,9 +15216,9 @@ cdef class GiacMethods_base: Ex4:sturm(x^5-x^3,x,-2,5) Ex5:sturm(x^3-1,x,-2-i,5+3i) ''' - return GiacMethods['sturm'](self,*args) + return GiacMethods['sturm'](self, *args) - def sturmab(self,*args): + def sturmab(self, *args): r'''From Giac's documentation: Help for sturmab: sturmab(Poly,Var,Cplx(a),Cplx(b)) @@ -15227,9 +15227,9 @@ cdef class GiacMethods_base: Ex1:sturmab(x^3-1,x,-2,5) Ex2:sturmab(x^3-1,x,-2-i,5+3i) ''' - return GiacMethods['sturmab'](self,*args) + return GiacMethods['sturmab'](self, *args) - def sturmseq(self,*args): + def sturmseq(self, *args): r'''From Giac's documentation: Help for sturmseq: sturmseq(Poly,[Var]) @@ -15239,9 +15239,9 @@ cdef class GiacMethods_base: Ex2:sturmseq(x^5-x^3,x) Ex3:sturmseq((x^5-x^3)/(x+2),x) ''' - return GiacMethods['sturmseq'](self,*args) + return GiacMethods['sturmseq'](self, *args) - def style(self,*args): + def style(self, *args): r'''From Giac's documentation: Help for style: style(Opt) @@ -15250,9 +15250,9 @@ cdef class GiacMethods_base: Ex1: segment(0,point(1,1),style=point) Ex2: line(y=x,style=point,display=green+line_width_2) ''' - return GiacMethods['style'](self,*args) + return GiacMethods['style'](self, *args) - def subMat(self,*args): + def subMat(self, *args): r'''From Giac's documentation: Help for subMat: subMat(Mtrx(A),Intg(n1),Intg(n2),Intg(n3),Intg(n4).) @@ -15260,9 +15260,9 @@ cdef class GiacMethods_base: See also: 1/ mid Ex1:subMat([[1,2],[3,4],[5,6]],1,0,2,1) ''' - return GiacMethods['subMat'](self,*args) + return GiacMethods['subMat'](self, *args) - def subdivide_edges(self,*args): + def subdivide_edges(self, *args): r'''From Giac's documentation: Help for subdivide_edges: subdivide_edges(Graph(G),Lst(E),[Intg(r)]) @@ -15270,9 +15270,9 @@ cdef class GiacMethods_base: See also: 1/ edges Ex1:subdivide_edges(complete_graph(2,3),[[1,3],[1,4]],2) ''' - return GiacMethods['subdivide_edges'](self,*args) + return GiacMethods['subdivide_edges'](self, *args) - def subgraph(self,*args): + def subgraph(self, *args): r'''From Giac's documentation: Help for subgraph: subgraph(Graph(G),Lst(E)) @@ -15280,9 +15280,9 @@ cdef class GiacMethods_base: See also: 1/ induced_subgraph 2/ highlight_subgraph Ex1:subgraph(complete_graph(5),[[1,2],[2,3],[3,4],[4,1]]) ''' - return GiacMethods['subgraph'](self,*args) + return GiacMethods['subgraph'](self, *args) - def subs(self,*args): + def subs(self, *args): r'''From Giac's documentation: Help for subs: subs(Expr or Var=value,Var=value or Expr) @@ -15292,9 +15292,9 @@ cdef class GiacMethods_base: Ex2:subs(x=2,1/(4+x^2)) Ex3: f:=1/(4+x^2);f(x=2) ''' - return GiacMethods['subs'](self,*args) + return GiacMethods['subs'](self, *args) - def subsop(self,*args): + def subsop(self, *args): r'''From Giac's documentation: Help for subsop: subsop(Lst||Mtrx,Intg(n)=Expr) @@ -15304,9 +15304,9 @@ cdef class GiacMethods_base: Ex3:subsop([[1,2],[3,4]],1=[10,8]) Ex4:subsop([0,1,2,3],'1=NULL') ''' - return GiacMethods['subsop'](self,*args) + return GiacMethods['subsop'](self, *args) - def subst(self,*args): + def subst(self, *args): r'''From Giac's documentation: Help for subst: subst(Expr,Var(v)=value(a)) @@ -15320,9 +15320,9 @@ cdef class GiacMethods_base: Ex6:subst('sum(x^(n+1)/((n+p+1)*(n+1)),n,0,inf)',n=k-1) Ex7: f:=1/(x^2+y^2;f(x=2,y=3) ''' - return GiacMethods['subst'](self,*args) + return GiacMethods['subst'](self, *args) - def substituer(self,*args): + def substituer(self, *args): r'''From Giac's documentation: Help for substituer: substituer(Expr,Var(v)=value(a)) @@ -15336,9 +15336,9 @@ cdef class GiacMethods_base: Ex6:substituer('sum(x^(n+1)/((n+p+1)*(n+1)),n,0,inf)',n=k-1) Ex7: f:=1/(x^2+y^2;f(x=2,y=3) ''' - return GiacMethods['substituer'](self,*args) + return GiacMethods['substituer'](self, *args) - def subtype(self,*args): + def subtype(self, *args): r'''From Giac's documentation: Help for subtype: subtype(Expr) @@ -15349,9 +15349,9 @@ cdef class GiacMethods_base: Ex3:subtype(poly1[1,2,3]) Ex4:subtype([1,2,3]) ''' - return GiacMethods['subtype'](self,*args) + return GiacMethods['subtype'](self, *args) - def sum(self,*args): + def sum(self, *args): r'''From Giac's documentation: Help for sum: sum(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) @@ -15368,9 +15368,9 @@ cdef class GiacMethods_base: Ex9:sum(1/(x*(x+1)),x) Ex10:sum(cos(n*x),n) ''' - return GiacMethods['sum'](self,*args) + return GiacMethods['sum'](self, *args) - def sum_riemann(self,*args): + def sum_riemann(self, *args): r'''From Giac's documentation: Help for sum_riemann: sum_riemann(Expr(Xpr),Lst(var1,var2)) @@ -15380,9 +15380,9 @@ cdef class GiacMethods_base: Ex2:sum_riemann(n/(n^2+k),[n,k]) Ex3:sum_riemann(n/(n^2+k^2),[n,k]) ''' - return GiacMethods['sum_riemann'](self,*args) + return GiacMethods['sum_riemann'](self, *args) - def suppress(self,*args): + def suppress(self, *args): r'''From Giac's documentation: Help for suppress: suppress(Vect(L)||Str(l),Intg(n)) @@ -15393,9 +15393,9 @@ cdef class GiacMethods_base: Ex3: L:=[0,1,2,3];L:=suppress(L,2) Ex4: L:=[0,1,2,3];L.suppress(2) ''' - return GiacMethods['suppress'](self,*args) + return GiacMethods['suppress'](self, *args) - def surd(self,*args): + def surd(self, *args): r'''From Giac's documentation: Help for surd: surd(Expr,Intg(n)) @@ -15404,18 +15404,18 @@ cdef class GiacMethods_base: Ex1:surd(8,3) Ex2:surd(-8,3) ''' - return GiacMethods['surd'](self,*args) + return GiacMethods['surd'](self, *args) - def svd(self,*args): + def svd(self, *args): r'''From Giac's documentation: Help for svd: svd(Mtrx(A)) For a square numerical real matrix A, returns U orthogonal, S vector of singular values, Q orthogonal such that A=U*diag(S)*tran(Q). Ex1:svd([[1,2],[3,4]]) ''' - return GiacMethods['svd'](self,*args) + return GiacMethods['svd'](self, *args) - def swapcol(self,*args): + def swapcol(self, *args): r'''From Giac's documentation: Help for swapcol: swapcol(Mtrx(A),Intg(n1),Intg(n2)) @@ -15423,9 +15423,9 @@ cdef class GiacMethods_base: See also: 1/ rowSwap Ex1:swapcol([[1,2],[3,4],[5,6]],0,1) ''' - return GiacMethods['swapcol'](self,*args) + return GiacMethods['swapcol'](self, *args) - def swaprow(self,*args): + def swaprow(self, *args): r'''From Giac's documentation: Help for swaprow: swaprow(Mtrx(A),Intg(n1),Intg(n2)) @@ -15433,9 +15433,9 @@ cdef class GiacMethods_base: See also: 1/ rowAdd 2/ colSwap Ex1:swaprow([[1,2],[3,4],[5,6]],1,2) ''' - return GiacMethods['swaprow'](self,*args) + return GiacMethods['swaprow'](self, *args) - def switch_axes(self,*args): + def switch_axes(self, *args): r'''From Giac's documentation: Help for switch_axes: switch_axes([Intg(0 or 1)]) @@ -15445,9 +15445,9 @@ cdef class GiacMethods_base: Ex2:switch_axes(0) Ex3:switch_axes(1) ''' - return GiacMethods['switch_axes'](self,*args) + return GiacMethods['switch_axes'](self, *args) - def sylvester(self,*args): + def sylvester(self, *args): r'''From Giac's documentation: Help for sylvester: sylvester(Poly,Poly,Var) @@ -15456,9 +15456,9 @@ cdef class GiacMethods_base: Ex1:sylvester(x^2-1,x^3-1,x) Ex2:sylvester(x^3-p*x+q,3*x^2-p,x) ''' - return GiacMethods['sylvester'](self,*args) + return GiacMethods['sylvester'](self, *args) - def symb2poly(self,*args): + def symb2poly(self, *args): r'''From Giac's documentation: Help for symb2poly: symb2poly(Expr, LstVar or [Var]) @@ -15471,9 +15471,9 @@ cdef class GiacMethods_base: Ex5:symb2poly(-x^4+x*3*y+2+y^2*z,[x,y,z]) Ex6:symb2poly(-x^4+x*3*y+2+y^2*z,[x,y,z]) ''' - return GiacMethods['symb2poly'](self,*args) + return GiacMethods['symb2poly'](self, *args) - def symbol(self,*args): + def symbol(self, *args): r'''From Giac's documentation: Help for symbol: symbol(Opt) @@ -15484,9 +15484,9 @@ cdef class GiacMethods_base: Ex3: a:=sqrt(2);type(a) Ex4: type(2x+1) ''' - return GiacMethods['symbol'](self,*args) + return GiacMethods['symbol'](self, *args) - def syst2mat(self,*args): + def syst2mat(self, *args): r'''From Giac's documentation: Help for syst2mat: syst2mat(LstLinEq,LstVar) @@ -15494,9 +15494,9 @@ cdef class GiacMethods_base: See also: 1/ linsolve 2/ rref Ex1:syst2mat([x-y=1,x+2*y],[x,y]) ''' - return GiacMethods['syst2mat'](self,*args) + return GiacMethods['syst2mat'](self, *args) - def tCollect(self,*args): + def tCollect(self, *args): r'''From Giac's documentation: Help for tCollect: tCollect(Expr) @@ -15504,9 +15504,9 @@ cdef class GiacMethods_base: See also: 1/ texpand 2/ tlin Ex1:tCollect(sin(x)+cos(x)) ''' - return GiacMethods['tCollect'](self,*args) + return GiacMethods['tCollect'](self, *args) - def tExpand(self,*args): + def tExpand(self, *args): r'''From Giac's documentation: Help for tExpand: tExpand(Expr) @@ -15516,9 +15516,9 @@ cdef class GiacMethods_base: Ex2:tExpand(cos(x+y)) Ex3:tExpand(cos(3*x)) ''' - return GiacMethods['tExpand'](self,*args) + return GiacMethods['tExpand'](self, *args) - def table(self,*args): + def table(self, *args): r'''From Giac's documentation: Help for table: table(SeqEqual(index=value)) @@ -15528,9 +15528,9 @@ cdef class GiacMethods_base: Ex2: A:=[[0,1],[2,3]];table(A) Ex3: B:=table([1,2]=12,[2,5]=25);matrix(B) ''' - return GiacMethods['table'](self,*args) + return GiacMethods['table'](self, *args) - def tablefunc(self,*args): + def tablefunc(self, *args): r'''From Giac's documentation: Help for tablefunc: tablefunc(Expr,Var) @@ -15539,9 +15539,9 @@ cdef class GiacMethods_base: Ex1:tablefunc(sin(x),x) Ex2:tablefunc(x^2-x-2,x) ''' - return GiacMethods['tablefunc'](self,*args) + return GiacMethods['tablefunc'](self, *args) - def tableseq(self,*args): + def tableseq(self, *args): r'''From Giac's documentation: Help for tableseq: tableseq(Expr,(Var or LstVar),(InitVal or LstInitVal)) @@ -15550,9 +15550,9 @@ cdef class GiacMethods_base: Ex1:tableseq(cos(x),x,0.0) Ex2:tableseq(x+y,[x,y],[1,1]) ''' - return GiacMethods['tableseq'](self,*args) + return GiacMethods['tableseq'](self, *args) - def tabsign(self,*args): + def tabsign(self, *args): r'''From Giac's documentation: Help for tabsign: tabsign(Expr,Var) @@ -15562,9 +15562,9 @@ cdef class GiacMethods_base: Ex2:tabsign(x^2,x,-3,5) Ex3:tabsign(sin(x),x) ''' - return GiacMethods['tabsign'](self,*args) + return GiacMethods['tabsign'](self, *args) - def tabvar(self,*args): + def tabvar(self, *args): r'''From Giac's documentation: Help for tabvar: tabvar(Expr,Var) @@ -15576,9 +15576,9 @@ cdef class GiacMethods_base: Ex4:tabvar(x^2,x,-3,5) Ex5:tabvar([sin(2t),cos(3t)]) ''' - return GiacMethods['tabvar'](self,*args) + return GiacMethods['tabvar'](self, *args) - def tail(self,*args): + def tail(self, *args): r'''From Giac's documentation: Help for tail: tail(Lst or Seq or Str) @@ -15588,9 +15588,9 @@ cdef class GiacMethods_base: Ex2:tail(3,2,4,1,0) Ex3:tail("bonjour") ''' - return GiacMethods['tail'](self,*args) + return GiacMethods['tail'](self, *args) - def tan(self,*args): + def tan(self, *args): r'''From Giac's documentation: Help for tan: tan(Expr) @@ -15600,9 +15600,9 @@ cdef class GiacMethods_base: Ex2:tan(pi/4) Ex3: convert(tan(x),tan) ''' - return GiacMethods['tan'](self,*args) + return GiacMethods['tan'](self, *args) - def tan2cossin2(self,*args): + def tan2cossin2(self, *args): r'''From Giac's documentation: Help for tan2cossin2: tan2cossin2(Expr) @@ -15610,9 +15610,9 @@ cdef class GiacMethods_base: See also: 1/ tan2sincos2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan Ex1:tan2cossin2(tan(x)) ''' - return GiacMethods['tan2cossin2'](self,*args) + return GiacMethods['tan2cossin2'](self, *args) - def tan2sincos(self,*args): + def tan2sincos(self, *args): r'''From Giac's documentation: Help for tan2sincos: tan2sincos(Expr) @@ -15620,9 +15620,9 @@ cdef class GiacMethods_base: See also: 1/ sin2costan 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 Ex1:tan2sincos(tan(x)) ''' - return GiacMethods['tan2sincos'](self,*args) + return GiacMethods['tan2sincos'](self, *args) - def tan2sincos2(self,*args): + def tan2sincos2(self, *args): r'''From Giac's documentation: Help for tan2sincos2: tan2sincos2(Expr) @@ -15630,9 +15630,9 @@ cdef class GiacMethods_base: See also: 1/ tan2cossin2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan Ex1:tan2sincos2(tan(x)) ''' - return GiacMethods['tan2sincos2'](self,*args) + return GiacMethods['tan2sincos2'](self, *args) - def tangent(self,*args): + def tangent(self, *args): r'''From Giac's documentation: Help for tangent: tangent(Curve(C),Pnt(A)) @@ -15647,9 +15647,9 @@ cdef class GiacMethods_base: Ex7:tangent(plotpolar(3*exp(t/2),t),7) Ex8: equation(tangente([2*cos(t),2*sin(t),3*t],t)) ''' - return GiacMethods['tangent'](self,*args) + return GiacMethods['tangent'](self, *args) - def tangente(self,*args): + def tangente(self, *args): r'''From Giac's documentation: Help for tangente: tangente(Curve(C),Pnt(A)) @@ -15664,9 +15664,9 @@ cdef class GiacMethods_base: Ex7:tangente(plotpolar(3*exp(t/2),t),7) Ex8: equation(tangente([2*cos(t),2*sin(t),3*t],t)) ''' - return GiacMethods['tangente'](self,*args) + return GiacMethods['tangente'](self, *args) - def tanh(self,*args): + def tanh(self, *args): r'''From Giac's documentation: Help for tanh: tanh(Expr) @@ -15675,9 +15675,9 @@ cdef class GiacMethods_base: Ex1:tanh(0) Ex2:tanh(hyp2exp(tanh(1))) ''' - return GiacMethods['tanh'](self,*args) + return GiacMethods['tanh'](self, *args) - def taux_accroissement(self,*args): + def taux_accroissement(self, *args): r'''From Giac's documentation: Help for taux_accroissement: taux_accroissement(Expr,Var,Val1,(Val1+Var or Val2)) @@ -15687,9 +15687,9 @@ cdef class GiacMethods_base: Ex2:taux_accroissement(x^2,1,2) Ex3:taux_accroissement(a^2,a,1,1+h) ''' - return GiacMethods['taux_accroissement'](self,*args) + return GiacMethods['taux_accroissement'](self, *args) - def taylor(self,*args): + def taylor(self, *args): r'''From Giac's documentation: Help for taylor: taylor(Expr,[Var=limit_point],[Order]) @@ -15706,9 +15706,9 @@ cdef class GiacMethods_base: Ex9:taylor(sin((1+h*t)*(pi/2+k*t)),t=0,3,polynom)(t=1) Ex10:taylor((-1+k*t)^2/(1+h*t)^3,t=0,3,polynom)(t=1) ''' - return GiacMethods['taylor'](self,*args) + return GiacMethods['taylor'](self, *args) - def tchebyshev1(self,*args): + def tchebyshev1(self, *args): r'''From Giac's documentation: Help for tchebyshev1: tchebyshev1(Intg(n)) @@ -15716,9 +15716,9 @@ cdef class GiacMethods_base: See also: 1/ tchebyshev2 2/ hermite Ex1:tchebyshev1(3) ''' - return GiacMethods['tchebyshev1'](self,*args) + return GiacMethods['tchebyshev1'](self, *args) - def tchebyshev2(self,*args): + def tchebyshev2(self, *args): r'''From Giac's documentation: Help for tchebyshev2: tchebyshev2(Intg(n)) @@ -15726,9 +15726,9 @@ cdef class GiacMethods_base: See also: 1/ tchebyshev1 2/ hermite Ex1:tchebyshev2(3) ''' - return GiacMethods['tchebyshev2'](self,*args) + return GiacMethods['tchebyshev2'](self, *args) - def tcoeff(self,*args): + def tcoeff(self, *args): r'''From Giac's documentation: Help for tcoeff: tcoeff(Poly||Lst) @@ -15737,9 +15737,9 @@ cdef class GiacMethods_base: Ex1:tcoeff(-2*x^3+x^2+7*x) Ex2:tcoeff([-2,1,7,0]) ''' - return GiacMethods['tcoeff'](self,*args) + return GiacMethods['tcoeff'](self, *args) - def tcollect(self,*args): + def tcollect(self, *args): r'''From Giac's documentation: Help for tcollect: tcollect(Expr) @@ -15747,18 +15747,18 @@ cdef class GiacMethods_base: See also: 1/ texpand 2/ tlin Ex1:tcollect(sin(x)+cos(x)) ''' - return GiacMethods['tcollect'](self,*args) + return GiacMethods['tcollect'](self, *args) - def tdeg(self,*args): + def tdeg(self, *args): r'''From Giac's documentation: Help for tdeg: tdeg(Opt) Option of the gbasis or greduce command to specify an order for monomials (complete degree then lexicographic order). See also: 1/ gbasis 2/ greduce ''' - return GiacMethods['tdeg'](self,*args) + return GiacMethods['tdeg'](self, *args) - def tensor_product(self,*args): + def tensor_product(self, *args): r'''From Giac's documentation: Help for tensor_product: tensor_product(Seq(G1,G2,..)) @@ -15766,9 +15766,9 @@ cdef class GiacMethods_base: See also: 1/ cartesian_product Ex1:tensor_product(graph(trail(1,2,3,4,5,2)),star_graph(3)) ''' - return GiacMethods['tensor_product'](self,*args) + return GiacMethods['tensor_product'](self, *args) - def tetrahedron(self,*args): + def tetrahedron(self, *args): r'''From Giac's documentation: Help for tetrahedron: tetrahedron(Pnt(A),Pnt(B),Pnt(C),[Pnt(D)]) @@ -15777,9 +15777,9 @@ cdef class GiacMethods_base: Ex1:tetrahedron([0,0,0],[3,0,0],[0,1,0]) Ex2:tetrahedron([0,0,0],[3,0,0],[0,3,0],[0,0,4]) ''' - return GiacMethods['tetrahedron'](self,*args) + return GiacMethods['tetrahedron'](self, *args) - def texpand(self,*args): + def texpand(self, *args): r'''From Giac's documentation: Help for texpand: texpand(Expr) @@ -15789,9 +15789,9 @@ cdef class GiacMethods_base: Ex2:texpand(cos(x+y)) Ex3:texpand(cos(3*x)) ''' - return GiacMethods['texpand'](self,*args) + return GiacMethods['texpand'](self, *args) - def thickness(self,*args): + def thickness(self, *args): r'''From Giac's documentation: Help for thickness: thickness(Opt) @@ -15800,9 +15800,9 @@ cdef class GiacMethods_base: Ex1: segment(0,point(1,1),thickness=5) Ex2: segment(0,point(1,1),epaisseur=5) ''' - return GiacMethods['thickness'](self,*args) + return GiacMethods['thickness'](self, *args) - def threshold(self,*args): + def threshold(self, *args): r'''From Giac's documentation: Help for threshold: threshold(Lst,Real(bound)[=Expr(repl)] or Lst[Real(lower)[=Expr(rl)],Real(upper)[=Expr(ru)]],[Fnc(compare)],[abs[=true or false]]) @@ -15811,9 +15811,9 @@ cdef class GiacMethods_base: Ex1:threshold([1,3,2,4,5,4,3,2,3,1],3,'>=') Ex2:threshold([-10,-5,0,5,10],7=a,abs=true) ''' - return GiacMethods['threshold'](self,*args) + return GiacMethods['threshold'](self, *args) - def throw(self,*args): + def throw(self, *args): r'''From Giac's documentation: Help for throw: throw(Str) @@ -15822,9 +15822,9 @@ cdef class GiacMethods_base: Ex1:throw("Argument should be integer") Ex2:throw("je provoque une erreur") ''' - return GiacMethods['throw'](self,*args) + return GiacMethods['throw'](self, *args) - def title(self,*args): + def title(self, *args): r'''From Giac's documentation: Help for title: title(Opt) @@ -15833,9 +15833,9 @@ cdef class GiacMethods_base: Ex1: title="segment";segment(0,point(1,1),epaisseur=5) Ex2: titre="segment";segment(0,point(1,1),epaisseur=5) ''' - return GiacMethods['title'](self,*args) + return GiacMethods['title'](self, *args) - def titre(self,*args): + def titre(self, *args): r'''From Giac's documentation: Help for titre: titre(Opt) @@ -15844,9 +15844,9 @@ cdef class GiacMethods_base: Ex1: title="segment";segment(0,point(1,1),epaisseur=5) Ex2: titre="segment";segment(0,point(1,1),epaisseur=5) ''' - return GiacMethods['titre'](self,*args) + return GiacMethods['titre'](self, *args) - def tlin(self,*args): + def tlin(self, *args): r'''From Giac's documentation: Help for tlin: tlin(ExprTrig) @@ -15855,9 +15855,9 @@ cdef class GiacMethods_base: Ex1:tlin(sin(x)^3) Ex2:tlin(cos(x)*cos(y)) ''' - return GiacMethods['tlin'](self,*args) + return GiacMethods['tlin'](self, *args) - def tonnetz(self,*args): + def tonnetz(self, *args): r'''From Giac's documentation: Help for tonnetz: tonnetz(Intg(a),Intg(b),Intg(c),[Intg(d)]) @@ -15866,9 +15866,9 @@ cdef class GiacMethods_base: Ex1:tonnetz(3,4,5) Ex2:tonnetz(2,3,3,4) ''' - return GiacMethods['tonnetz'](self,*args) + return GiacMethods['tonnetz'](self, *args) - def topologic_sort(self,*args): + def topologic_sort(self, *args): r'''From Giac's documentation: Help for topologic_sort: topologic_sort(Graph(G)) @@ -15876,9 +15876,9 @@ cdef class GiacMethods_base: See also: 1/ digraph 2/ is_acyclic Ex1:topologic_sort(digraph(%{[c,a],[c,b],[c,d],[a,d],[b,d],[a,b]%})) ''' - return GiacMethods['topologic_sort'](self,*args) + return GiacMethods['topologic_sort'](self, *args) - def topological_sort(self,*args): + def topological_sort(self, *args): r'''From Giac's documentation: Help for topological_sort: topological_sort(Graph(G)) @@ -15886,9 +15886,9 @@ cdef class GiacMethods_base: See also: 1/ digraph 2/ is_acyclic Ex1:topological_sort(digraph(%{[c,a],[c,b],[c,d],[a,d],[b,d],[a,b]%})) ''' - return GiacMethods['topological_sort'](self,*args) + return GiacMethods['topological_sort'](self, *args) - def torus_grid_graph(self,*args): + def torus_grid_graph(self, *args): r'''From Giac's documentation: Help for torus_grid_graph: torus_grid_graph(Intg(m),Intg(n)) @@ -15896,9 +15896,9 @@ cdef class GiacMethods_base: See also: 1/ grid_graph Ex1:torus_grid_graph(6,12) ''' - return GiacMethods['torus_grid_graph'](self,*args) + return GiacMethods['torus_grid_graph'](self, *args) - def total_degree(self,*args): + def total_degree(self, *args): r'''From Giac's documentation: Help for total_degree: total_degree(Poly(P),Lst(Vars)) @@ -15906,9 +15906,9 @@ cdef class GiacMethods_base: See also: 1/ valuation 2/ size 3/ degree Ex1:total_degree(x^3*y+x*y,[x,y]) ''' - return GiacMethods['total_degree'](self,*args) + return GiacMethods['total_degree'](self, *args) - def tourne_droite(self,*args): + def tourne_droite(self, *args): r'''From Giac's documentation: Help for tourne_droite: tourne_droite(NULL or Real(n)) @@ -15917,9 +15917,9 @@ cdef class GiacMethods_base: Ex1: tourne_droite 60 Ex2:tourne_droite(60) ''' - return GiacMethods['tourne_droite'](self,*args) + return GiacMethods['tourne_droite'](self, *args) - def tourne_gauche(self,*args): + def tourne_gauche(self, *args): r'''From Giac's documentation: Help for tourne_gauche: tourne_gauche(NULL or Real(n)) @@ -15928,9 +15928,9 @@ cdef class GiacMethods_base: Ex1: tourne_gauche 60 Ex2:tourne_gauche(60) ''' - return GiacMethods['tourne_gauche'](self,*args) + return GiacMethods['tourne_gauche'](self, *args) - def tpsolve(self,*args): + def tpsolve(self, *args): r'''From Giac's documentation: Help for tpsolve: tpsolve(supply,demand,cost_matrix) @@ -15940,9 +15940,9 @@ cdef class GiacMethods_base: Ex3:tpsolve([95,70,165,165],[195,150,30,45,75],[[15,M,45,M,0],[12,40,M,M,0],[0,15,25,25,0],[M,0,M,12,0]]) Ex4:tpsolve([1,1,1,1],[1,1,1,1],[[10,12,9,11],[5,10,7,8],[12,14,13,11],[8,15,11,9]]) ''' - return GiacMethods['tpsolve'](self,*args) + return GiacMethods['tpsolve'](self, *args) - def trace(self,*args): + def trace(self, *args): r'''From Giac's documentation: Help for trace: trace(Mtrx or GeoObj) @@ -15953,9 +15953,9 @@ cdef class GiacMethods_base: Ex3: assume(a=[0.7,-5,5,0.1]);trace(point(a-i*a)) Ex4: assume(a=[0.7,-5,5,0.1]);trace(inter_unique(droite(y=a*x+a),droite(y=2*a*x+1))) ''' - return GiacMethods['trace'](self,*args) + return GiacMethods['trace'](self, *args) - def trail(self,*args): + def trail(self, *args): r'''From Giac's documentation: Help for trail: trail(Seq(V)) @@ -15963,9 +15963,9 @@ cdef class GiacMethods_base: See also: 1/ graph 2/ digraph Ex1:trail(1,2,3,4,1) ''' - return GiacMethods['trail'](self,*args) + return GiacMethods['trail'](self, *args) - def trail2edges(self,*args): + def trail2edges(self, *args): r'''From Giac's documentation: Help for trail2edges: trail2edges(Trail(T)) @@ -15974,9 +15974,9 @@ cdef class GiacMethods_base: Ex1:trail2edges(trail(1,2,3,4,1,3)) Ex2:trail2edges([1,2,3,4,1,3]) ''' - return GiacMethods['trail2edges'](self,*args) + return GiacMethods['trail2edges'](self, *args) - def trames(self,*args): + def trames(self, *args): r'''From Giac's documentation: Help for trames: trames(Opt) @@ -15985,9 +15985,9 @@ cdef class GiacMethods_base: Ex1: animate(sin(x*t),x=-pi..pi,t=-3..3,frames=30) Ex2: animate3d(x^2+t*y^2,[x=-2..2,y=-2..2],t=-3..3,frames=10) ''' - return GiacMethods['trames'](self,*args) + return GiacMethods['trames'](self, *args) - def tran(self,*args): + def tran(self, *args): r'''From Giac's documentation: Help for tran: tran(Mtrx) @@ -15997,9 +15997,9 @@ cdef class GiacMethods_base: Ex2:tran([[1+i,2,3],[1,3,6],[2,5,9-i]]) Ex3:tran(conj([[1+i,2,3],[1,3,6],[2,5,9-i]])) ''' - return GiacMethods['tran'](self,*args) + return GiacMethods['tran'](self, *args) - def transitive_closure(self,*args): + def transitive_closure(self, *args): r'''From Giac's documentation: Help for transitive_closure: transitive_closure(Graph(G),[weighted[=true||false]]) @@ -16007,9 +16007,9 @@ cdef class GiacMethods_base: See also: 1/ allpairs_distance 2/ is_connected 3/ shortest_path 4/ vertex_distance Ex1:transitive_closure(digraph([1,2,3,4,5,6],%{[1,2],[2,3],[2,4],[4,5],[3,5]%}),weighted) ''' - return GiacMethods['transitive_closure'](self,*args) + return GiacMethods['transitive_closure'](self, *args) - def translation(self,*args): + def translation(self, *args): r'''From Giac's documentation: Help for translation: translation(Vect, Pnt(C)) @@ -16020,9 +16020,9 @@ cdef class GiacMethods_base: Ex3: t:=translation(1+i);t(i) Ex4: t:=translation([1,1,1]);t(point([1,2,3])) ''' - return GiacMethods['translation'](self,*args) + return GiacMethods['translation'](self, *args) - def transpose(self,*args): + def transpose(self, *args): r'''From Giac's documentation: Help for transpose: transpose(Mtrx) @@ -16032,9 +16032,9 @@ cdef class GiacMethods_base: Ex2:transpose([[1+i,2,3],[1,3,6],[2,5,9-i]]) Ex3:transpose(conj([[1+i,2,3],[1,3,6],[2,5,9-i]])) ''' - return GiacMethods['transpose'](self,*args) + return GiacMethods['transpose'](self, *args) - def trapeze(self,*args): + def trapeze(self, *args): r'''From Giac's documentation: Help for trapeze: trapeze(Opt) @@ -16047,9 +16047,9 @@ cdef class GiacMethods_base: Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) ''' - return GiacMethods['trapeze'](self,*args) + return GiacMethods['trapeze'](self, *args) - def trapezoid(self,*args): + def trapezoid(self, *args): r'''From Giac's documentation: Help for trapezoid: trapezoid(Opt) @@ -16062,9 +16062,9 @@ cdef class GiacMethods_base: Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) ''' - return GiacMethods['trapezoid'](self,*args) + return GiacMethods['trapezoid'](self, *args) - def traveling_salesman(self,*args): + def traveling_salesman(self, *args): r'''From Giac's documentation: Help for traveling_salesman: traveling_salesman(Graph(G),[Mtrx(M)],[opts]) @@ -16076,18 +16076,18 @@ cdef class GiacMethods_base: Ex4: G:=set_vertex_positions(complete_graph(42),[randvector(2,1000)$(k=1..42)]); traveling_salesman(G,vertex_distance) Ex5: G:=set_vertex_positions(complete_graph(120),[randvector(2,1000)$(k=1..120)]); c,T:=traveling_salesman(G,vertex_distance,approx) ''' - return GiacMethods['traveling_salesman'](self,*args) + return GiacMethods['traveling_salesman'](self, *args) - def tree(self,*args): + def tree(self, *args): r'''From Giac's documentation: Help for tree: tree(Opt) Option for the draw_graph command. See also: 1/ planar 2/ spring 3/ draw_graph ''' - return GiacMethods['tree'](self,*args) + return GiacMethods['tree'](self, *args) - def tree_height(self,*args): + def tree_height(self, *args): r'''From Giac's documentation: Help for tree_height: tree_height(Graph(T),Vrtx(r)) @@ -16095,9 +16095,9 @@ cdef class GiacMethods_base: See also: 1/ is_tree 2/ random_tree Ex1:tree_height(graph(%{[1,2],[2,3],[2,4],[4,5]%}),1) ''' - return GiacMethods['tree_height'](self,*args) + return GiacMethods['tree_height'](self, *args) - def tri(self,*args): + def tri(self, *args): r'''From Giac's documentation: Help for tri: tri(Expr(x)) @@ -16105,9 +16105,9 @@ cdef class GiacMethods_base: See also: 1/ rect 2/ Heaviside Ex1:tri(x-1) ''' - return GiacMethods['tri'](self,*args) + return GiacMethods['tri'](self, *args) - def triangle(self,*args): + def triangle(self, *args): r'''From Giac's documentation: Help for triangle: triangle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) @@ -16117,9 +16117,9 @@ cdef class GiacMethods_base: Ex2:triangle(0,1,1+i) Ex3:triangle(point(0,0,0),point(3,3,3),point(0,3,3)) ''' - return GiacMethods['triangle'](self,*args) + return GiacMethods['triangle'](self, *args) - def triangle_paper(self,*args): + def triangle_paper(self, *args): r'''From Giac's documentation: Help for triangle_paper: triangle_paper(Real(ux),Real(t),Real(uy),[x=xmin..xmax,y=ymin..ymax]) @@ -16129,9 +16129,9 @@ cdef class GiacMethods_base: Ex3:triangle_paper(papier_triangule(1,pi/3,sqrt(3)/2,x=-2..6,y=-4*sqrt(3)..4*sqrt(3))) Ex4:triangle_paper(0.5,3*pi/4,0.5) ''' - return GiacMethods['triangle_paper'](self,*args) + return GiacMethods['triangle_paper'](self, *args) - def triangle_plein(self,*args): + def triangle_plein(self, *args): r'''From Giac's documentation: Help for triangle_plein: triangle_plein(Real(a),[Real(b)],[Real(t)]) @@ -16142,9 +16142,9 @@ cdef class GiacMethods_base: Ex3:triangle_plein(30,40) Ex4:triangle_plein(30,40,60) ''' - return GiacMethods['triangle_plein'](self,*args) + return GiacMethods['triangle_plein'](self, *args) - def triangle_point(self,*args): + def triangle_point(self, *args): r'''From Giac's documentation: Help for triangle_point: triangle_point(Opt) @@ -16153,9 +16153,9 @@ cdef class GiacMethods_base: Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) ''' - return GiacMethods['triangle_point'](self,*args) + return GiacMethods['triangle_point'](self, *args) - def triangle_window(self,*args): + def triangle_window(self, *args): r'''From Giac's documentation: Help for triangle_window: triangle_window(Lst,[Intg(d)],[Interval(n1..n2)]) @@ -16163,9 +16163,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ bartlett_hann_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(triangle_window(randvector(1000,0..1),1)) ''' - return GiacMethods['triangle_window'](self,*args) + return GiacMethods['triangle_window'](self, *args) - def trig2exp(self,*args): + def trig2exp(self, *args): r'''From Giac's documentation: Help for trig2exp: trig2exp(Expr) @@ -16173,9 +16173,9 @@ cdef class GiacMethods_base: See also: 1/ exp2trig 2/ atrig2ln Ex1:trig2exp(sin(x)) ''' - return GiacMethods['trig2exp'](self,*args) + return GiacMethods['trig2exp'](self, *args) - def trigcos(self,*args): + def trigcos(self, *args): r'''From Giac's documentation: Help for trigcos: trigcos(Expr) @@ -16183,9 +16183,9 @@ cdef class GiacMethods_base: See also: 1/ trigsin 2/ trigtan Ex1:trigcos(sin(x)^4+sin(x)^2) ''' - return GiacMethods['trigcos'](self,*args) + return GiacMethods['trigcos'](self, *args) - def trigexpand(self,*args): + def trigexpand(self, *args): r'''From Giac's documentation: Help for trigexpand: trigexpand(Expr) @@ -16193,9 +16193,9 @@ cdef class GiacMethods_base: See also: 1/ texpand 2/ lnexpand 3/ expexpand Ex1:trigexpand(sin(3*x)) ''' - return GiacMethods['trigexpand'](self,*args) + return GiacMethods['trigexpand'](self, *args) - def triginterp(self,*args): + def triginterp(self, *args): r'''From Giac's documentation: Help for triginterp: triginterp(List,Var=xmin..xmax) @@ -16204,9 +16204,9 @@ cdef class GiacMethods_base: Ex1:triginterp([11,10,17,24,32,26,23,19],x=0..21) Ex2:triginterp([11,10,17,24,32,26,23,19],0,21,x) ''' - return GiacMethods['triginterp'](self,*args) + return GiacMethods['triginterp'](self, *args) - def trigsimplify(self,*args): + def trigsimplify(self, *args): r'''From Giac's documentation: Help for trigsimplify: trigsimplify(Expr) @@ -16214,9 +16214,9 @@ cdef class GiacMethods_base: See also: 1/ simplify Ex1:trigsimplify(3*sin(x)-4*sin(x)^3) ''' - return GiacMethods['trigsimplify'](self,*args) + return GiacMethods['trigsimplify'](self, *args) - def trigsin(self,*args): + def trigsin(self, *args): r'''From Giac's documentation: Help for trigsin: trigsin(Expr) @@ -16224,9 +16224,9 @@ cdef class GiacMethods_base: See also: 1/ trigcos 2/ trigtan Ex1:trigsin(cos(x)^4+sin(x)^2) ''' - return GiacMethods['trigsin'](self,*args) + return GiacMethods['trigsin'](self, *args) - def trigtan(self,*args): + def trigtan(self, *args): r'''From Giac's documentation: Help for trigtan: trigtan(Expr) @@ -16234,9 +16234,9 @@ cdef class GiacMethods_base: See also: 1/ trigsin 2/ trigcos Ex1:trigtan(cos(x)^4+sin(x)^2) ''' - return GiacMethods['trigtan'](self,*args) + return GiacMethods['trigtan'](self, *args) - def trn(self,*args): + def trn(self, *args): r'''From Giac's documentation: Help for trn: trn(Mtrx) @@ -16244,9 +16244,9 @@ cdef class GiacMethods_base: See also: 1/ tran 2/ conj Ex1:trn([[1,2+i],[3,4]]) ''' - return GiacMethods['trn'](self,*args) + return GiacMethods['trn'](self, *args) - def true(self,*args): + def true(self, *args): r'''From Giac's documentation: Help for true: true() @@ -16254,9 +16254,9 @@ cdef class GiacMethods_base: See also: 1/ false Ex1: a:=true ''' - return GiacMethods['true'](self,*args) + return GiacMethods['true'](self, *args) - def trunc(self,*args): + def trunc(self, *args): r'''From Giac's documentation: Help for trunc: trunc(Real||LstReal,Int(n)) @@ -16268,9 +16268,9 @@ cdef class GiacMethods_base: Ex4:trunc([4.3333,sqrt(2)],2) Ex5:trunc(sqrt(2)+i*sqrt(5),4) ''' - return GiacMethods['trunc'](self,*args) + return GiacMethods['trunc'](self, *args) - def truncate(self,*args): + def truncate(self, *args): r'''From Giac's documentation: Help for truncate: truncate(Poly(P),Intg(n)) @@ -16278,9 +16278,9 @@ cdef class GiacMethods_base: See also: 1/ series Ex1:truncate((x^2+x)^2,3) ''' - return GiacMethods['truncate'](self,*args) + return GiacMethods['truncate'](self, *args) - def truncate_graph(self,*args): + def truncate_graph(self, *args): r'''From Giac's documentation: Help for truncate_graph: truncate_graph(Graph(G)) @@ -16288,9 +16288,9 @@ cdef class GiacMethods_base: See also: 1/ is_biconnected 2/ is_planar 3/ plane_dual Ex1:truncate_graph(graph("tetrahedron")) ''' - return GiacMethods['truncate_graph'](self,*args) + return GiacMethods['truncate_graph'](self, *args) - def tsimplify(self,*args): + def tsimplify(self, *args): r'''From Giac's documentation: Help for tsimplify: tsimplify(Expr) @@ -16298,9 +16298,9 @@ cdef class GiacMethods_base: See also: 1/ simplify Ex1:tsimplify(exp(2*x)+exp(x)) ''' - return GiacMethods['tsimplify'](self,*args) + return GiacMethods['tsimplify'](self, *args) - def tuer(self,*args): + def tuer(self, *args): r'''From Giac's documentation: Help for tuer: tuer(NULL) @@ -16308,9 +16308,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:tuer() ''' - return GiacMethods['tuer'](self,*args) + return GiacMethods['tuer'](self, *args) - def tukey_window(self,*args): + def tukey_window(self, *args): r'''From Giac's documentation: Help for tukey_window: tukey_window(Lst,[Real(a)],[Interval(n1..n2)]) @@ -16318,9 +16318,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ bartlett_hann_window 14/ welch_window Ex1: scatterplot(tukey_window(randvector(1000,0..1),0.4)) ''' - return GiacMethods['tukey_window'](self,*args) + return GiacMethods['tukey_window'](self, *args) - def tutte_polynomial(self,*args): + def tutte_polynomial(self, *args): r'''From Giac's documentation: Help for tutte_polynomial: tutte_polynomial(Graph(G),[Var(x),Var(y)]) @@ -16329,9 +16329,9 @@ cdef class GiacMethods_base: Ex1:tutte_polynomial(graph("tetrahedron")) Ex2:tutte_polynomial(graph("tetrahedron"),1,1) ''' - return GiacMethods['tutte_polynomial'](self,*args) + return GiacMethods['tutte_polynomial'](self, *args) - def two_edge_connected_components(self,*args): + def two_edge_connected_components(self, *args): r'''From Giac's documentation: Help for two_edge_connected_components: two_edge_connected_components(Graph(G)) @@ -16339,9 +16339,9 @@ cdef class GiacMethods_base: See also: 1/ is_two_edge_connected 2/ connected_components Ex1:two_edge_connected_components(graph(trail(1,2,3,4,5,3,1),trail(5,6,7,8,6))) ''' - return GiacMethods['two_edge_connected_components'](self,*args) + return GiacMethods['two_edge_connected_components'](self, *args) - def ufactor(self,*args): + def ufactor(self, *args): r'''From Giac's documentation: Help for ufactor: ufactor(Unit,Unit) @@ -16349,9 +16349,9 @@ cdef class GiacMethods_base: See also: 1/ convert 2/ mksa 3/ usimplify Ex1:ufactor(100_C,1_A) ''' - return GiacMethods['ufactor'](self,*args) + return GiacMethods['ufactor'](self, *args) - def ugamma(self,*args): + def ugamma(self, *args): r'''From Giac's documentation: Help for ugamma: ugamma(Real(a),Real(x),[1]) @@ -16360,9 +16360,9 @@ cdef class GiacMethods_base: Ex1:ugamma(5.0,2.0) Ex2:ugamma(-5.1,2.1) ''' - return GiacMethods['ugamma'](self,*args) + return GiacMethods['ugamma'](self, *args) - def unapply(self,*args): + def unapply(self, *args): r'''From Giac's documentation: Help for unapply: unapply(Expr,Var) @@ -16371,9 +16371,9 @@ cdef class GiacMethods_base: Ex1:unapply(2*x^2,x) Ex2: f(x):=x*exp(x);g:=unapply(diff(f(x),x),x) ''' - return GiacMethods['unapply'](self,*args) + return GiacMethods['unapply'](self, *args) - def unarchive(self,*args): + def unarchive(self, *args): r'''From Giac's documentation: Help for unarchive: unarchive(Str(namefich),Seq(Var)) @@ -16382,9 +16382,9 @@ cdef class GiacMethods_base: Ex1:unarchive("toto") Ex2:unarchive("aa.txt") ''' - return GiacMethods['unarchive'](self,*args) + return GiacMethods['unarchive'](self, *args) - def underlying_graph(self,*args): + def underlying_graph(self, *args): r'''From Giac's documentation: Help for underlying_graph: underlying_graph(Graph(G)) @@ -16392,9 +16392,9 @@ cdef class GiacMethods_base: See also: 1/ is_directed 2/ is_weighted 3/ make_directed 4/ make_weighted Ex1:underlying_graph(digraph(trail(1,2,3,4,1))) ''' - return GiacMethods['underlying_graph'](self,*args) + return GiacMethods['underlying_graph'](self, *args) - def unfactored(self,*args): + def unfactored(self, *args): r'''From Giac's documentation: Help for unfactored: unfactored(Opt.) @@ -16406,9 +16406,9 @@ cdef class GiacMethods_base: Ex4: plotimplicit(x^2+y^2+z^2-1,[x,y,z],xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex5: plotimplicit(x^2+y^2+z^2-1,x=0..1,y=0..1,z=0..1,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) ''' - return GiacMethods['unfactored'](self,*args) + return GiacMethods['unfactored'](self, *args) - def uniform(self,*args): + def uniform(self, *args): r'''From Giac's documentation: Help for uniform: uniform(Real(a),Real(b),Real(x)) @@ -16419,9 +16419,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,uniform,1.2,3.5) Ex4: ranm(4,3,uniform,1.2,3.5) ''' - return GiacMethods['uniform'](self,*args) + return GiacMethods['uniform'](self, *args) - def uniform_cdf(self,*args): + def uniform_cdf(self, *args): r'''From Giac's documentation: Help for uniform_cdf: uniform_cdf(Real(a),Real(b),Real(x0),[Real(y0)]) @@ -16430,9 +16430,9 @@ cdef class GiacMethods_base: Ex1:uniform_cdf(3.2,5.7,4.4) Ex2:uniform_cdf(3.2,5.7,4.4,5.4) ''' - return GiacMethods['uniform_cdf'](self,*args) + return GiacMethods['uniform_cdf'](self, *args) - def uniform_icdf(self,*args): + def uniform_icdf(self, *args): r'''From Giac's documentation: Help for uniform_icdf: uniform_icdf(Real(a),Real(b),Real(p)) @@ -16441,9 +16441,9 @@ cdef class GiacMethods_base: Ex1:uniform_icdf(4.2,10.3,0.95) Ex2:uniform_icdf(3.2,5.7,0.48) ''' - return GiacMethods['uniform_icdf'](self,*args) + return GiacMethods['uniform_icdf'](self, *args) - def uniformd(self,*args): + def uniformd(self, *args): r'''From Giac's documentation: Help for uniformd: uniformd(Real(a),Real(b),Real(x)) @@ -16454,9 +16454,9 @@ cdef class GiacMethods_base: Ex3: randvector(3,uniform,1.2,3.5) Ex4: ranm(4,3,uniform,1.2,3.5) ''' - return GiacMethods['uniformd'](self,*args) + return GiacMethods['uniformd'](self, *args) - def uniformd_cdf(self,*args): + def uniformd_cdf(self, *args): r'''From Giac's documentation: Help for uniformd_cdf: uniformd_cdf(Real(a),Real(b),Real(x0),[Real(y0)]) @@ -16465,9 +16465,9 @@ cdef class GiacMethods_base: Ex1:uniformd_cdf(3.2,5.7,4.4) Ex2:uniformd_cdf(3.2,5.7,4.4,5.4) ''' - return GiacMethods['uniformd_cdf'](self,*args) + return GiacMethods['uniformd_cdf'](self, *args) - def uniformd_icdf(self,*args): + def uniformd_icdf(self, *args): r'''From Giac's documentation: Help for uniformd_icdf: uniformd_icdf(Real(a),Real(b),Real(p)) @@ -16476,9 +16476,9 @@ cdef class GiacMethods_base: Ex1:uniformd_icdf(4.2,10.3,0.95) Ex2:uniformd_icdf(3.2,5.7,0.48) ''' - return GiacMethods['uniformd_icdf'](self,*args) + return GiacMethods['uniformd_icdf'](self, *args) - def unitV(self,*args): + def unitV(self, *args): r'''From Giac's documentation: Help for unitV: unitV(Lst||Cplx) @@ -16489,9 +16489,9 @@ cdef class GiacMethods_base: Ex3: fieldplot(-t*y,[t,y],normalize) Ex4: fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) ''' - return GiacMethods['unitV'](self,*args) + return GiacMethods['unitV'](self, *args) - def unquote(self,*args): + def unquote(self, *args): r'''From Giac's documentation: Help for unquote: unquote(Expr) @@ -16499,9 +16499,9 @@ cdef class GiacMethods_base: See also: 1/ quote Ex1:unquote(a) ''' - return GiacMethods['unquote'](self,*args) + return GiacMethods['unquote'](self, *args) - def upper(self,*args): + def upper(self, *args): r'''From Giac's documentation: Help for upper: upper(Mtrx||Strng) @@ -16510,9 +16510,9 @@ cdef class GiacMethods_base: Ex1:upper([[1,2,3],[4,5,6],[7,8,9]]) Ex2:upper("hello") ''' - return GiacMethods['upper'](self,*args) + return GiacMethods['upper'](self, *args) - def user_operator(self,*args): + def user_operator(self, *args): r'''From Giac's documentation: Help for user_operator: user_operator(Str(R),Fnc(f),Opt(Binary||Unary||Delete)) @@ -16521,9 +16521,9 @@ cdef class GiacMethods_base: Ex1:user_operator("R",(x,y)->x*y+x+y,Binary) Ex2:user_operator("R",(x,y)->x*y+x+y,Delete) ''' - return GiacMethods['user_operator'](self,*args) + return GiacMethods['user_operator'](self, *args) - def usimplify(self,*args): + def usimplify(self, *args): r'''From Giac's documentation: Help for usimplify: usimplify(Unit) @@ -16531,9 +16531,9 @@ cdef class GiacMethods_base: See also: 1/ convert 2/ mksa 3/ ufactor Ex1:usimplify(100_(W*s)) ''' - return GiacMethods['usimplify'](self,*args) + return GiacMethods['usimplify'](self, *args) - def valuation(self,*args): + def valuation(self, *args): r'''From Giac's documentation: Help for valuation: valuation(Poly(P)) @@ -16544,9 +16544,9 @@ cdef class GiacMethods_base: Ex3:valuation(x^5+3*x^2) Ex4:valuation([5,0,0,3,0,0]) ''' - return GiacMethods['valuation'](self,*args) + return GiacMethods['valuation'](self, *args) - def vandermonde(self,*args): + def vandermonde(self, *args): r'''From Giac's documentation: Help for vandermonde: vandermonde(Vect(V)) @@ -16554,9 +16554,9 @@ cdef class GiacMethods_base: See also: 1/ det Ex1:vandermonde([1,2,a]) ''' - return GiacMethods['vandermonde'](self,*args) + return GiacMethods['vandermonde'](self, *args) - def variables_are_files(self,*args): + def variables_are_files(self, *args): r'''From Giac's documentation: Help for variables_are_files: variables_are_files(:=Intg(0 or 1)) @@ -16565,9 +16565,9 @@ cdef class GiacMethods_base: Ex1: variables_are_files:=1 Ex2: variables_are_files:=0 ''' - return GiacMethods['variables_are_files'](self,*args) + return GiacMethods['variables_are_files'](self, *args) - def variance(self,*args): + def variance(self, *args): r'''From Giac's documentation: Help for variance: variance(Lst||Mtrx,[Lst]) @@ -16577,9 +16577,9 @@ cdef class GiacMethods_base: Ex2:variance([1,2,3],[1,2,1]) Ex3:variance([[1,2,3],[5,6,7]]) ''' - return GiacMethods['variance'](self,*args) + return GiacMethods['variance'](self, *args) - def version(self,*args): + def version(self, *args): r'''From Giac's documentation: Help for version: version(NULL) @@ -16587,9 +16587,9 @@ cdef class GiacMethods_base: See also: 1/ Ex1:version() ''' - return GiacMethods['version'](self,*args) + return GiacMethods['version'](self, *args) - def vertex_connectivity(self,*args): + def vertex_connectivity(self, *args): r'''From Giac's documentation: Help for vertex_connectivity: vertex_connectivity(Graph(G)) @@ -16599,9 +16599,9 @@ cdef class GiacMethods_base: Ex2:vertex_connectivity(graph("clebsch")) Ex3:vertex_connectivity(complete_graph(5)) ''' - return GiacMethods['vertex_connectivity'](self,*args) + return GiacMethods['vertex_connectivity'](self, *args) - def vertex_degree(self,*args): + def vertex_degree(self, *args): r'''From Giac's documentation: Help for vertex_degree: vertex_degree(Graph(G),Vrtx(v)) @@ -16609,9 +16609,9 @@ cdef class GiacMethods_base: See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_in_degree 6/ vertex_out_degree Ex1:vertex_degree(digraph(trail(1,2,3,4,2)),2) ''' - return GiacMethods['vertex_degree'](self,*args) + return GiacMethods['vertex_degree'](self, *args) - def vertex_distance(self,*args): + def vertex_distance(self, *args): r'''From Giac's documentation: Help for vertex_distance: vertex_distance(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) @@ -16620,9 +16620,9 @@ cdef class GiacMethods_base: Ex1:vertex_distance(graph("petersen"),1,4) Ex2:vertex_distance(graph("petersen"),1,[2,4]) ''' - return GiacMethods['vertex_distance'](self,*args) + return GiacMethods['vertex_distance'](self, *args) - def vertex_in_degree(self,*args): + def vertex_in_degree(self, *args): r'''From Giac's documentation: Help for vertex_in_degree: vertex_in_degree(Graph(G),Vrtx(v)) @@ -16630,9 +16630,9 @@ cdef class GiacMethods_base: See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_out_degree Ex1:vertex_in_degree(digraph(trail(1,2,3,4,2)),2) ''' - return GiacMethods['vertex_in_degree'](self,*args) + return GiacMethods['vertex_in_degree'](self, *args) - def vertex_out_degree(self,*args): + def vertex_out_degree(self, *args): r'''From Giac's documentation: Help for vertex_out_degree: vertex_out_degree(Graph(G),Vrtx(v)) @@ -16640,9 +16640,9 @@ cdef class GiacMethods_base: See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_in_degree Ex1:vertex_out_degree(digraph(trail(1,2,3,4,2)),2) ''' - return GiacMethods['vertex_out_degree'](self,*args) + return GiacMethods['vertex_out_degree'](self, *args) - def vertices(self,*args): + def vertices(self, *args): r'''From Giac's documentation: Help for vertices: vertices(Polygon or Polyedr(P)) @@ -16652,9 +16652,9 @@ cdef class GiacMethods_base: Ex2:vertices(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices(isosceles_triangle(0,1,pi/4))[2] ''' - return GiacMethods['vertices'](self,*args) + return GiacMethods['vertices'](self, *args) - def vertices_abc(self,*args): + def vertices_abc(self, *args): r'''From Giac's documentation: Help for vertices_abc: vertices_abc(Polygon or Polyedr(P)) @@ -16664,9 +16664,9 @@ cdef class GiacMethods_base: Ex2:vertices_abc(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices_abc(isosceles_triangle(0,1,pi/4))[2] ''' - return GiacMethods['vertices_abc'](self,*args) + return GiacMethods['vertices_abc'](self, *args) - def vertices_abca(self,*args): + def vertices_abca(self, *args): r'''From Giac's documentation: Help for vertices_abca: vertices_abca(Polygon or Polyedr(P)) @@ -16676,9 +16676,9 @@ cdef class GiacMethods_base: Ex2:vertices_abca(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices_abca(isosceles_triangle(0,1,pi/4))[2] ''' - return GiacMethods['vertices_abca'](self,*args) + return GiacMethods['vertices_abca'](self, *args) - def vpotential(self,*args): + def vpotential(self, *args): r'''From Giac's documentation: Help for vpotential: vpotential(Vect(V),LstVar) @@ -16686,9 +16686,9 @@ cdef class GiacMethods_base: See also: 1/ curl 2/ potential Ex1:vpotential([2*x*y+3,x^2-4*z,-2*y*z],[x,y,z]) ''' - return GiacMethods['vpotential'](self,*args) + return GiacMethods['vpotential'](self, *args) - def web_graph(self,*args): + def web_graph(self, *args): r'''From Giac's documentation: Help for web_graph: web_graph(Intg(a),Intg(b)) @@ -16696,9 +16696,9 @@ cdef class GiacMethods_base: See also: 1/ prism_graph 2/ wheel_graph Ex1:web_graph(5,3) ''' - return GiacMethods['web_graph'](self,*args) + return GiacMethods['web_graph'](self, *args) - def weibull(self,*args): + def weibull(self, *args): r'''From Giac's documentation: Help for weibull: weibull(Real(k),Real(lambda),Real(theta),Real(x)) @@ -16708,9 +16708,9 @@ cdef class GiacMethods_base: Ex2:weibull(2.1,1.2,0.0,1.3) Ex3:weibull(2.1,1.2,0.5,1.8) ''' - return GiacMethods['weibull'](self,*args) + return GiacMethods['weibull'](self, *args) - def weibull_cdf(self,*args): + def weibull_cdf(self, *args): r'''From Giac's documentation: Help for weibull_cdf: weibull_cdf(Real(k),Real(lambda),Real(theta),Real(x0)) @@ -16722,9 +16722,9 @@ cdef class GiacMethods_base: Ex4:weibull_cdf(2.2,1.5,0.4,1.2) Ex5:weibull_cdf(2.2,1.5,0.4,1.2,1.9) ''' - return GiacMethods['weibull_cdf'](self,*args) + return GiacMethods['weibull_cdf'](self, *args) - def weibull_icdf(self,*args): + def weibull_icdf(self, *args): r'''From Giac's documentation: Help for weibull_icdf: weibull_icdf(Real(k),Real(lambda),Real(theta),Real(p)) @@ -16733,9 +16733,9 @@ cdef class GiacMethods_base: Ex1:weibull_icdf(4.2,1.3,0.0,0.95) Ex2:weibull_icdf(2.2,1.5,0.4,0.632) ''' - return GiacMethods['weibull_icdf'](self,*args) + return GiacMethods['weibull_icdf'](self, *args) - def weibulld(self,*args): + def weibulld(self, *args): r'''From Giac's documentation: Help for weibulld: weibulld(Real(k),Real(lambda),Real(theta),Real(x)) @@ -16745,9 +16745,9 @@ cdef class GiacMethods_base: Ex2:weibulld(2.1,1.2,0.0,1.3) Ex3:weibulld(2.1,1.2,0.5,1.8) ''' - return GiacMethods['weibulld'](self,*args) + return GiacMethods['weibulld'](self, *args) - def weibulld_cdf(self,*args): + def weibulld_cdf(self, *args): r'''From Giac's documentation: Help for weibulld_cdf: weibulld_cdf(Real(k),Real(lambda),Real(theta),Real(x0)) @@ -16759,9 +16759,9 @@ cdef class GiacMethods_base: Ex4:weibulld_cdf(2.2,1.5,0.4,1.2) Ex5:weibulld_cdf(2.2,1.5,0.4,1.2,1.9) ''' - return GiacMethods['weibulld_cdf'](self,*args) + return GiacMethods['weibulld_cdf'](self, *args) - def weibulld_icdf(self,*args): + def weibulld_icdf(self, *args): r'''From Giac's documentation: Help for weibulld_icdf: weibulld_icdf(Real(k),Real(lambda),Real(theta),Real(p)) @@ -16770,9 +16770,9 @@ cdef class GiacMethods_base: Ex1:weibulld_icdf(4.2,1.3,0.0,0.95) Ex2:weibulld_icdf(2.2,1.5,0.4,0.632) ''' - return GiacMethods['weibulld_icdf'](self,*args) + return GiacMethods['weibulld_icdf'](self, *args) - def weibullvariate(self,*args): + def weibullvariate(self, *args): r'''From Giac's documentation: Help for weibullvariate: weibullvariate(Real(a),Real(b)) @@ -16781,9 +16781,9 @@ cdef class GiacMethods_base: Ex1:weibullvariate(1,2) Ex2:weibullvariate(1.5,4) ''' - return GiacMethods['weibullvariate'](self,*args) + return GiacMethods['weibullvariate'](self, *args) - def weight_matrix(self,*args): + def weight_matrix(self, *args): r'''From Giac's documentation: Help for weight_matrix: weight_matrix(Graph(G)) @@ -16791,27 +16791,27 @@ cdef class GiacMethods_base: See also: 1/ set_edge_weight 2/ get_edge_weights 3/ is_weighted 4/ make_weighted 5/ assign_edge_weights Ex1:weight_matrix(graph(%{[[1,2],2],[[2,3],1]%}) ''' - return GiacMethods['weight_matrix'](self,*args) + return GiacMethods['weight_matrix'](self, *args) - def weighted(self,*args): + def weighted(self, *args): r'''From Giac's documentation: Help for weighted: weighted(Opt) Option for graph and digraph commands. See also: 1/ directed 2/ graph 3/ digraph ''' - return GiacMethods['weighted'](self,*args) + return GiacMethods['weighted'](self, *args) - def weights(self,*args): + def weights(self, *args): r'''From Giac's documentation: Help for weights: weights(Opt) Option for the edges command. See also: 1/ edges ''' - return GiacMethods['weights'](self,*args) + return GiacMethods['weights'](self, *args) - def welch_window(self,*args): + def welch_window(self, *args): r'''From Giac's documentation: Help for welch_window: welch_window(Lst,[Interval(n1..n2)]) @@ -16819,9 +16819,9 @@ cdef class GiacMethods_base: See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ bartlett_hann_window Ex1: scatterplot(welch_window(randvector(1000,0..1))) ''' - return GiacMethods['welch_window'](self,*args) + return GiacMethods['welch_window'](self, *args) - def wheel_graph(self,*args): + def wheel_graph(self, *args): r'''From Giac's documentation: Help for wheel_graph: wheel_graph(Intg(n)) @@ -16829,9 +16829,9 @@ cdef class GiacMethods_base: See also: 1/ star_graph 2/ web_graph Ex1:wheel_graph(5) ''' - return GiacMethods['wheel_graph'](self,*args) + return GiacMethods['wheel_graph'](self, *args) - def widget_size(self,*args): + def widget_size(self, *args): r'''From Giac's documentation: Help for widget_size: widget_size(Intg(n)) @@ -16841,9 +16841,9 @@ cdef class GiacMethods_base: Ex2:widget_size(8) Ex3:widget_size(20,58,49,697,563,1,1,0) ''' - return GiacMethods['widget_size'](self,*args) + return GiacMethods['widget_size'](self, *args) - def wilcoxonp(self,*args): + def wilcoxonp(self, *args): r'''From Giac's documentation: Help for wilcoxonp: wilcoxonp(Intg,[Intg]) @@ -16852,9 +16852,9 @@ cdef class GiacMethods_base: Ex1:wilcoxonp(4) Ex2:wilcoxonp(7,5) ''' - return GiacMethods['wilcoxonp'](self,*args) + return GiacMethods['wilcoxonp'](self, *args) - def wilcoxons(self,*args): + def wilcoxons(self, *args): r'''From Giac's documentation: Help for wilcoxons: wilcoxons(List,List || Real) @@ -16863,9 +16863,9 @@ cdef class GiacMethods_base: Ex1:wilcoxons([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , [2, 6, 10, 11, 13, 14, 15, 18, 19, 20]) Ex2:wilcoxons([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10) ''' - return GiacMethods['wilcoxons'](self,*args) + return GiacMethods['wilcoxons'](self, *args) - def wilcoxont(self,*args): + def wilcoxont(self, *args): r'''From Giac's documentation: Help for wilcoxont: wilcoxont(List,List || Real,[Func],[Real]) @@ -16876,9 +16876,9 @@ cdef class GiacMethods_base: Ex3:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10,'>') Ex4:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10,'>',0.05) ''' - return GiacMethods['wilcoxont'](self,*args) + return GiacMethods['wilcoxont'](self, *args) - def writergb(self,*args): + def writergb(self, *args): r'''From Giac's documentation: Help for writergb: writergb(Str(s),Lst) @@ -16888,9 +16888,9 @@ cdef class GiacMethods_base: Ex2:writergb("image.png",[[255,0],[0,0]],[[0,255],[0,0]],[[0,0],[255,0]]) Ex3: a:=readrgb("rgb_image.png");writergb("brg_image.png",[a[0],a[4],a[1],a[3],a[2]]) ''' - return GiacMethods['writergb'](self,*args) + return GiacMethods['writergb'](self, *args) - def writewav(self,*args): + def writewav(self, *args): r'''From Giac's documentation: Help for writewav: writewav(Str(s),Lst(l)) @@ -16899,9 +16899,9 @@ cdef class GiacMethods_base: Ex1:writewav("la.wav",2^14*(sin(2*pi*440*soundsec(1)))) Ex2:writewav("beep.wav",[[1,16,44100,80000],[65000$10000,0$10000,65000$10000,0$10000]]) ''' - return GiacMethods['writewav'](self,*args) + return GiacMethods['writewav'](self, *args) - def xcas_mode(self,*args): + def xcas_mode(self, *args): r'''From Giac's documentation: Help for xcas_mode: xcas_mode(Intg(0) or 1 or 2 or 3) @@ -16910,9 +16910,9 @@ cdef class GiacMethods_base: Ex1:xcas_mode(1) Ex2:xcas_mode(0) ''' - return GiacMethods['xcas_mode'](self,*args) + return GiacMethods['xcas_mode'](self, *args) - def xml_print(self,*args): + def xml_print(self, *args): r'''From Giac's documentation: Help for xml_print: xml_print(Str) @@ -16920,18 +16920,18 @@ cdef class GiacMethods_base: See also: 1/ export_mathml Ex1:xml_print(export_mathml(a+2*b)) ''' - return GiacMethods['xml_print'](self,*args) + return GiacMethods['xml_print'](self, *args) - def xyztrange(self,*args): + def xyztrange(self, *args): r'''From Giac's documentation: Help for xyztrange: xyztrange(SeqReal) xyztrange puts or erases the axes on the graphic-screen (cf button Cfg). Ex1:xyztrange(-5.0,5.0,-5.0,2.0,-10.0,10.0,-1.0,6.0,-5.0,5.0,-1.2384,2.0,1,0.0,1.0) ''' - return GiacMethods['xyztrange'](self,*args) + return GiacMethods['xyztrange'](self, *args) - def zeros(self,*args): + def zeros(self, *args): r'''From Giac's documentation: Help for zeros: zeros(Expr,[Var]) @@ -16942,9 +16942,9 @@ cdef class GiacMethods_base: Ex3:zeros(ln(y)^2-2,y) Ex4:zeros([x^2-1,x^2-y^2],[x,y]) ''' - return GiacMethods['zeros'](self,*args) + return GiacMethods['zeros'](self, *args) - def ztrans(self,*args): + def ztrans(self, *args): r'''From Giac's documentation: Help for ztrans: ztrans(Expr,[Var],[ZtransVar]) @@ -16953,9 +16953,9 @@ cdef class GiacMethods_base: Ex1:ztrans(a^x) Ex2:ztrans(a^n,n,z) ''' - return GiacMethods['ztrans'](self,*args) + return GiacMethods['ztrans'](self, *args) - def type(self,*args): + def type(self, *args): r'''From Giac's documentation: Help for type: type(Expr) @@ -16964,9 +16964,9 @@ cdef class GiacMethods_base: Ex1:type("abc") Ex2:type([1,2,3]) ''' - return GiacMethods['type'](self,*args) + return GiacMethods['type'](self, *args) - def zip(self,*args): + def zip(self, *args): r'''From Giac's documentation: Help for zip: zip(Fnc2d(f),Lst(l1),Lst(l2),[Val(default)]) @@ -16977,5 +16977,5 @@ cdef class GiacMethods_base: Ex3:zip('+',[a,b,c,d], [1,2,3],5) Ex4:zip(sum,[a,b,c,d], [1,2,3,4]) ''' - return GiacMethods['zip'](self,*args) + return GiacMethods['zip'](self, *args) diff --git a/src/sage/libs/giac/giac.pyx b/src/sage/libs/giac/giac.pyx index aeeee3185fa..91c42f3132c 100644 --- a/src/sage/libs/giac/giac.pyx +++ b/src/sage/libs/giac/giac.pyx @@ -642,7 +642,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[6])._val - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] pl[6] = value @@ -655,7 +655,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[9])._val == 1 - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] if value: @@ -683,7 +683,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[2])._val == 1 - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] if value: @@ -712,7 +712,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[7][3])._val - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] pl[7] = [l[7][0],l[7][1],l[7][2], value] @@ -736,7 +736,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[5][1])._double - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] pl[5] = [l[5][0],value] @@ -759,7 +759,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[5][0])._double - def __set__(self,value): + def __set__(self, value): l = Pygen('cas_setup()').eval() pl = [ i for i in l ] pl[5] = [value,l[5][1]] @@ -772,7 +772,7 @@ cdef class GiacSetting(Pygen): def __get__(self): return (self.cas_setup()[7][0])._val - def __set__(self,value): + def __set__(self, value): Pygen('threads:=%s' % str(value)).eval() ######################################################## @@ -1222,8 +1222,8 @@ cdef class Pygen(GiacMethods_base): return self # To be able to use the eval function before the GiacMethods initialisation - def cas_setup(self,*args): - return Pygen('cas_setup')(self,*args) + def cas_setup(self, *args): + return Pygen('cas_setup')(self, *args) def savegen(self, str filename): """ @@ -1337,7 +1337,7 @@ cdef class Pygen(GiacMethods_base): sig_off() return result - def _integer_(self,Z=None): + def _integer_(self, Z=None): """ Convert giac integers or modular integers to sage Integers (via gmp). @@ -1798,7 +1798,7 @@ cdef vecteur _wrap_pylist(L) except +: ################################# # slice wrapper for a giac list ################################# -cdef vecteur _getgiacslice(Pygen L,slice sl) except +: +cdef vecteur _getgiacslice(Pygen L, slice sl) except +: cdef vecteur * V cdef int u @@ -2038,7 +2038,7 @@ class GiacInstance: def __init__(self): self.__dict__.update(GiacMethods) - def __call__(self,s): + def __call__(self, s): return _giac(s) def _sage_doc_(self): diff --git a/src/sage/libs/gsl/array.pyx b/src/sage/libs/gsl/array.pyx index 3916929cca4..2dc98555dbd 100644 --- a/src/sage/libs/gsl/array.pyx +++ b/src/sage/libs/gsl/array.pyx @@ -14,7 +14,7 @@ cdef class GSLDoubleArray: sage: a[:6:2] [0.0, 1.0, 1.0] """ - def __init__(self, size_t n, size_t stride = 1, data = None): + def __init__(self, size_t n, size_t stride=1, data=None): """ EXAMPLES:: diff --git a/src/sage/libs/gsl/errno.pxd b/src/sage/libs/gsl/errno.pxd index 02d599289fd..3d54c6ee0ef 100644 --- a/src/sage/libs/gsl/errno.pxd +++ b/src/sage/libs/gsl/errno.pxd @@ -5,9 +5,9 @@ from libc.stdio cimport FILE cdef extern from "gsl/gsl_errno.h": - ctypedef void gsl_error_handler_t (char * reason, char * file,int line, int gsl_errno) + ctypedef void gsl_error_handler_t (char * reason, char * file, int line, int gsl_errno) - ctypedef void gsl_stream_handler_t (char * label, char * file,int line, char * reason) + ctypedef void gsl_stream_handler_t (char * label, char * file, int line, char * reason) void gsl_error (char * reason,char * file, int line, int gsl_errno) diff --git a/src/sage/libs/lcalc/lcalc_Lfunction.pxd b/src/sage/libs/lcalc/lcalc_Lfunction.pxd index 715fa46bba0..b7d3126953c 100644 --- a/src/sage/libs/lcalc/lcalc_Lfunction.pxd +++ b/src/sage/libs/lcalc/lcalc_Lfunction.pxd @@ -105,12 +105,12 @@ ctypedef double Double cdef class Lfunction: cdef void *thisptr cdef void _init_fun(self, char *NAME, int what_type, dirichlet_coeff, long long Period, double q, c_Complex w, int A, double *g, c_Complex *l, int n_poles, c_Complex *p, c_Complex *r) noexcept - cdef c_Complex _value(self,c_Complex s,int derivative) noexcept - cdef c_Complex _hardy_z_function(self,c_Complex s) noexcept + cdef c_Complex _value(self, c_Complex s, int derivative) noexcept + cdef c_Complex _hardy_z_function(self, c_Complex s) noexcept cdef int _compute_rank(self) noexcept #strange bug, replacing Double with double gives me a compile error cdef Double _typedN(self, double T) noexcept - cdef void _find_zeros_v(self, double T1, double T2, double stepsize,doublevec *result) noexcept + cdef void _find_zeros_v(self, double T1, double T2, double stepsize, doublevec *result) noexcept cdef int _find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result) noexcept cdef str _repr diff --git a/src/sage/libs/lcalc/lcalc_Lfunction.pyx b/src/sage/libs/lcalc/lcalc_Lfunction.pyx index f1173543ab1..a8a71c2955a 100644 --- a/src/sage/libs/lcalc/lcalc_Lfunction.pyx +++ b/src/sage/libs/lcalc/lcalc_Lfunction.pyx @@ -402,19 +402,19 @@ cdef class Lfunction: cdef void _init_fun(self, char *NAME, int what_type, dirichlet_coeff, long long Period, double q, c_Complex w, int A, double *g, c_Complex *l, int n_poles, c_Complex *p, c_Complex *r) noexcept: raise NotImplementedError - cdef c_Complex _value(self,c_Complex s,int derivative) noexcept: + cdef c_Complex _value(self, c_Complex s, int derivative) noexcept: raise NotImplementedError - cdef c_Complex _hardy_z_function(self,c_Complex s) noexcept: + cdef c_Complex _hardy_z_function(self, c_Complex s) noexcept: raise NotImplementedError cdef int _compute_rank(self) noexcept: raise NotImplementedError - cdef double _typedN(self,double T) noexcept: + cdef double _typedN(self, double T) noexcept: raise NotImplementedError - cdef void _find_zeros_v(self,double T1, double T2, double stepsize, doublevec *result) noexcept: + cdef void _find_zeros_v(self, double T1, double T2, double stepsize, doublevec *result) noexcept: raise NotImplementedError cdef int _find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result) noexcept: @@ -498,10 +498,10 @@ cdef class Lfunction_I(Lfunction): self.thisptr=new_c_Lfunction_I(NAME, what_type, N, coeffs, Period, q, w, A, g, l, n_poles, p, r) del_ints(coeffs) - cdef inline c_Complex _value(self,c_Complex s,int derivative) noexcept: + cdef inline c_Complex _value(self, c_Complex s, int derivative) noexcept: return ((self.thisptr)).value(s, derivative, "pure") - cdef inline c_Complex _hardy_z_function(self,c_Complex s) noexcept: + cdef inline c_Complex _hardy_z_function(self, c_Complex s) noexcept: return ((self.thisptr)).value(s, 0, "rotated pure") cdef int _compute_rank(self) noexcept: @@ -635,10 +635,10 @@ cdef class Lfunction_D(Lfunction): self.thisptr=new_c_Lfunction_D(NAME, what_type, N, coeffs, Period, q, w, A, g, l, n_poles, p, r) del_doubles(coeffs) - cdef inline c_Complex _value(self,c_Complex s,int derivative) noexcept: + cdef inline c_Complex _value(self, c_Complex s, int derivative) noexcept: return ((self.thisptr)).value(s, derivative, "pure") - cdef inline c_Complex _hardy_z_function(self,c_Complex s) noexcept: + cdef inline c_Complex _hardy_z_function(self, c_Complex s) noexcept: return ((self.thisptr)).value(s, 0, "rotated pure") cdef inline int _compute_rank(self) noexcept: @@ -650,7 +650,7 @@ cdef class Lfunction_D(Lfunction): cdef double _typedN(self, double T) noexcept: return (self.thisptr).N(T) - cdef int _find_zeros(self, long count, long start,double max_refine, int rank, const char* message_stamp, doublevec *result) noexcept: + cdef int _find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result) noexcept: (self.thisptr).find_zeros(count, start, max_refine, rank, message_stamp, result) # debug tools @@ -777,10 +777,10 @@ cdef class Lfunction_C: del_Complexes(coeffs) - cdef inline c_Complex _value(self,c_Complex s,int derivative) noexcept: + cdef inline c_Complex _value(self, c_Complex s, int derivative) noexcept: return ((self.thisptr)).value(s, derivative, "pure") - cdef inline c_Complex _hardy_z_function(self,c_Complex s) noexcept: + cdef inline c_Complex _hardy_z_function(self, c_Complex s) noexcept: return ((self.thisptr)).value(s, 0,"rotated pure") cdef inline int _compute_rank(self) noexcept: @@ -858,10 +858,10 @@ cdef class Lfunction_Zeta(Lfunction): self.thisptr = new_c_Lfunction_Zeta() self._repr = "The Riemann zeta function" - cdef inline c_Complex _value(self,c_Complex s,int derivative) noexcept: + cdef inline c_Complex _value(self, c_Complex s, int derivative) noexcept: return ((self.thisptr)).value(s, derivative, "pure") - cdef inline c_Complex _hardy_z_function(self,c_Complex s) noexcept: + cdef inline c_Complex _hardy_z_function(self, c_Complex s) noexcept: return ((self.thisptr)).value(s, 0, "rotated pure") cdef inline int _compute_rank(self) noexcept: diff --git a/src/sage/libs/linkages/padics/unram_shared.pxi b/src/sage/libs/linkages/padics/unram_shared.pxi index e3edc87bc39..c13f060a227 100644 --- a/src/sage/libs/linkages/padics/unram_shared.pxi +++ b/src/sage/libs/linkages/padics/unram_shared.pxi @@ -83,7 +83,7 @@ def frobenius_unram(self, arithmetic=True): @cython.binding(True) -def norm_unram(self, base = None): +def norm_unram(self, base=None): r""" Return the absolute or relative norm of this element. @@ -170,7 +170,7 @@ def norm_unram(self, base = None): @cython.binding(True) -def trace_unram(self, base = None): +def trace_unram(self, base=None): r""" Return the absolute or relative trace of this element. diff --git a/src/sage/libs/mpmath/utils.pyx b/src/sage/libs/mpmath/utils.pyx index 0123d4190be..5f681852c68 100644 --- a/src/sage/libs/mpmath/utils.pyx +++ b/src/sage/libs/mpmath/utils.pyx @@ -75,7 +75,7 @@ cpdef isqrt(n): mpz_sqrt(y.value, m.value) return y -cpdef from_man_exp(man, exp, long prec = 0, str rnd = 'd'): +cpdef from_man_exp(man, exp, long prec=0, str rnd='d'): """ Create normalized mpf value tuple from mantissa and exponent. diff --git a/src/sage/libs/ntl/ntl_GF2X.pyx b/src/sage/libs/ntl/ntl_GF2X.pyx index 7f790b540e0..1a48250dc44 100644 --- a/src/sage/libs/ntl/ntl_GF2X.pyx +++ b/src/sage/libs/ntl/ntl_GF2X.pyx @@ -674,7 +674,7 @@ cdef class ntl_GF2X(): d.x = GF2X_diff(self.x) return d - def reverse(self, int hi = -2): + def reverse(self, int hi=-2): """ Return reverse of a[0]..a[hi] (hi >= -1) hi defaults to deg(a) diff --git a/src/sage/libs/ntl/ntl_ZZ_pE.pyx b/src/sage/libs/ntl/ntl_ZZ_pE.pyx index 2763c41cb54..4a39cf14051 100644 --- a/src/sage/libs/ntl/ntl_ZZ_pE.pyx +++ b/src/sage/libs/ntl/ntl_ZZ_pE.pyx @@ -328,7 +328,7 @@ cdef class ntl_ZZ_pE(): [1 1 1] """ self.c.restore_c() - cdef ntl_ZZ_pX r = ntl_ZZ_pX(v = None, modulus=self.c.pc) + cdef ntl_ZZ_pX r = ntl_ZZ_pX(v=None, modulus=self.c.pc) r.x = (self.c.f).x return r diff --git a/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx b/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx index 84f5f55f9ec..c9937943824 100644 --- a/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx +++ b/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx @@ -134,11 +134,11 @@ cdef class ntl_ZZ_pEContext_class(): self.pc.restore_c() self.x.restore() - #def ZZ_pX(self,v = None): + #def ZZ_pX(self, v=None): # from ntl_ZZ_pX import ntl_ZZ_pX # return ntl_ZZ_pX(v,modulus=self) - def ZZ_pE(self, v = None): + def ZZ_pE(self, v=None): """ Return a ZZ_pE object with modulus ``self`` out of the data v. @@ -151,7 +151,7 @@ cdef class ntl_ZZ_pEContext_class(): from sage.libs.ntl.ntl_ZZ_pE import ntl_ZZ_pE return ntl_ZZ_pE(v,modulus=self) - def ZZ_pEX(self, v = None): + def ZZ_pEX(self, v=None): """ Return a ZZ_pE object with modulus ``self`` out of the data v. diff --git a/src/sage/libs/ntl/ntl_ZZ_pEX.pyx b/src/sage/libs/ntl/ntl_ZZ_pEX.pyx index caeaa26e984..9aa36ce9fc2 100644 --- a/src/sage/libs/ntl/ntl_ZZ_pEX.pyx +++ b/src/sage/libs/ntl/ntl_ZZ_pEX.pyx @@ -1060,7 +1060,7 @@ cdef class ntl_ZZ_pEX(): [8 1] """ self.c.restore_c() - cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus = self.c) + cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus=self.c) sig_on() ZZ_pEX_TraceMod(r.x, self.x, modulus.x) sig_off() @@ -1115,7 +1115,7 @@ cdef class ntl_ZZ_pEX(): [] """ self.c.restore_c() - cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus = self.c) + cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus=self.c) sig_on() ZZ_pEX_resultant(r.x, self.x, other.x) sig_off() @@ -1138,7 +1138,7 @@ cdef class ntl_ZZ_pEX(): [9 2] """ self.c.restore_c() - cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus = self.c) + cdef ntl_ZZ_pE r = ntl_ZZ_pE(modulus=self.c) sig_on() ZZ_pEX_NormMod(r.x, self.x, modulus.x) sig_off() diff --git a/src/sage/libs/ntl/ntl_mat_GF2.pyx b/src/sage/libs/ntl/ntl_mat_GF2.pyx index ae33d4fbb49..479f4505b71 100644 --- a/src/sage/libs/ntl/ntl_mat_GF2.pyx +++ b/src/sage/libs/ntl/ntl_mat_GF2.pyx @@ -520,7 +520,7 @@ cdef class ntl_mat_GF2(): sig_off() return r - def IsIdent(self, n = -1): + def IsIdent(self, n=-1): """ Test if this matrix is the n x n identity matrix. diff --git a/src/sage/libs/ntl/ntl_mat_GF2E.pyx b/src/sage/libs/ntl/ntl_mat_GF2E.pyx index 795ad9674fa..eb044cbfc37 100644 --- a/src/sage/libs/ntl/ntl_mat_GF2E.pyx +++ b/src/sage/libs/ntl/ntl_mat_GF2E.pyx @@ -49,7 +49,7 @@ cdef class ntl_mat_GF2E(): r""" The \class{mat_GF2E} class implements arithmetic with matrices over `GF(2**x)`. """ - def __init__(self, modulus = None, nrows=0, ncols=0, v=None): + def __init__(self, modulus=None, nrows=0, ncols=0, v=None): """ Construct a matrix over ntl.GF2E. @@ -585,7 +585,7 @@ cdef class ntl_mat_GF2E(): sig_off() return r - def IsIdent(self, n = -1): + def IsIdent(self, n=-1): r""" Test if `A` is the `n \times n` identity matrix. diff --git a/src/sage/libs/ntl/ntlwrap_impl.h b/src/sage/libs/ntl/ntlwrap_impl.h index 083bab824cc..094cfb52280 100644 --- a/src/sage/libs/ntl/ntlwrap_impl.h +++ b/src/sage/libs/ntl/ntlwrap_impl.h @@ -487,13 +487,13 @@ static CYTHON_INLINE mat_ZZ* mat_ZZ_HNF(const mat_ZZ* A, const struct ZZ* D) static CYTHON_INLINE long mat_ZZ_LLL(struct ZZ **det, mat_ZZ *x, long a, long b, long verbose) { *det = new ZZ(); - return LLL(**det,*x,a,b,verbose); + return LLL(**det, *x, a, b, verbose); } static CYTHON_INLINE long mat_ZZ_LLL_U(struct ZZ **det, mat_ZZ *x, mat_ZZ *U, long a, long b, long verbose) { *det = new ZZ(); - return LLL(**det,*x,*U,a,b,verbose); + return LLL(**det, *x, *U, a, b, verbose); } diff --git a/src/sage/libs/singular/decl.pxd b/src/sage/libs/singular/decl.pxd index dddc452fd98..d8c6d9a1201 100644 --- a/src/sage/libs/singular/decl.pxd +++ b/src/sage/libs/singular/decl.pxd @@ -983,7 +983,7 @@ cdef extern from "singular/Singular/libsingular.h": void setFlag(leftv *A, int F) void resetFlag(leftv *A, int F) - ctypedef number* (*nMapFunc)(number *c,const n_Procs_s* src,const n_Procs_s* dst) + ctypedef number* (*nMapFunc)(number *c, const n_Procs_s* src, const n_Procs_s* dst) cdef extern from "singular/coeffs/coeffs.h": diff --git a/src/sage/libs/singular/function.pxd b/src/sage/libs/singular/function.pxd index facdcae674a..a83017e74ab 100644 --- a/src/sage/libs/singular/function.pxd +++ b/src/sage/libs/singular/function.pxd @@ -52,7 +52,7 @@ cdef class Converter(SageObject): cdef leftv * append_module(self, m) except NULL cdef to_sage_integer_matrix(self, intvec *mat) cdef object to_sage_module_element_sequence_destructive(self, ideal *i) - cdef to_sage_vector_destructive(self, poly *p, free_module = ?) + cdef to_sage_vector_destructive(self, poly *p, free_module=?) cdef to_sage_matrix(self, matrix* mat) cdef to_python(self, leftv* to_convert) diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx index c6f65eb718a..da6a1d8c7a5 100644 --- a/src/sage/libs/singular/function.pyx +++ b/src/sage/libs/singular/function.pyx @@ -352,7 +352,7 @@ cdef leftv* new_leftv(void *data, res_type) noexcept: res.rtyp = res_type return res -cdef free_leftv(leftv *args, ring *r = NULL): +cdef free_leftv(leftv *args, ring *r=NULL): """ Kills this ``leftv`` and all ``leftv``s in the tail. @@ -692,7 +692,7 @@ cdef class Converter(SageObject): result[i,j] = p return result - cdef to_sage_vector_destructive(self, poly *p, free_module = None): + cdef to_sage_vector_destructive(self, poly *p, free_module=None): cdef int rank if free_module: rank = free_module.rank() @@ -826,7 +826,7 @@ cdef class Converter(SageObject): cdef poly *p ncols = mat.ncols() nrows = mat.nrows() - cdef matrix* _m=mpNew(nrows,ncols) + cdef matrix* _m=mpNew(nrows, ncols) for i in range(nrows): for j in range(ncols): #FIXME diff --git a/src/sage/libs/singular/polynomial.pyx b/src/sage/libs/singular/polynomial.pyx index 6f7f576cb02..db4b2ff35e2 100644 --- a/src/sage/libs/singular/polynomial.pyx +++ b/src/sage/libs/singular/polynomial.pyx @@ -200,7 +200,7 @@ cdef int singular_polynomial_call(poly **ret, poly *p, ring *r, list args, Leaked 0 bytes """ cdef long l = len(args) - cdef ideal *to_id = idInit(l,1) + cdef ideal *to_id = idInit(l, 1) cdef bint constant_args = 1 for i from 0 <= i < l: to_id.m[i]= p_Copy( get_element(args[i]), r) @@ -391,7 +391,7 @@ cdef int singular_polynomial_pow(poly **ret, poly *p, unsigned long exp, ring *r if r != currRing: rChangeCurrRing(r) - cdef int count = singular_polynomial_length_bounded(p,15) + cdef int count = singular_polynomial_length_bounded(p, 15) if count >= 15 or exp > 15: sig_on() ret[0] = pPower( p_Copy(p,r), exp) diff --git a/src/sage/libs/singular/singular.pxd b/src/sage/libs/singular/singular.pxd index ca31d02456c..9d764b51a6f 100644 --- a/src/sage/libs/singular/singular.pxd +++ b/src/sage/libs/singular/singular.pxd @@ -42,10 +42,10 @@ cpdef tuple si2sa_resolution_graded(Resolution res, tuple degrees) # Conversion from Sage to Singular types # ====================================== -cdef number *sa2si_QQ(Rational ,ring (*)) noexcept +cdef number *sa2si_QQ(Rational, ring (*)) noexcept cdef number *sa2si_ZZ(Integer d, ring *_ring) noexcept -cdef number *sa2si_GFqGivaro(int exp ,ring (*)) noexcept +cdef number *sa2si_GFqGivaro(int exp, ring (*)) noexcept cdef number *sa2si_GFqNTLGF2E(FFgf2eE elem, ring *_ring) noexcept cdef number *sa2si_GFq_generic(object vector, ring *_ring) noexcept cdef number *sa2si_ZZmod(IntegerMod_abstract d, ring *_ring) noexcept diff --git a/src/sage/manifolds/differentiable/affine_connection.py b/src/sage/manifolds/differentiable/affine_connection.py index d1e25cc3e31..73b6e5d42cd 100644 --- a/src/sage/manifolds/differentiable/affine_connection.py +++ b/src/sage/manifolds/differentiable/affine_connection.py @@ -1608,7 +1608,7 @@ def _derive_paral(self, tensor): # definition of the parallel function @parallel(p_iter='multiprocessing',ncpus=nproc) - def make_CovDerivative(ind_part,tc,gam,frame,n_con,rank,manif): + def make_CovDerivative(ind_part, tc, gam, frame, n_con, rank, manif): partial = [] for ind in ind_part: p = ind[-1] # derivation index diff --git a/src/sage/manifolds/differentiable/integrated_curve.py b/src/sage/manifolds/differentiable/integrated_curve.py index 135e6d53d32..17784f555e1 100644 --- a/src/sage/manifolds/differentiable/integrated_curve.py +++ b/src/sage/manifolds/differentiable/integrated_curve.py @@ -1293,7 +1293,7 @@ def system(t, y): # of the system to be provided if T.jacobian is None: - def jacobian(t,y): + def jacobian(t, y): jac = [] par = self._curve_parameter for i in range(dim): diff --git a/src/sage/manifolds/differentiable/levi_civita_connection.py b/src/sage/manifolds/differentiable/levi_civita_connection.py index 55c4aca9416..215756f00d3 100644 --- a/src/sage/manifolds/differentiable/levi_civita_connection.py +++ b/src/sage/manifolds/differentiable/levi_civita_connection.py @@ -507,7 +507,7 @@ def coef(self, frame=None): # definition of the parallel function @parallel(p_iter='multiprocessing',ncpus=nproc) - def make_Connect(local_list_ijk,chart,ginv,gg,manif): + def make_Connect(local_list_ijk, chart, ginv, gg, manif): partial = [] for i,j,k in local_list_ijk: rsum = 0 diff --git a/src/sage/manifolds/differentiable/metric.py b/src/sage/manifolds/differentiable/metric.py index e25033a8cb7..4a783db3478 100644 --- a/src/sage/manifolds/differentiable/metric.py +++ b/src/sage/manifolds/differentiable/metric.py @@ -2598,7 +2598,7 @@ def __init__(self, vector_field_module, name, signature=None, m sage: Int = M.open_subset('Int') sage: X.=Int.chart(r"t r:(0,2*m) th:(0,pi):\theta ph:(0,2*pi):\phi") - sage: XM = M.vector_field_module(); e= X.frame() + sage: XM = M.vector_field_module(); e = X.frame() sage: from sage.manifolds.differentiable.metric import \ ....: DegenerateMetric sage: g = DegenerateMetric(XM, 'g', signature=(2,1,1)); g diff --git a/src/sage/manifolds/differentiable/vectorfield_module.py b/src/sage/manifolds/differentiable/vectorfield_module.py index 43efcb19aa6..67cd1abd614 100644 --- a/src/sage/manifolds/differentiable/vectorfield_module.py +++ b/src/sage/manifolds/differentiable/vectorfield_module.py @@ -1385,7 +1385,7 @@ class VectorFieldFreeModule(FiniteRankFreeModule): Let us introduce an open subset of `J\subset I` and the vector field module corresponding to the restriction of `\Phi` to it:: - sage: J = I.open_subset('J', coord_def= {canon: t self._entries.nrows: raise TypeError("Expected highr <= self.nrows(), but got %d > %d instead."%(highr, self._entries.nrows)) - cdef Matrix_gf2e_dense A = self.new_matrix(nrows = nrows, ncols = ncols) + cdef Matrix_gf2e_dense A = self.new_matrix(nrows=nrows, ncols=ncols) if ncols == 0 or nrows == 0: return A A._entries = mzed_submatrix(A._entries, self._entries, row, col, highr, highc) diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx index c0e0a1fff44..9ea2335b297 100644 --- a/src/sage/matrix/matrix_integer_dense.pyx +++ b/src/sage/matrix/matrix_integer_dense.pyx @@ -868,7 +868,7 @@ cdef class Matrix_integer_dense(Matrix_dense): [ 9 11 13] [ 9 11 13] """ - cdef Matrix_integer_dense M = self._new(self._nrows,self._ncols) + cdef Matrix_integer_dense M = self._new(self._nrows, self._ncols) sig_on() fmpz_mat_add(M._matrix,self._matrix,( right)._matrix) @@ -888,7 +888,7 @@ cdef class Matrix_integer_dense(Matrix_dense): [-2 0 2] [ 4 6 8] """ - cdef Matrix_integer_dense M = self._new(self._nrows,self._ncols) + cdef Matrix_integer_dense M = self._new(self._nrows, self._ncols) sig_on() fmpz_mat_sub(M._matrix,self._matrix,( right)._matrix) @@ -4164,7 +4164,7 @@ cdef class Matrix_integer_dense(Matrix_dense): raise ArithmeticError("non-invertible matrix") return A - def _solve_right_nonsingular_square(self, B, check_rank=True, algorithm = 'iml'): + def _solve_right_nonsingular_square(self, B, check_rank=True, algorithm='iml'): r""" If ``self`` is a matrix `A` of full rank, then this function returns a vector or matrix `X` such that `A X = B`. @@ -4606,7 +4606,7 @@ cdef class Matrix_integer_dense(Matrix_dense): M,d = self.transpose()._solve_flint(B.transpose(), right=True) return M.transpose(),d - def _rational_echelon_via_solve(self, solver = 'iml'): + def _rational_echelon_via_solve(self, solver='iml'): r""" Compute information that gives the reduced row echelon form (over QQ!) of a matrix with integer entries. @@ -5029,7 +5029,7 @@ cdef class Matrix_integer_dense(Matrix_dense): t = verbose('hermite mod %s' % D, caller_name='matrix_integer_dense') if self._nrows != self._ncols: raise ValueError("matrix is not square") - cdef Matrix_integer_dense res = self._new(self._nrows,self._ncols) + cdef Matrix_integer_dense res = self._new(self._nrows, self._ncols) self._hnf_modn(res, D) verbose('finished hnf mod', t, caller_name='matrix_integer_dense') return res diff --git a/src/sage/matrix/matrix_modn_dense_template.pxi b/src/sage/matrix/matrix_modn_dense_template.pxi index 36830da0549..177cebffb38 100644 --- a/src/sage/matrix/matrix_modn_dense_template.pxi +++ b/src/sage/matrix/matrix_modn_dense_template.pxi @@ -431,7 +431,7 @@ cpdef __matrix_from_rows_of_matrices(X): T = X[0] m = T._nrows * T._ncols - cdef Matrix_modn_dense_template A = T.new_matrix(nrows = n, ncols = m) + cdef Matrix_modn_dense_template A = T.new_matrix(nrows=n, ncols=m) for i from 0 <= i < n: T = X[i] @@ -2807,7 +2807,7 @@ cdef class Matrix_modn_dense_template(Matrix_dense): cdef Py_ssize_t nrows = self._nrows cdef Py_ssize_t ncols = self._ncols - cdef Matrix_modn_dense_template M = self.new_matrix(nrows = ncols, ncols = nrows) + cdef Matrix_modn_dense_template M = self.new_matrix(nrows=ncols, ncols=nrows) cdef Py_ssize_t i,j for i from 0 <= i < ncols: diff --git a/src/sage/matrix/matrix_polynomial_dense.pyx b/src/sage/matrix/matrix_polynomial_dense.pyx index 5b3c56ae573..99979a37ed8 100644 --- a/src/sage/matrix/matrix_polynomial_dense.pyx +++ b/src/sage/matrix/matrix_polynomial_dense.pyx @@ -291,7 +291,7 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense): return all([self[i,j].is_constant() for j in range(self.ncols()) for i in range(self.nrows())]) - def coefficient_matrix(self,d,row_wise=True): + def coefficient_matrix(self, d, row_wise=True): r""" Return the constant matrix which is obtained from this matrix by taking the coefficient of its entries with degree specified by `d`. @@ -3106,7 +3106,7 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense): If the option ``row_wise`` is set to ``False``, the same operation is performed, but with everything considered column-wise: column space of `B`, `i` th column of `R` and `A`, column-wise `s`-leading positions - and `s`-Popov form, and submatrices `R_{J,*}` and `P_{J,*}`. + and `s`-Popov form, and submatrices `R_{J, *}` and `P_{J, *}`. The operation above can be seen as a matrix generalization of division with remainder for univariate polynomials. If the option diff --git a/src/sage/matrix/matrix_rational_dense.pyx b/src/sage/matrix/matrix_rational_dense.pyx index 533f6b55c67..40c63470617 100644 --- a/src/sage/matrix/matrix_rational_dense.pyx +++ b/src/sage/matrix/matrix_rational_dense.pyx @@ -2776,7 +2776,7 @@ cdef class Matrix_rational_dense(Matrix_dense): We verify that 0 rows or columns works:: - sage: x = matrix(QQ,2,0); y= matrix(QQ,0,2); x*y + sage: x = matrix(QQ,2,0); y = matrix(QQ,0,2); x*y [0 0] [0 0] sage: matrix(ZZ, 0, 0) * matrix(QQ, 0, 5) diff --git a/src/sage/matrix/matrix_sparse.pyx b/src/sage/matrix/matrix_sparse.pyx index 95b8969e0aa..92a2d18d846 100644 --- a/src/sage/matrix/matrix_sparse.pyx +++ b/src/sage/matrix/matrix_sparse.pyx @@ -927,7 +927,7 @@ cdef class Matrix_sparse(matrix.Matrix): ncols = PyList_GET_SIZE(columns) nrows = PyList_GET_SIZE(rows) - cdef Matrix_sparse A = self.new_matrix(nrows = nrows, ncols = ncols) + cdef Matrix_sparse A = self.new_matrix(nrows=nrows, ncols=ncols) tmp = [el for el in columns if 0 <= el < self._ncols] columns = tmp diff --git a/src/sage/matrix/misc.pyx b/src/sage/matrix/misc.pyx index de0afe6c9e7..5f8f834b33f 100644 --- a/src/sage/matrix/misc.pyx +++ b/src/sage/matrix/misc.pyx @@ -281,10 +281,10 @@ def matrix_rational_echelon_form_multimodular(Matrix self, height_guess=None, pr if cmp_pivots(best_pivots, X[i].pivots()) <= 0: p = X[i].base_ring().order() if p not in lifts: - t0 = verbose("Lifting a good matrix", level=2, caller_name = "multimod echelon") + t0 = verbose("Lifting a good matrix", level=2, caller_name="multimod echelon") lift = X[i].lift() lifts[p] = (lift, p) - verbose("Finished lift", level=2, caller_name= "multimod echelon", t=t0) + verbose("Finished lift", level=2, caller_name="multimod echelon", t=t0) Y.append(lifts[p]) prod = prod * X[i].base_ring().order() verbose("finished comparing pivots", level=2, t=t, caller_name="multimod echelon") diff --git a/src/sage/matrix/special.py b/src/sage/matrix/special.py index b81703b6fe7..dbb0214994e 100644 --- a/src/sage/matrix/special.py +++ b/src/sage/matrix/special.py @@ -3050,7 +3050,7 @@ def random_unimodular_matrix(parent, upper_bound=None, max_tries=100): @matrix_method -def random_diagonalizable_matrix(parent,eigenvalues=None,dimensions=None): +def random_diagonalizable_matrix(parent, eigenvalues=None, dimensions=None): """ Create a random matrix that diagonalizes nicely. diff --git a/src/sage/matrix/strassen.pyx b/src/sage/matrix/strassen.pyx index 978773e3a27..7298dddabd3 100644 --- a/src/sage/matrix/strassen.pyx +++ b/src/sage/matrix/strassen.pyx @@ -20,7 +20,7 @@ from sage.matrix.matrix_window cimport MatrixWindow from cysignals.signals cimport sig_on, sig_off -def strassen_window_multiply(C, A,B, cutoff): +def strassen_window_multiply(C, A, B, cutoff): """ Multiply the submatrices specified by A and B, places result in C. Assumes that A and B have compatible dimensions to be diff --git a/src/sage/matroids/lean_matrix.pyx b/src/sage/matroids/lean_matrix.pyx index f7051f45c92..e0f86c6db83 100644 --- a/src/sage/matroids/lean_matrix.pyx +++ b/src/sage/matroids/lean_matrix.pyx @@ -593,8 +593,8 @@ cdef class LeanMatrix: cdef list lU_2 = sorted(list(U_2)) cdef list lV_2 = sorted(list(V_2)) - cdef dict rU = dict(zip(lU_2,range(len(U_2)))) - cdef dict rV = dict(zip(lV_2,range(len(V_2)))) + cdef dict rU = dict(zip(lU_2, range(len(U_2)))) + cdef dict rV = dict(zip(lV_2, range(len(V_2)))) # find a unique representation of every column in U_1xY_3 using columns in U_1xV_2 B = self.matrix_from_rows_and_columns(list(U_1), range(len(Y))) @@ -2550,7 +2550,7 @@ cdef class QuaternaryMatrix(LeanMatrix): Return a submatrix indexed by indicated rows and columns, as well as the column order of the resulting submatrix. """ - cdef QuaternaryMatrix A = QuaternaryMatrix(len(rows), len(columns), ring = self._gf4) + cdef QuaternaryMatrix A = QuaternaryMatrix(len(rows), len(columns), ring=self._gf4) cdef long r, c, lc, lg cdef mp_bitcnt_t *cols # deal with trivial case diff --git a/src/sage/matroids/linear_matroid.pyx b/src/sage/matroids/linear_matroid.pyx index f180976979d..9030ce47f25 100644 --- a/src/sage/matroids/linear_matroid.pyx +++ b/src/sage/matroids/linear_matroid.pyx @@ -3861,7 +3861,7 @@ cdef class BinaryMatroid(LinearMatroid): if len(C[e] & C[f] & C[g]) > 0: M.append([0,col[e,f], col[e,g], col[f,e], col[f,g], col[g,e], col[g,f]]) r += 1 - cdef BinaryMatrix m = BinaryMatrix(r,c) + cdef BinaryMatrix m = BinaryMatrix(r, c) for r in range(len(M)): for c in M[r]: m.set(r,c) @@ -3891,7 +3891,7 @@ cdef class BinaryMatroid(LinearMatroid): # representability - cpdef binary_matroid(self, randomized_tests=1, verify = True): + cpdef binary_matroid(self, randomized_tests=1, verify=True): r""" Return a binary matroid representing ``self``. @@ -4757,7 +4757,7 @@ cdef class TernaryMatroid(LinearMatroid): # representability - cpdef ternary_matroid(self, randomized_tests=1, verify = True): + cpdef ternary_matroid(self, randomized_tests=1, verify=True): r""" Return a ternary matroid representing ``self``. @@ -6337,7 +6337,7 @@ cdef class RegularMatroid(LinearMatroid): """ return True - cpdef binary_matroid(self, randomized_tests=1, verify = True): + cpdef binary_matroid(self, randomized_tests=1, verify=True): r""" Return a binary matroid representing ``self``. @@ -6392,7 +6392,7 @@ cdef class RegularMatroid(LinearMatroid): """ return True - cpdef ternary_matroid(self, randomized_tests=1, verify = True): + cpdef ternary_matroid(self, randomized_tests=1, verify=True): r""" Return a ternary matroid representing ``self``. diff --git a/src/sage/matroids/matroid.pxd b/src/sage/matroids/matroid.pxd index bbd025c1ed5..fb8d8a2939c 100644 --- a/src/sage/matroids/matroid.pxd +++ b/src/sage/matroids/matroid.pxd @@ -234,9 +234,9 @@ cdef class Matroid(SageObject): cpdef broken_circuit_complex(self, ordering=*) # visualization - cpdef plot(self,B=*,lineorders=*,pos_method=*,pos_dict=*,save_pos=*) - cpdef show(self,B=*,lineorders=*,pos_method=*,pos_dict=*,save_pos=*,lims=*) - cpdef _fix_positions(self,pos_dict=*,lineorders=*) + cpdef plot(self, B=*, lineorders=*, pos_method=*, pos_dict=*, save_pos=*) + cpdef show(self, B=*, lineorders=*, pos_method=*, pos_dict=*, save_pos=*, lims=*) + cpdef _fix_positions(self, pos_dict=*, lineorders=*) # construction cpdef direct_sum(self, matroids) diff --git a/src/sage/matroids/matroid.pyx b/src/sage/matroids/matroid.pyx index e06f9b423cf..ff853ba9f5a 100644 --- a/src/sage/matroids/matroid.pyx +++ b/src/sage/matroids/matroid.pyx @@ -6313,7 +6313,7 @@ cdef class Matroid(SageObject): from sage.matroids.linear_matroid import BinaryMatroid return BinaryMatroid(groundset=E, matrix=A, basis=list(basis), keep_initial_representation=False) - cpdef binary_matroid(self, randomized_tests=1, verify = True): + cpdef binary_matroid(self, randomized_tests=1, verify=True): r""" Return a binary matroid representing ``self``, if such a representation exists. @@ -6492,7 +6492,7 @@ cdef class Matroid(SageObject): from sage.matroids.linear_matroid import TernaryMatroid return TernaryMatroid(groundset=E, matrix=A, basis=basis, keep_initial_representation=False) - cpdef ternary_matroid(self, randomized_tests=1, verify = True): + cpdef ternary_matroid(self, randomized_tests=1, verify=True): r""" Return a ternary matroid representing ``self``, if such a representation exists. @@ -8111,7 +8111,7 @@ cdef class Matroid(SageObject): from sage.matroids.chow_ring import ChowRing return ChowRing(M=self, R=R, augmented=augmented, presentation=presentation) - cpdef plot(self, B=None, lineorders=None, pos_method=None,pos_dict=None,save_pos=False): + cpdef plot(self, B=None, lineorders=None, pos_method=None, pos_dict=None, save_pos=False): """ Return geometric representation as a sage graphics object. diff --git a/src/sage/misc/binary_tree.pyx b/src/sage/misc/binary_tree.pyx index 583e397a845..0756218e53c 100644 --- a/src/sage/misc/binary_tree.pyx +++ b/src/sage/misc/binary_tree.pyx @@ -491,7 +491,7 @@ class Test: def random(self): self.binary_tree() - def binary_tree(self, values = 100, cycles = 100000): + def binary_tree(self, values=100, cycles=100000): """ Perform a sequence of random operations, given random inputs to stress test the binary tree structure. diff --git a/src/sage/misc/c3.pyx b/src/sage/misc/c3.pyx index bd8057b361f..8dc7e9a9feb 100644 --- a/src/sage/misc/c3.pyx +++ b/src/sage/misc/c3.pyx @@ -177,7 +177,7 @@ cpdef list C3_algorithm(object start, str bases, str attribute, bint proper): out = [] else: out = [start] - cdef list args = getattr(start,bases) + cdef list args = getattr(start, bases) if not args: return out # Data structure / invariants: diff --git a/src/sage/misc/c3_controlled.pyx b/src/sage/misc/c3_controlled.pyx index e072d5f2ae9..885dcf673f0 100644 --- a/src/sage/misc/c3_controlled.pyx +++ b/src/sage/misc/c3_controlled.pyx @@ -953,7 +953,7 @@ cpdef tuple C3_sorted_merge(list lists, key=identity): last_list_non_empty = False #check_state() suggestion.update(holder.values()) - cdef list suggestion_list = sorted(suggestion, key = key, reverse=True) + cdef list suggestion_list = sorted(suggestion, key=key, reverse=True) #assert C3_merge(lists[:-1]+[suggestion_list]) == out return (out, suggestion_list) diff --git a/src/sage/misc/cachefunc.pyx b/src/sage/misc/cachefunc.pyx index f5fc873e5a9..52c10174dca 100644 --- a/src/sage/misc/cachefunc.pyx +++ b/src/sage/misc/cachefunc.pyx @@ -69,7 +69,7 @@ be defined by simply using the decorator. However, an indirect approach is still needed for cpdef methods:: sage: # needs sage.misc.cython - sage: cython_code = ['cpdef test_meth(self,x):', + sage: cython_code = ['cpdef test_meth(self, x):', ....: ' "some doc for a wrapped cython method"', ....: ' return -x', ....: 'from sage.misc.cachefunc import cached_method', @@ -154,7 +154,7 @@ hardly by used. sage: cython_code = ["from sage.structure.element cimport Element, ElementWithCachedMethod", "from cpython.object cimport PyObject_RichCompare", ....: "cdef class MyBrokenElement(Element):", ....: " cdef public object x", - ....: " def __init__(self,P,x):", + ....: " def __init__(self, P, x):", ....: " self.x=x", ....: " Element.__init__(self,P)", ....: " def __neg__(self):", @@ -169,7 +169,7 @@ hardly by used. ....: " return -self", ....: "cdef class MyElement(ElementWithCachedMethod):", ....: " cdef public object x", - ....: " def __init__(self,P,x):", + ....: " def __init__(self, P, x):", ....: " self.x=x", ....: " ElementWithCachedMethod.__init__(self,P)", ....: " def __neg__(self):", @@ -267,7 +267,7 @@ Introspection works:: Some doc for direct method sage: print(sage_getsource(O.wrapped_method)) - cpdef test_meth(self,x): + cpdef test_meth(self, x): "some doc for a wrapped cython method" return -x sage: print(sage_getsource(O.direct_method)) @@ -312,7 +312,7 @@ latter is easy:: ....: "cdef class MyClass:", ....: " cdef public dict _cached_methods", ....: " @cached_method", - ....: " def f(self, a,b):", + ....: " def f(self, a, b):", ....: " return a*b"] sage: cython(os.linesep.join(cython_code)) sage: P = MyClass() @@ -333,7 +333,7 @@ enough in the following example:: ....: " cdef dict D", ....: " def __init__(self):", ....: " self.D = {}", - ....: " def __setattr__(self, n,v):", + ....: " def __setattr__(self, n, v):", ....: " self.D[n] = v", ....: " def __getattribute__(self, n):", ....: " try:", @@ -342,7 +342,7 @@ enough in the following example:: ....: " pass", ....: " return getattr(type(self),n).__get__(self)", ....: " @cached_method", - ....: " def f(self, a,b):", + ....: " def f(self, a, b):", ....: " return a+b"] sage: cython(os.linesep.join(cython_code)) sage: Q = MyOtherClass() @@ -1607,7 +1607,7 @@ class CachedMethodPickle(): """ return CachedMethodPickle,(self._instance,self._name,self._cache) - def __call__(self,*args,**kwds): + def __call__(self, *args, **kwds): """ The purpose of this call method is to kill ``self`` and to replace it by an actual :class:`CachedMethodCaller`. The last @@ -1636,9 +1636,9 @@ class CachedMethodPickle(): else: for k, v in self._cache: CM.cache[k] = v - return CM(*args,**kwds) + return CM(*args, **kwds) - def __getattr__(self,s): + def __getattr__(self, s): """ TESTS:: @@ -1692,7 +1692,7 @@ cdef class CachedMethodCaller(CachedFunction): sage: class A: ....: @cached_method - ....: def bar(self,x): + ....: def bar(self, x): ....: return x^2 sage: a = A() sage: a.bar @@ -1718,7 +1718,7 @@ cdef class CachedMethodCaller(CachedFunction): sage: class A: ....: @cached_method(do_pickle=True) - ....: def bar(self,x): + ....: def bar(self, x): ....: return x^2 sage: __main__.A = A @@ -1739,7 +1739,7 @@ cdef class CachedMethodCaller(CachedFunction): ....: def __init__(self, x): ....: self._x = x ....: @cached_method - ....: def f(self,*args): + ....: def f(self, *args): ....: return self._x^2 sage: a = Foo(2) sage: a.f.cache @@ -1812,7 +1812,7 @@ cdef class CachedMethodCaller(CachedFunction): ....: def __init__(self, x): ....: self._x = x ....: @cached_method - ....: def f(self,n=2): + ....: def f(self, n=2): ....: return self._x^n sage: a = Foo(2) sage: a.f() @@ -1865,7 +1865,7 @@ cdef class CachedMethodCaller(CachedFunction): sage: from sage.misc.superseded import deprecated_function_alias sage: class Foo: ....: @cached_method - ....: def f(self, x,y=1): + ....: def f(self, x, y=1): ....: return x+y ....: g = deprecated_function_alias(57, f) sage: a = Foo() @@ -2629,7 +2629,7 @@ cdef class CachedMethod(): ....: def __init__(self, x): ....: self._x = x ....: @cached_method - ....: def f(self,n): + ....: def f(self, n): ....: return self._x^n ....: @cached_method ....: def f0(self): @@ -2708,7 +2708,7 @@ cdef class CachedMethod(): ....: def __init__(self, x): ....: self._x = x ....: @cached_method - ....: def f(self,n=2): + ....: def f(self, n=2): ....: return self._x^n ....: g = deprecated_function_alias(57, f) sage: a = Foo(2) @@ -2742,7 +2742,7 @@ cdef class CachedMethod(): ....: def __init__(self, x): ....: self._x = x ....: @cached_method - ....: def f(self,n=2): + ....: def f(self, n=2): ....: return self._x^n sage: a = Foo(2) sage: a.f() @@ -2778,7 +2778,7 @@ cdef class CachedMethod(): ....: def f(self): ....: return 1 ....: @cached_method - ....: def g(self, x,n=3): + ....: def g(self, x, n=3): ....: return x^n sage: a = Foo() sage: type(a.f) @@ -3685,7 +3685,7 @@ class disk_cached_function: sage: foo(200) 1/200 """ - def __init__(self, dir, memory_cache = False, key=None): + def __init__(self, dir, memory_cache=False, key=None): """ EXAMPLES:: diff --git a/src/sage/misc/decorators.py b/src/sage/misc/decorators.py index e91acf5b5a9..f93f1227448 100644 --- a/src/sage/misc/decorators.py +++ b/src/sage/misc/decorators.py @@ -319,19 +319,19 @@ def decorator_defaults(func): sage: from sage.misc.decorators import decorator_defaults sage: @decorator_defaults - ....: def my_decorator(f,*args,**kwds): + ....: def my_decorator(f, *args, **kwds): ....: print(kwds) ....: print(args) ....: print(f.__name__) sage: @my_decorator - ....: def my_fun(a,b): + ....: def my_fun(a, b): ....: return a,b {} () my_fun sage: @my_decorator(3,4,c=1,d=2) - ....: def my_fun(a,b): + ....: def my_fun(a, b): ....: return a,b {'c': 1, 'd': 2} (3, 4) diff --git a/src/sage/misc/fpickle.pyx b/src/sage/misc/fpickle.pyx index fd192f1bf02..7a45ecc4f75 100644 --- a/src/sage/misc/fpickle.pyx +++ b/src/sage/misc/fpickle.pyx @@ -17,7 +17,7 @@ def code_ctor(*args): This indirectly tests this function. :: - sage: def foo(a,b,c=10): return a+b+c + sage: def foo(a, b, c=10): return a+b+c sage: sage.misc.fpickle.reduce_code(foo.__code__) (, ...) sage: unpickle_function(pickle_function(foo)) @@ -96,7 +96,7 @@ def unpickle_function(pickled): EXAMPLES:: - sage: def f(N,M): return N*M + sage: def f(N, M): return N*M ... sage: unpickle_function(pickle_function(f))(3,5) 15 diff --git a/src/sage/misc/function_mangling.pyx b/src/sage/misc/function_mangling.pyx index fc9241ca79d..e410a49a900 100644 --- a/src/sage/misc/function_mangling.pyx +++ b/src/sage/misc/function_mangling.pyx @@ -47,7 +47,7 @@ cdef class ArgumentFixer: watching the caller. For example, :: - sage: def f(x = 10): + sage: def f(x=10): ....: return min(1,x) the following calls are equivalent, @@ -63,7 +63,7 @@ cdef class ArgumentFixer: but from the perspective of a wrapper, they are different:: sage: def wrap(g): - ....: def _g(*args,**kwargs): + ....: def _g(*args, **kwargs): ....: print("{} {}".format(args, kwargs)) ....: return g(*args, **kwargs) ....: return _g @@ -92,7 +92,7 @@ cdef class ArgumentFixer: ....: af = ArgumentFixer(g) ....: def _g(*args, **kwargs): ....: print(af.fix_to_pos()) - ....: return g(*args,**kwargs) + ....: return g(*args, **kwargs) ....: return _g sage: h2 = wrap2(f) sage: t = h2() @@ -105,13 +105,13 @@ cdef class ArgumentFixer: :: sage: class one: - ....: def __init__(self, x = 1): + ....: def __init__(self, x=1): ....: self.x = x sage: af = ArgumentFixer(one.__init__, classmethod=True) sage: af.fix_to_pos(1,2,3,a=31,b=2,n=3) ((1, 2, 3), (('a', 31), ('b', 2), ('n', 3))) """ - def __init__(self, f, classmethod = False): + def __init__(self, f, classmethod=False): try: arg_names, varargs, varkw, defaults, kwonlyargs, kwonlydefaults, annotations = sage_getargspec(f) except AttributeError: @@ -159,7 +159,7 @@ cdef class ArgumentFixer: """ return "Argument Fixer of %s" % self.f - def fix_to_named(self, *args,**kwargs): + def fix_to_named(self, *args, **kwargs): """ Normalize the arguments with a preference for named arguments. @@ -185,7 +185,7 @@ cdef class ArgumentFixer: :: A,K = self.fix_to_pos(...) - self.f(*A,**dict(K))` + self.f(*A, **dict(K))` and :: @@ -247,7 +247,7 @@ cdef class ArgumentFixer: :: A,K = self.fix_to_pos(...) - self.f(*A,**dict(K)) + self.f(*A, **dict(K)) are equivalent to :: diff --git a/src/sage/misc/parser.pyx b/src/sage/misc/parser.pyx index 7a2c2cc99a4..522f5ebf55e 100644 --- a/src/sage/misc/parser.pyx +++ b/src/sage/misc/parser.pyx @@ -204,7 +204,7 @@ cdef class Tokenizer: token = self.next() return all - cpdef reset(self, int pos = 0): + cpdef reset(self, int pos=0): """ Reset the tokenizer to a given position. diff --git a/src/sage/misc/persist.pyx b/src/sage/misc/persist.pyx index a89db8557d1..7429388112e 100644 --- a/src/sage/misc/persist.pyx +++ b/src/sage/misc/persist.pyx @@ -456,14 +456,14 @@ def register_unpickle_override(module, name, callable, call_name=None): :: sage: class A(): - ....: def __init__(self,value): + ....: def __init__(self, value): ....: self.original_attribute = value ....: def __repr__(self): ....: return 'A(%s)' % self.original_attribute sage: class B(): - ....: def __init__(self,value): + ....: def __init__(self, value): ....: self.new_attribute = value - ....: def __setstate__(self,state): + ....: def __setstate__(self, state): ....: try: ....: self.new_attribute = state['new_attribute'] ....: except KeyError: # an old pickle diff --git a/src/sage/misc/sageinspect.py b/src/sage/misc/sageinspect.py index 1f2a39d7c78..c948099d09b 100644 --- a/src/sage/misc/sageinspect.py +++ b/src/sage/misc/sageinspect.py @@ -238,11 +238,11 @@ def _extract_embedded_position(docstring): The following has been fixed in :issue:`13916`:: - sage: cython('''cpdef test_funct(x,y): return''') # needs sage.misc.cython + sage: cython('''cpdef test_funct(x, y): return''') # needs sage.misc.cython sage: func_doc = inspect.getdoc(test_funct) # needs sage.misc.cython sage: with open(_extract_embedded_position(func_doc)[1]) as f: # needs sage.misc.cython ....: print(f.read()) - cpdef test_funct(x,y): return + cpdef test_funct(x, y): return Ensure that the embedded filename of the compiled function is correct. In particular it should be relative to ``spyx_tmp()`` in @@ -252,11 +252,11 @@ def _extract_embedded_position(docstring): sage: from sage.env import DOT_SAGE sage: from sage.misc.sage_ostools import restore_cwd sage: with restore_cwd(DOT_SAGE): # needs sage.misc.cython - ....: cython('''cpdef test_funct(x,y): return''') + ....: cython('''cpdef test_funct(x, y): return''') sage: func_doc = inspect.getdoc(test_funct) # needs sage.misc.cython sage: with open(_extract_embedded_position(func_doc)[1]) as f: # needs sage.misc.cython ....: print(f.read()) - cpdef test_funct(x,y): return + cpdef test_funct(x, y): return """ try: res = __embedded_position_re.search(docstring) @@ -1093,7 +1093,7 @@ def _sage_getargspec_cython(source): Some malformed input is detected:: - sage: sgc('def f(x,y') + sage: sgc('def f(x, y') Traceback (most recent call last): ... SyntaxError: Unexpected EOF while parsing argument list @@ -1484,7 +1484,7 @@ def sage_getargspec(obj): ....: 'cdef class MyClass:', ....: ' def _sage_src_(self):', ....: ' return "def foo(x, a=\\\')\\\"\\\', b={(2+1):\\\'bar\\\', not 1:3, 3<<4:5}): return\\n"', - ....: ' def __call__(self, m,n): return "something"'] + ....: ' def __call__(self, m, n): return "something"'] sage: cython('\n'.join(cython_code)) sage: O = MyClass() sage: print(sage.misc.sageinspect.sage_getsource(O)) @@ -1525,11 +1525,11 @@ def foo(x, a='\')"', b={not (2+1==3):'bar'}): return ....: ''' ....: class Foo: ....: @staticmethod - ....: def join(categories, bint as_list = False, tuple ignore_axioms=(), tuple axioms=()): pass + ....: def join(categories, bint as_list=False, tuple ignore_axioms=(), tuple axioms=()): pass ....: cdef class Bar: ....: @staticmethod - ....: def join(categories, bint as_list = False, tuple ignore_axioms=(), tuple axioms=()): pass - ....: cpdef meet(categories, bint as_list = False, tuple ignore_axioms=(), tuple axioms=()): pass + ....: def join(categories, bint as_list=False, tuple ignore_axioms=(), tuple axioms=()): pass + ....: cpdef meet(categories, bint as_list=False, tuple ignore_axioms=(), tuple axioms=()): pass ....: ''') sage: sage_getargspec(Foo.join) FullArgSpec(args=['categories', 'as_list', 'ignore_axioms', 'axioms'], varargs=None, varkw=None, @@ -2005,7 +2005,7 @@ def sage_getdoc(obj, obj_name='', embedded=False): sage: from sage.misc.sageinspect import sage_getdoc sage: sage_getdoc(identity_matrix)[87:124] # needs sage.modules 'Return the n x n identity matrix over' - sage: def f(a,b,c,d=1): return a+b+c+d + sage: def f(a, b, c, d=1): return a+b+c+d ... sage: import functools sage: f1 = functools.partial(f, 1,c=2) @@ -2244,9 +2244,9 @@ def sage_getsourcelines(obj): TESTS:: sage: # needs sage.misc.cython - sage: cython('''cpdef test_funct(x,y): return''') + sage: cython('''cpdef test_funct(x, y): return''') sage: sage_getsourcelines(test_funct) - (['cpdef test_funct(x,y): return\n'], 1) + (['cpdef test_funct(x, y): return\n'], 1) The following tests that an instance of ``functools.partial`` is correctly dealt with (see :issue:`9976`):: diff --git a/src/sage/modular/arithgroup/arithgroup_perm.py b/src/sage/modular/arithgroup/arithgroup_perm.py index 388cabfeed1..4238875048b 100644 --- a/src/sage/modular/arithgroup/arithgroup_perm.py +++ b/src/sage/modular/arithgroup/arithgroup_perm.py @@ -1019,7 +1019,7 @@ def _index_to_lr_cusp_width(self): return (l_cycle_length, r_cycle_length) - def _contains_sl2(self, a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" Test whether ``[a,b;c,d]`` is in the group or not. @@ -1145,7 +1145,7 @@ def is_normal(self): return False return True - def _conjugate(self,j0): + def _conjugate(self, j0): r""" Return the conjugate of ``self`` rooted at j0. @@ -1654,7 +1654,7 @@ def is_even(self): """ return False - def to_even_subgroup(self,relabel=True): + def to_even_subgroup(self, relabel=True): r""" Return the group with `-Id` added in it. @@ -1784,7 +1784,7 @@ def nregcusps(self): n += 1 return n//2 - def cusp_widths(self,exp=False): + def cusp_widths(self, exp=False): r""" Return the list of cusp widths. @@ -2391,7 +2391,7 @@ def coset_reps(self): """ return self.todd_coxeter()[0] - def cusp_widths(self,exp=False): + def cusp_widths(self, exp=False): r""" Return the list of cusp widths of the group. @@ -2462,7 +2462,7 @@ def to_even_subgroup(self, relabel=True): else: return self - def one_odd_subgroup(self,random=False): + def one_odd_subgroup(self, random=False): r""" Return an odd subgroup of index 2 in `\Gamma`, where `\Gamma` is this subgroup. If the optional argument ``random`` is False (the default), diff --git a/src/sage/modular/arithgroup/congroup_gamma.py b/src/sage/modular/arithgroup/congroup_gamma.py index 78d878aaf9d..2860ad5ad0a 100644 --- a/src/sage/modular/arithgroup/congroup_gamma.py +++ b/src/sage/modular/arithgroup/congroup_gamma.py @@ -140,7 +140,7 @@ def index(self): """ return prod([p**(3*e-2)*(p*p-1) for (p,e) in self.level().factor()]) - def _contains_sl2(self, a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" EXAMPLES:: @@ -326,7 +326,7 @@ def is_Gamma(x): return isinstance(x, Gamma_class) -def _lift_pair(U,V,N): +def _lift_pair(U, V, N): r""" Utility function. Given integers ``U, V, N``, with `N \ge 1` and `{\rm gcd}(U, V, N) = 1`, return a pair `(u, v)` congruent to `(U, V) \bmod N`, diff --git a/src/sage/modular/arithgroup/congroup_gamma0.py b/src/sage/modular/arithgroup/congroup_gamma0.py index ca0d050fe6f..611b67afe03 100644 --- a/src/sage/modular/arithgroup/congroup_gamma0.py +++ b/src/sage/modular/arithgroup/congroup_gamma0.py @@ -414,7 +414,7 @@ def gamma_h_subgroups(self): R = IntegerModRing(N) return [GammaH(N, H) for H in R.multiplicative_subgroups()] - def _contains_sl2(self, a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" Test whether x is an element of this group. diff --git a/src/sage/modular/arithgroup/congroup_gamma1.py b/src/sage/modular/arithgroup/congroup_gamma1.py index c450d98a783..b107686d7ad 100644 --- a/src/sage/modular/arithgroup/congroup_gamma1.py +++ b/src/sage/modular/arithgroup/congroup_gamma1.py @@ -238,7 +238,7 @@ def generators(self, algorithm='farey'): else: raise ValueError("Unknown algorithm '%s' (should be either 'farey' or 'todd-coxeter')" % algorithm) - def _contains_sl2(self, a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" Test whether x is an element of this group. diff --git a/src/sage/modular/arithgroup/congroup_generic.py b/src/sage/modular/arithgroup/congroup_generic.py index 41a09602a88..b94568522f6 100644 --- a/src/sage/modular/arithgroup/congroup_generic.py +++ b/src/sage/modular/arithgroup/congroup_generic.py @@ -332,7 +332,7 @@ def __reduce__(self): """ return CongruenceSubgroup_constructor, (self.image_mod_n(),) - def _contains_sl2(self, a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" Test whether ``[a,b;c,d]`` is an element of ``self``. @@ -455,7 +455,7 @@ def image_mod_n(self): """ raise NotImplementedError - def __init__(self,*args, **kwds): + def __init__(self, *args, **kwds): r""" Bypass the init function of the CongruenceSubgroupFromGroup class. diff --git a/src/sage/modular/arithgroup/congroup_sl2z.py b/src/sage/modular/arithgroup/congroup_sl2z.py index d95c9e18764..f7f6d47efed 100644 --- a/src/sage/modular/arithgroup/congroup_sl2z.py +++ b/src/sage/modular/arithgroup/congroup_sl2z.py @@ -118,7 +118,7 @@ def _element_constructor_(self, x, check=True): """ return ArithmeticSubgroupElement(self, x, check=check) - def _contains_sl2(self,a,b,c,d): + def _contains_sl2(self, a, b, c, d): r""" Test whether [a,b,c,d] is an element of self, where a,b,c,d are integers with `ad-bc=1`. In other words, always return True. diff --git a/src/sage/modular/btquotients/pautomorphicform.py b/src/sage/modular/btquotients/pautomorphicform.py index 53a7d2ac6f6..3d49d59bdfc 100644 --- a/src/sage/modular/btquotients/pautomorphicform.py +++ b/src/sage/modular/btquotients/pautomorphicform.py @@ -870,14 +870,14 @@ def is_simple(self): EXAMPLES:: - sage: X = BruhatTitsQuotient(3,29) - sage: H = X.harmonic_cocycles(4,prec =10) + sage: X = BruhatTitsQuotient(3, 29) + sage: H = X.harmonic_cocycles(4, prec=10) sage: H.rank() 14 sage: H.is_simple() False - sage: X = BruhatTitsQuotient(7,2) - sage: H = X.harmonic_cocycles(2,prec=10) + sage: X = BruhatTitsQuotient(7, 2) + sage: H = X.harmonic_cocycles(2, prec=10) sage: H.rank() 1 sage: H.is_simple() diff --git a/src/sage/modular/hecke/module.py b/src/sage/modular/hecke/module.py index e22ed609da6..bbc76fd1cbc 100644 --- a/src/sage/modular/hecke/module.py +++ b/src/sage/modular/hecke/module.py @@ -1695,7 +1695,7 @@ def system_of_eigenvalues(self, n, name='alpha'): Next we define a function that does the above:: - sage: def b(N,k=2): + sage: def b(N, k=2): ....: S = ModularSymbols(N,k,sign=-1).cuspidal_submodule().new_submodule() ....: for A in S.decomposition(): ....: print("{} {}".format(N, A.system_of_eigenvalues(5))) diff --git a/src/sage/modular/local_comp/local_comp.py b/src/sage/modular/local_comp/local_comp.py index 04d9123ab57..349c1e407e1 100644 --- a/src/sage/modular/local_comp/local_comp.py +++ b/src/sage/modular/local_comp/local_comp.py @@ -987,7 +987,7 @@ class ImprimitiveLocalComponent(LocalComponentBase): component and a character to twist by. """ - def __init__(self,newform, prime, twist_factor, min_twist, chi): + def __init__(self, newform, prime, twist_factor, min_twist, chi): r""" EXAMPLES:: diff --git a/src/sage/modular/modform/ambient_R.py b/src/sage/modular/modform/ambient_R.py index c07597e25dc..47b032176e6 100644 --- a/src/sage/modular/modform/ambient_R.py +++ b/src/sage/modular/modform/ambient_R.py @@ -39,7 +39,7 @@ def __init__(self, M, base_ring): ambient.ModularFormsAmbient.__init__(self, M.group(), M.weight(), base_ring, M.character(), M._eis_only) @cached_method(key=lambda self,sign: ZZ(sign)) # convert sign to an Integer before looking this up in the cache - def modular_symbols(self,sign=0): + def modular_symbols(self, sign=0): r""" Return the space of modular symbols attached to this space, with the given sign (default 0). diff --git a/src/sage/modular/modsym/manin_symbol.pyx b/src/sage/modular/modsym/manin_symbol.pyx index 7a98b5d1a40..726f78c55a6 100644 --- a/src/sage/modular/modsym/manin_symbol.pyx +++ b/src/sage/modular/modsym/manin_symbol.pyx @@ -287,7 +287,7 @@ cdef class ManinSymbol(Element): matrix[0]*self.u + matrix[2]*self.v, matrix[1]*self.u + matrix[3]*self.v)) - def apply(self, a,b,c,d): + def apply(self, a, b, c, d): """ Return the image of ``self`` under the matrix `[a,b;c,d]`. diff --git a/src/sage/modular/overconvergent/hecke_series.py b/src/sage/modular/overconvergent/hecke_series.py index 455e9e1bad2..f347da9a278 100644 --- a/src/sage/modular/overconvergent/hecke_series.py +++ b/src/sage/modular/overconvergent/hecke_series.py @@ -153,7 +153,7 @@ def low_weight_bases(N, p, m, NN, weightbound): return generators -def random_low_weight_bases(N,p,m,NN,weightbound): +def random_low_weight_bases(N, p, m, NN, weightbound): r""" Return list of random integral bases of modular forms of level `N` and (even) weight at most weightbound with coefficients reduced modulo @@ -197,7 +197,7 @@ def random_low_weight_bases(N,p,m,NN,weightbound): return RandomLWB -def low_weight_generators(N,p,m,NN): +def low_weight_generators(N, p, m, NN): r""" Return a list of lists of modular forms, and an even natural number. @@ -248,7 +248,7 @@ def low_weight_generators(N,p,m,NN): return generators, weightbound -def random_solution(B,K): +def random_solution(B, K): r""" Return a random solution in nonnegative integers to the equation `a_1 + 2 a_2 + 3 a_3 + ... + B a_B = K`, using a greedy algorithm. diff --git a/src/sage/modular/pollack_stevens/modsym.py b/src/sage/modular/pollack_stevens/modsym.py index 8df8655e5e9..ddb1f861f1b 100644 --- a/src/sage/modular/pollack_stevens/modsym.py +++ b/src/sage/modular/pollack_stevens/modsym.py @@ -1574,7 +1574,7 @@ def specialize(self, new_base_ring=None): return self.__class__(self._map.specialize(new_base_ring), self.parent()._specialize_parent_space(new_base_ring), construct=True) - def padic_lseries(self,*args, **kwds): + def padic_lseries(self, *args, **kwds): """ Return the `p`-adic `L`-series of this modular symbol. diff --git a/src/sage/modules/free_module_element.pyx b/src/sage/modules/free_module_element.pyx index 4aaaa354d66..f840143a073 100644 --- a/src/sage/modules/free_module_element.pyx +++ b/src/sage/modules/free_module_element.pyx @@ -4141,7 +4141,7 @@ cdef class FreeModuleElement(Vector): # abstract base class (1/2, 1/3, -cos(1) + 1) """ from sage.misc.functional import integral - return self.apply_map(lambda x: integral(x,*args, **kwds)) + return self.apply_map(lambda x: integral(x, *args, **kwds)) integrate = integral @@ -4179,11 +4179,11 @@ cdef class FreeModuleElement(Vector): # abstract base class # return self.apply_map(lambda x: x.nintegral(*args, **kwds) for x in self) if self.is_sparse(): - v = [(i,z.nintegral(*args,**kwds)) for i,z in self.dict(copy=False).items()] + v = [(i,z.nintegral(*args, **kwds)) for i,z in self.dict(copy=False).items()] answers = dict([(i,a[0]) for i,a in v]) v=dict(v) else: - v = [z.nintegral(*args,**kwds) for z in self.list()] + v = [z.nintegral(*args, **kwds) for z in self.list()] answers = [a[0] for a in v] return (vector(answers,sparse=self.is_sparse()), v) @@ -4850,7 +4850,7 @@ cdef class FreeModuleElement_generic_sparse(FreeModuleElement): We can initialize with dicts, lists, tuples and derived types:: sage: from sage.modules.free_module_element import FreeModuleElement_generic_sparse - sage: def S(R,n): + sage: def S(R, n): ....: return FreeModule(R, n, sparse=True) sage: # needs sage.symbolic diff --git a/src/sage/modules/vector_integer_dense.pyx b/src/sage/modules/vector_integer_dense.pyx index 9517b8487d8..12b3cfead87 100644 --- a/src/sage/modules/vector_integer_dense.pyx +++ b/src/sage/modules/vector_integer_dense.pyx @@ -190,7 +190,7 @@ cdef class Vector_integer_dense(free_module_element.FreeModuleElement): """ mpz_set(self._entries[i], (value).value) - def list(self,copy=True): + def list(self, copy=True): """ The list of entries of the vector. diff --git a/src/sage/modules/vector_numpy_dense.pyx b/src/sage/modules/vector_numpy_dense.pyx index b6e6d37473f..f04163d2e82 100644 --- a/src/sage/modules/vector_numpy_dense.pyx +++ b/src/sage/modules/vector_numpy_dense.pyx @@ -128,7 +128,7 @@ cdef class Vector_numpy_dense(FreeModuleElement): from copy import copy return self._new(copy(self._vector_numpy)) - def __init__(self, parent, entries, coerce = True, copy = True): + def __init__(self, parent, entries, coerce=True, copy=True): """ Fill the vector with entries. diff --git a/src/sage/modules/with_basis/invariant.py b/src/sage/modules/with_basis/invariant.py index 5c4202419a5..b97539d5a27 100644 --- a/src/sage/modules/with_basis/invariant.py +++ b/src/sage/modules/with_basis/invariant.py @@ -170,7 +170,7 @@ class FiniteDimensionalInvariantModule(SubmoduleWithBasis): sage: C = IntegerVectors(4, length=3, min_part=0) # representing degree-4 monomials sage: M = CombinatorialFreeModule(QQ, C) # isomorphic to deg-4 homog. polynomials sage: G = SymmetricGroup(3) - sage: def perm_action(g,x): return M.monomial(C(g(list(x)))) + sage: def perm_action(g, x): return M.monomial(C(g(list(x)))) sage: perm_action(G((1,2,3)), C([4,3,2])) B[[3, 2, 4]] sage: R = Representation(G, M, perm_action) @@ -227,7 +227,7 @@ def __init__(self, M, S, action=operator.mul, side='left', *args, **kwargs): sage: G = GroupExp()(QQ) # a group that is not finitely generated sage: M = CombinatorialFreeModule(QQ, [1,2,3]) - sage: def on_basis(g,m): return M.monomial(m) # trivial rep'n + sage: def on_basis(g, m): return M.monomial(m) # trivial rep'n sage: from sage.modules.with_basis.representation import Representation sage: R = Representation(G, M, on_basis) sage: R.invariant_module() @@ -372,7 +372,7 @@ def semigroup(self): sage: G = SymmetricGroup(3) sage: M = CombinatorialFreeModule(QQ, [1,2,3], prefix='M') - sage: def action(g,x): return M.monomial(g(x)) + sage: def action(g, x): return M.monomial(g(x)) sage: I = M.invariant_module(G, action_on_basis=action) sage: I.semigroup() Symmetric group of order 3! as a permutation group @@ -422,7 +422,7 @@ def _mul_(self, other): sage: G = CyclicPermutationGroup(3); G.rename('G') sage: M = algebras.Exterior(QQ, 'x', 3) - sage: def on_basis(g,m): return M.prod([M.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators + sage: def on_basis(g, m): return M.prod([M.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators sage: R = Representation(G, M, on_basis, category=Algebras(QQ).WithBasis().FiniteDimensional(), side='right') sage: I = R.invariant_module(); I.rename('I') sage: B = I.basis() @@ -504,7 +504,7 @@ def _acted_upon_(self, scalar, self_on_left=False): sage: E = algebras.Exterior(QQ, 'x', 3) - sage: def on_basis(g,m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators + sage: def on_basis(g, m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators sage: R = Representation(G, E, on_basis, category=Algebras(QQ).WithBasis().FiniteDimensional()) sage: I = R.invariant_module() sage: B = I.basis() @@ -552,7 +552,7 @@ def _acted_upon_(self, scalar, self_on_left=False): sage: [b._acted_upon_(G((1,3,2)), self_on_left=True) for b in I.basis()] [B[0]] - sage: def on_basis(g,m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators + sage: def on_basis(g, m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) # cyclically permute generators sage: R = Representation(G, E, on_basis, category=Algebras(QQ).WithBasis().FiniteDimensional(), side='right') sage: I = R.invariant_module() sage: B = I.basis() @@ -711,7 +711,7 @@ class FiniteDimensionalTwistedInvariantModule(SubmoduleWithBasis): sage: G = SymmetricGroup(3); G.rename('S3') sage: E = algebras.Exterior(QQ, 'x', 3); E.rename('E') - sage: def action(g,m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) + sage: def action(g, m): return E.prod([E.monomial(FrozenBitset([g(j+1)-1])) for j in m]) sage: from sage.modules.with_basis.representation import Representation sage: EA = Representation(G, E, action, category=Algebras(QQ).WithBasis().FiniteDimensional()) sage: T = EA.twisted_invariant_module([2,0,-1]) @@ -758,7 +758,7 @@ def __classcall_private__(cls, M, G, chi, sage: M = CombinatorialFreeModule(QQ, [1,2,3]) sage: G = SymmetricGroup(3) - sage: def action(g,x): return M.term(g(x)) + sage: def action(g, x): return M.term(g(x)) sage: T = M.twisted_invariant_module(G, [2,0,-1], action_on_basis=action) Check that it works for tuples:: @@ -844,7 +844,7 @@ def __init__(self, M, G, chi, action=operator.mul, side='left', **kwargs): Conjugacy class of cycle type [3] in Symmetric group of order 3! as a permutation group] sage: from sage.groups.class_function import ClassFunction sage: chi = ClassFunction(G, [2,0,-1]) # the standard representation character values - sage: def action(g,x): return M.term(g(x)) + sage: def action(g, x): return M.term(g(x)) sage: import __main__ sage: __main__.action = action sage: T = M.twisted_invariant_module(G, chi, action_on_basis=action) @@ -946,7 +946,7 @@ def project(self, x): sage: M = CombinatorialFreeModule(QQ, [1,2,3]); M.rename('M') sage: B = M.basis() sage: G = SymmetricGroup(3); G.rename('S3') - sage: def action(g,x): return M.term(g(x)) + sage: def action(g, x): return M.term(g(x)) sage: T = M.twisted_invariant_module(G, [2,0,-1], action_on_basis=action) sage: m = B[1] + B[2] + B[3] sage: parent(m) @@ -975,7 +975,7 @@ def project_ambient(self, x): sage: M = CombinatorialFreeModule(QQ, [1,2,3]); M.rename('M') sage: B = M.basis() sage: G = SymmetricGroup(3); G.rename('S3') - sage: def action(g,x): return M.term(g(x)) + sage: def action(g, x): return M.term(g(x)) sage: T = M.twisted_invariant_module(G, [2,0,-1], action_on_basis=action) To compare with ``self.project``, we can inspect the parents. @@ -1017,7 +1017,7 @@ def projection_matrix(self): EXAMPLES:: sage: M = CombinatorialFreeModule(QQ, [1,2,3]) - sage: def action(g,x): return(M.term(g(x))) + sage: def action(g, x): return(M.term(g(x))) sage: G = SymmetricGroup(3) If the matrix `A` has columns form a basis for diff --git a/src/sage/modules/with_basis/morphism.py b/src/sage/modules/with_basis/morphism.py index 68ad2521493..2359672a055 100644 --- a/src/sage/modules/with_basis/morphism.py +++ b/src/sage/modules/with_basis/morphism.py @@ -515,7 +515,7 @@ class TriangularModuleMorphism(ModuleMorphism): A lower triangular (but not unitriangular) morphism:: sage: X = CombinatorialFreeModule(QQ, [1, 2, 3]); X.rename('X'); x = X.basis() - sage: def lt(i): return sum(j*x[j] for j in range(i,4)) + sage: def lt(i): return sum(j*x[j] for j in range(i, 4)) sage: phi = X.module_morphism(lt, triangular='lower', codomain=X) sage: phi(x[2]) 2*B[2] + 3*B[3] @@ -635,7 +635,7 @@ def __init__(self, triangular='upper', unitriangular=False, TESTS:: sage: X = CombinatorialFreeModule(QQ, [1, 2, 3]); X.rename('X'); x = X.basis() - sage: def lt(i): return sum(j*x[j] for j in range(i,4)) + sage: def lt(i): return sum(j*x[j] for j in range(i, 4)) sage: import __main__; __main__.lt = lt # Fake lt being defined in a python module sage: phi = X.module_morphism(lt, triangular='lower', codomain=X) sage: phi.__class__ @@ -1180,7 +1180,7 @@ def __init__(self, domain, on_basis, codomain=None, category=None, **keywords): sage: X = CombinatorialFreeModule(QQ, ZZ) sage: from sage.modules.with_basis.morphism import TriangularModuleMorphismByLinearity - sage: def on_basis(i): return X.sum_of_monomials(range(i-2,i+1)) + sage: def on_basis(i): return X.sum_of_monomials(range(i-2, i+1)) sage: import __main__; __main__.on_basis = on_basis # Fake on_basis being defined in a python module sage: phi = TriangularModuleMorphismByLinearity( ....: X, on_basis=on_basis, codomain=X) @@ -1198,7 +1198,7 @@ def _richcmp_(self, other, op): sage: X = CombinatorialFreeModule(QQ, ZZ) sage: from sage.modules.with_basis.morphism import TriangularModuleMorphismByLinearity - sage: def on_basis(i): return X.sum_of_monomials(range(i-2,i+1)) + sage: def on_basis(i): return X.sum_of_monomials(range(i-2, i+1)) sage: phi = TriangularModuleMorphismByLinearity( ....: X, on_basis=on_basis, codomain=X) sage: phi == phi diff --git a/src/sage/monoids/automatic_semigroup.py b/src/sage/monoids/automatic_semigroup.py index c4926239f8d..fac295b2341 100644 --- a/src/sage/monoids/automatic_semigroup.py +++ b/src/sage/monoids/automatic_semigroup.py @@ -169,7 +169,7 @@ class AutomaticSemigroup(UniqueRepresentation, Parent): sage: M2 = matrix([[0,0,0],[1,1,0],[0,0,1]]) sage: M1.set_immutable() sage: M2.set_immutable() - sage: def prod_m(x,y): + sage: def prod_m(x, y): ....: z=x*y ....: z.set_immutable() ....: return z @@ -483,7 +483,7 @@ def ambient(self): sage: M2 = matrix([[0,0,0],[1,1,0],[0,0,1]]) sage: M1.set_immutable() sage: M2.set_immutable() - sage: def prod_m(x,y): + sage: def prod_m(x, y): ....: z=x*y ....: z.set_immutable() ....: return z diff --git a/src/sage/numerical/backends/cvxopt_backend.pyx b/src/sage/numerical/backends/cvxopt_backend.pyx index 14c60dc3167..085340726fb 100644 --- a/src/sage/numerical/backends/cvxopt_backend.pyx +++ b/src/sage/numerical/backends/cvxopt_backend.pyx @@ -55,7 +55,7 @@ cdef class CVXOPTBackend(GenericBackend): cdef dict answer cdef dict param - def __cinit__(self, maximization = True): + def __cinit__(self, maximization=True): """ Cython constructor. @@ -276,7 +276,7 @@ cdef class CVXOPTBackend(GenericBackend): else: return self.objective_function[variable] - cpdef set_objective(self, list coeff, d = 0.0): + cpdef set_objective(self, list coeff, d=0.0): """ Set the objective function. @@ -915,7 +915,7 @@ cdef class CVXOPTBackend(GenericBackend): return self.col_name_var[index] return "x_" + repr(index) - cpdef variable_upper_bound(self, int index, value = False): + cpdef variable_upper_bound(self, int index, value=False): """ Return or define the upper bound on a variable. @@ -944,7 +944,7 @@ cdef class CVXOPTBackend(GenericBackend): else: return self.col_upper_bound[index] - cpdef variable_lower_bound(self, int index, value = False): + cpdef variable_lower_bound(self, int index, value=False): """ Return or define the lower bound on a variable. @@ -973,7 +973,7 @@ cdef class CVXOPTBackend(GenericBackend): else: return self.col_lower_bound[index] - cpdef solver_parameter(self, name, value = None): + cpdef solver_parameter(self, name, value=None): """ Return or define a solver parameter. diff --git a/src/sage/numerical/backends/glpk_backend.pyx b/src/sage/numerical/backends/glpk_backend.pyx index dddde9a07b6..5e1f0dcdf82 100644 --- a/src/sage/numerical/backends/glpk_backend.pyx +++ b/src/sage/numerical/backends/glpk_backend.pyx @@ -37,7 +37,7 @@ cdef class GLPKBackend(GenericBackend): MIP Backend that uses the GLPK solver. """ - def __cinit__(self, maximization = True): + def __cinit__(self, maximization=True): """ Constructor. @@ -537,7 +537,7 @@ cdef class GLPKBackend(GenericBackend): Removing fancy constraints does not make Sage crash:: - sage: MixedIntegerLinearProgram(solver= "GLPK").remove_constraints([0, -2]) + sage: MixedIntegerLinearProgram(solver="GLPK").remove_constraints([0, -2]) Traceback (most recent call last): ... ValueError: The constraint's index i must satisfy 0 <= i < number_of_constraints diff --git a/src/sage/numerical/backends/glpk_exact_backend.pyx b/src/sage/numerical/backends/glpk_exact_backend.pyx index a9289264a42..96f18df6fe8 100644 --- a/src/sage/numerical/backends/glpk_exact_backend.pyx +++ b/src/sage/numerical/backends/glpk_exact_backend.pyx @@ -28,7 +28,7 @@ cdef class GLPKExactBackend(GLPKBackend): There is no support for integer variables. """ - def __cinit__(self, maximization = True): + def __cinit__(self, maximization=True): """ Constructor. diff --git a/src/sage/numerical/backends/glpk_graph_backend.pxd b/src/sage/numerical/backends/glpk_graph_backend.pxd index 2e4b29a25a9..f72ad9ba077 100644 --- a/src/sage/numerical/backends/glpk_graph_backend.pxd +++ b/src/sage/numerical/backends/glpk_graph_backend.pxd @@ -51,5 +51,5 @@ cdef class GLPKGraphBackend(): cdef int s cdef int t cpdef int write_maxflow(self, fname) except -1 - cpdef double maxflow_ffalg(self, u = ?, v = ?) except -1 + cpdef double maxflow_ffalg(self, u=?, v=?) except -1 cpdef double cpp(self) noexcept diff --git a/src/sage/numerical/backends/glpk_graph_backend.pyx b/src/sage/numerical/backends/glpk_graph_backend.pyx index ca3907e2fdb..71dc49e46f5 100644 --- a/src/sage/numerical/backends/glpk_graph_backend.pyx +++ b/src/sage/numerical/backends/glpk_graph_backend.pyx @@ -183,7 +183,7 @@ cdef class GLPKGraphBackend(): 3.0 """ - def __cinit__(self, data = None, format = "plain"): + def __cinit__(self, data=None, format="plain"): """ Constructor. diff --git a/src/sage/numerical/backends/interactivelp_backend.pyx b/src/sage/numerical/backends/interactivelp_backend.pyx index ea1a53aedce..3519303a817 100644 --- a/src/sage/numerical/backends/interactivelp_backend.pyx +++ b/src/sage/numerical/backends/interactivelp_backend.pyx @@ -41,7 +41,7 @@ cdef class InteractiveLPBackend: sage: p = get_solver(solver = "InteractiveLP") """ - def __cinit__(self, maximization = True, base_ring = None): + def __cinit__(self, maximization=True, base_ring=None): """ Cython constructor. diff --git a/src/sage/numerical/backends/ppl_backend.pyx b/src/sage/numerical/backends/ppl_backend.pyx index 24b0c8e80ac..72074210054 100644 --- a/src/sage/numerical/backends/ppl_backend.pyx +++ b/src/sage/numerical/backends/ppl_backend.pyx @@ -49,7 +49,7 @@ cdef class PPLBackend(GenericBackend): # Common denominator for objective function in self.mip (not for the constant term) cdef Integer obj_denominator - def __cinit__(self, maximization = True, base_ring = None): + def __cinit__(self, maximization=True, base_ring=None): """ Constructor. diff --git a/src/sage/numerical/mip.pyx b/src/sage/numerical/mip.pyx index 2395868b43d..78ac846d3df 100644 --- a/src/sage/numerical/mip.pyx +++ b/src/sage/numerical/mip.pyx @@ -670,7 +670,7 @@ cdef class MixedIntegerLinearProgram(SageObject): """ return self._backend.base_ring() - def set_problem_name(self,name): + def set_problem_name(self, name): r""" Set the name of the ``MixedIntegerLinearProgram``. @@ -914,7 +914,7 @@ cdef class MixedIntegerLinearProgram(SageObject): """ return self._backend.ncols() - def constraints(self, indices = None): + def constraints(self, indices=None): r""" Return a list of constraints, as 3-tuples. @@ -970,7 +970,7 @@ cdef class MixedIntegerLinearProgram(SageObject): solver used, we define a short function reordering it before it is printed. The output would look the same without this function applied:: - sage: def reorder_constraint(lb,indcoef,ub): + sage: def reorder_constraint(lb, indcoef, ub): ....: ind, coef = indcoef ....: d = dict(zip(ind, coef)) ....: ind.sort() @@ -1310,7 +1310,7 @@ cdef class MixedIntegerLinearProgram(SageObject): lb if lb is not None else "-oo", ub if ub is not None else "+oo")) - def write_mps(self,filename,modern=True): + def write_mps(self, filename, modern=True): r""" Write the linear program as a MPS file. @@ -1343,7 +1343,7 @@ cdef class MixedIntegerLinearProgram(SageObject): """ self._backend.write_mps(filename, modern) - def write_lp(self,filename): + def write_lp(self, filename): r""" Write the linear program as a LP file. @@ -1782,7 +1782,7 @@ cdef class MixedIntegerLinearProgram(SageObject): else: return val - def set_objective(self,obj): + def set_objective(self, obj): r""" Set the objective of the ``MixedIntegerLinearProgram``. @@ -2492,7 +2492,7 @@ cdef class MixedIntegerLinearProgram(SageObject): """ return self._backend.is_variable_integer(self._variables[e]) - def set_real(self,ee): + def set_real(self, ee): r""" Set a variable or a ``MIPVariable`` as real. @@ -2778,7 +2778,7 @@ cdef class MixedIntegerLinearProgram(SageObject): except TypeError: return self._backend.variable_upper_bound(self._variables[v]) - def solver_parameter(self, name, value = None): + def solver_parameter(self, name, value=None): """ Return or define a solver parameter. @@ -3026,7 +3026,7 @@ cdef class MixedIntegerLinearProgram(SageObject): """ return self._backend.get_relative_objective_gap() - def interactive_lp_problem(self,form='standard'): + def interactive_lp_problem(self, form='standard'): r""" Return an InteractiveLPProblem and, if available, a basis. diff --git a/src/sage/numerical/optimize.py b/src/sage/numerical/optimize.py index 098fe0ce95f..cdcd3a524b3 100644 --- a/src/sage/numerical/optimize.py +++ b/src/sage/numerical/optimize.py @@ -442,7 +442,7 @@ def minimize(func, x0, gradient=None, hessian=None, algorithm='default', return vector(RDF, min) -def minimize_constrained(func,cons,x0,gradient=None,algorithm='default', **args): +def minimize_constrained(func, cons, x0, gradient=None, algorithm='default', **args): r""" Minimize a function with constraints. diff --git a/src/sage/numerical/sdp.pyx b/src/sage/numerical/sdp.pyx index 7c08ed08e10..6693b943806 100644 --- a/src/sage/numerical/sdp.pyx +++ b/src/sage/numerical/sdp.pyx @@ -459,7 +459,7 @@ cdef class SemidefiniteProgram(SageObject): """ return self._backend.base_ring() - def set_problem_name(self,name): + def set_problem_name(self, name): r""" Set the name of the ``SemidefiniteProgram``. @@ -1049,7 +1049,7 @@ cdef class SemidefiniteProgram(SageObject): """ return self._backend.slack(i, sparse=sparse) - def solver_parameter(self, name, value = None): + def solver_parameter(self, name, value=None): """ Return or define a solver parameter. diff --git a/src/sage/parallel/decorate.py b/src/sage/parallel/decorate.py index a01d680bdcc..90ee3a5cc42 100644 --- a/src/sage/parallel/decorate.py +++ b/src/sage/parallel/decorate.py @@ -110,7 +110,7 @@ def __call__(self, f): sage: P = sage.parallel.decorate.Parallel() - sage: def g(n,m): return n+m + sage: def g(n, m): return n+m sage: h = P(g) # indirect doctest sage: list(h([(2,3)])) [(((2, 3), {}), 5)] @@ -358,7 +358,7 @@ def parallel(p_iter='fork', ncpus=None, **kwds): when calling the parallel function:: sage: @parallel - ....: def f(a,b): return a*b + ....: def f(a, b): return a*b sage: for X, Y in sorted(list(f([(2,3),(3,5),(5,7)]))): print((X, Y)) (((2, 3), {}), 6) (((3, 5), {}), 15) @@ -456,7 +456,7 @@ def __call__(self, f): EXAMPLES:: sage: F = sage.parallel.decorate.Fork(timeout=3) - sage: def g(n,m): return n+m + sage: def g(n, m): return n+m sage: h = F(g) # indirect doctest sage: h(2,3) 5 diff --git a/src/sage/parallel/reference.py b/src/sage/parallel/reference.py index 6a855874330..e5587022576 100644 --- a/src/sage/parallel/reference.py +++ b/src/sage/parallel/reference.py @@ -26,7 +26,7 @@ def parallel_iter(f, inputs): EXAMPLES:: - sage: def f(N,M=10): return N*M + sage: def f(N, M=10): return N*M sage: inputs = [((2,3),{}), (tuple(), {'M':5,'N':3}), ((2,),{})] sage: set_random_seed(0) sage: for a, val in sage.parallel.reference.parallel_iter(f, inputs): diff --git a/src/sage/plot/animate.py b/src/sage/plot/animate.py index 16672405c8e..c37a17531d8 100644 --- a/src/sage/plot/animate.py +++ b/src/sage/plot/animate.py @@ -432,7 +432,7 @@ def make_image(self, frame, filename, **kwds): sage: class MyAnimation(Animation): ....: def make_image(self, frame, filename, **kwds): ....: P = parametric_plot(frame[0], frame[1], **frame[2]) - ....: P.save_image(filename,**kwds) + ....: P.save_image(filename, **kwds) sage: t = SR.var("t") sage: x = lambda t: cos(t) diff --git a/src/sage/plot/contour_plot.py b/src/sage/plot/contour_plot.py index 26874790ec5..a59397e8b23 100644 --- a/src/sage/plot/contour_plot.py +++ b/src/sage/plot/contour_plot.py @@ -415,7 +415,7 @@ def contour_plot(f, xrange, yrange, **options): .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2)) sphinx_plot(g) @@ -427,7 +427,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2, 2), (-2, 2), contours=2, cmap=[(1,0,0), (0,1,0), (0,0,1)]) sphinx_plot(g) @@ -440,7 +440,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2), contours=(0.1,1.0,1.2,1.4), cmap='hsv') sphinx_plot(g) @@ -452,7 +452,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2), contours=(1.0,), fill=False) sphinx_plot(g) @@ -475,7 +475,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2), fill=False, linewidths=10) sphinx_plot(g) @@ -488,7 +488,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2), fill=False, linestyles='dashdot') sphinx_plot(g) @@ -667,7 +667,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (-2,2), (-2,2), labels=True, label_colors='red') sphinx_plot(g) @@ -680,7 +680,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), colorbar=True) sphinx_plot(g) @@ -692,7 +692,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), colorbar=True, colorbar_orientation='horizontal') sphinx_plot(g) @@ -704,7 +704,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), contours=[-2,-1,4], colorbar=True) sphinx_plot(g) @@ -718,7 +718,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), contours=[-2,-1,4], colorbar=True, colorbar_spacing='uniform') sphinx_plot(g) @@ -732,7 +732,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), contours=[0,2,3,6], colorbar=True, colorbar_format='%.3f') sphinx_plot(g) @@ -747,7 +747,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), labels=True, label_colors='red', contours=[0,2,3,6], colorbar=True) @@ -762,7 +762,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 + y**2 + def f(x, y): return x**2 + y**2 g = contour_plot(f, (x,-3,3), (y,-3,3), cmap='winter', contours=20, fill=False, colorbar=True) sphinx_plot(g) @@ -793,7 +793,7 @@ def f(x,y): return x**2 + y**2 .. PLOT:: x,y = var('x,y') - def f(x,y): return cos(x) + sin(y) + def f(x, y): return cos(x) + sin(y) g = contour_plot(f, (0,pi), (0,pi), axes=True) sphinx_plot(g) @@ -819,7 +819,7 @@ def f(x,y): return cos(x) + sin(y) .. PLOT:: x,y = var('x,y') - def f(x,y): return cos(x) + sin(y) + def f(x, y): return cos(x) + sin(y) g = contour_plot(f, (-pi,pi), (-pi,pi), fill=False, axes=True) sphinx_plot(g) @@ -1132,7 +1132,7 @@ def implicit_plot(f, xrange, yrange, **options): .. PLOT:: - def f(x,y): return x**2 + y**2 - 2 + def f(x, y): return x**2 + y**2 - 2 g = implicit_plot(f, (-3,3), (-3,3), fill=True, plot_points=500) sphinx_plot(g) @@ -1143,7 +1143,7 @@ def f(x,y): return x**2 + y**2 - 2 .. PLOT:: - def f(x,y): return x**2 + y**2 - 2 + def f(x, y): return x**2 + y**2 - 2 g = implicit_plot(f, (-3,3), (-3,3), linewidth=6) sphinx_plot(g) @@ -1155,7 +1155,7 @@ def f(x,y): return x**2 + y**2 - 2 .. PLOT:: x, y =var("x y") - def f(x,y): return x**2 + y**2 - 2 + def f(x, y): return x**2 + y**2 - 2 g = implicit_plot(f, (-3,3), (-3,3), linestyle='dashdot') sphinx_plot(g) @@ -1168,7 +1168,7 @@ def f(x,y): return x**2 + y**2 - 2 .. PLOT:: - def f(x,y): return x**2 + y**2 - 2 + def f(x, y): return x**2 + y**2 - 2 g = implicit_plot(f, (-3,3), (-3,3), color='red', fill=True, fillcolor='green', plot_points=500) sphinx_plot(g) @@ -1237,7 +1237,7 @@ def f(x,y): return x**2 + y**2 - 2 ....: z = 0 ....: for i in range(n): ....: z = z*z + c - ....: def f(x,y): + ....: def f(x, y): ....: val = z(CDF(x, y)) ....: return val.norm() - 4 ....: return f @@ -1254,7 +1254,7 @@ def mandel(n): z = 0 for i in range(n): z = z*z + c - def f(x,y): + def f(x, y): val = z(CDF(x, y)) return val.norm() - 4 return f @@ -1273,7 +1273,7 @@ def mandel(n): z = 0 for i in range(n): z = z*z + c - def f(x,y): + def f(x, y): val = z(CDF(x, y)) return val.norm() - 4 return f @@ -1296,7 +1296,7 @@ def mandel(n): z = 0 for i in range(n): z = z*z + c - def f(x,y): + def f(x, y): val = z(CDF(x, y)) return val.norm() - 4 return f diff --git a/src/sage/plot/density_plot.py b/src/sage/plot/density_plot.py index 84d08518a0b..dbbeb767775 100644 --- a/src/sage/plot/density_plot.py +++ b/src/sage/plot/density_plot.py @@ -212,7 +212,7 @@ def density_plot(f, xrange, yrange, **options): .. PLOT:: x,y = var('x,y') - def f(x,y): return x**2 * cos(x*y) + def f(x, y): return x**2 * cos(x*y) g = density_plot(f, (x,-10,5), (y,-5,5), interpolation='sinc', plot_points=100) sphinx_plot(g) @@ -296,7 +296,7 @@ def f(x,y): return x**2 * cos(x*y) Check that :issue:`17684` is fixed, i.e., symbolic values can be plotted:: - sage: def f(x,y): + sage: def f(x, y): ....: return SR(x) sage: density_plot(f, (0,1), (0,1)) Graphics object consisting of 1 graphics primitive diff --git a/src/sage/plot/matrix_plot.py b/src/sage/plot/matrix_plot.py index 900ac9989e0..aa8309b5bc0 100644 --- a/src/sage/plot/matrix_plot.py +++ b/src/sage/plot/matrix_plot.py @@ -234,7 +234,7 @@ def _render_on_subplot(self, subplot): if options.get('colorbar', False): colorbar_options = options['colorbar_options'] from matplotlib import colorbar - cax,kwds = colorbar.make_axes_gridspec(subplot,**colorbar_options) + cax,kwds = colorbar.make_axes_gridspec(subplot, **colorbar_options) colorbar.Colorbar(cax, image, **kwds) if flip_y: diff --git a/src/sage/plot/plot.py b/src/sage/plot/plot.py index d1e21abe20a..c8f5a0fca96 100644 --- a/src/sage/plot/plot.py +++ b/src/sage/plot/plot.py @@ -641,7 +641,7 @@ def f(x): return (x-3)*(x-5)*(x-7)+40 # Currently not used - see comment above about # figure.canvas.mpl_connect('draw_event', pad_for_tick_labels) # TODO - figure out how to use this, add documentation -# def adjust_figure_to_contain_bbox(fig, bbox,pad=1.1): +# def adjust_figure_to_contain_bbox(fig, bbox, pad=1.1): # """ # For each amount we are over (in axes coordinates), we adjust by over*pad # to give ourselves a bit of padding. @@ -2194,7 +2194,7 @@ def _plot(funcs, xrange, parametric=False, # Check to see if funcs is a list of functions that will be all plotted together. if isinstance(funcs, (list, tuple)) and not parametric: - def golden_rainbow(i,lightness=0.4): + def golden_rainbow(i, lightness=0.4): # note: sage's "blue" has hue-saturation-lightness values (2/3, 1, 1/2). g = 0.61803398875 return Color((0.66666666666666 + i*g) % 1, 1, lightness, space='hsl') diff --git a/src/sage/plot/plot3d/index_face_set.pyx b/src/sage/plot/plot3d/index_face_set.pyx index 04cd6866f8d..9fb52e59923 100644 --- a/src/sage/plot/plot3d/index_face_set.pyx +++ b/src/sage/plot/plot3d/index_face_set.pyx @@ -1012,7 +1012,7 @@ cdef class IndexFaceSet(PrimitiveObject): sage: var('x,y,z') # needs sage.symbolic (x, y, z) sage: P = implicit_plot3d(z-x*y,(-2,2),(-2,2),(-2,2)) # needs sage.symbolic - sage: def condi(x,y,z): + sage: def condi(x, y, z): ....: return bool(x*x+y*y+z*z <= Integer(1)) sage: R = P.add_condition(condi, 20); R # needs sage.symbolic Graphics3d Object @@ -1021,13 +1021,13 @@ cdef class IndexFaceSet(PrimitiveObject): x,y,z = var('x,y,z') P = implicit_plot3d(z-x*y,(-2,2),(-2,2),(-2,2)) - def condi(x,y,z): + def condi(x, y, z): return bool(x*x+y*y+z*z <= Integer(1)) sphinx_plot(P.add_condition(condi,40)) An example with colors:: - sage: def condi(x,y,z): + sage: def condi(x, y, z): ....: return bool(x*x+y*y <= 1.1) sage: cm = colormaps.hsv sage: cf = lambda x,y,z: float(x+y) % 1 @@ -1039,7 +1039,7 @@ cdef class IndexFaceSet(PrimitiveObject): .. PLOT:: x,y,z = var('x,y,z') - def condi(x,y,z): + def condi(x, y, z): return bool(x*x+y*y <= 1.1) cm = colormaps.hsv cf = lambda x,y,z: float(x+y) % 1 @@ -1050,7 +1050,7 @@ cdef class IndexFaceSet(PrimitiveObject): sage: P = implicit_plot3d(x**4+y**4+z**2-4, (x,-2,2), (y,-2,2), (z,-2,2), # needs sage.symbolic ....: alpha=0.3) - sage: def cut(a,b,c): + sage: def cut(a, b, c): ....: return a*a+c*c > 2 sage: Q = P.add_condition(cut,40); Q # needs sage.symbolic Graphics3d Object @@ -1059,7 +1059,7 @@ cdef class IndexFaceSet(PrimitiveObject): x,y,z = var('x,y,z') P = implicit_plot3d(x**4+y**4+z**2-4,(x,-2,2),(y,-2,2),(z,-2,2),alpha=0.3) - def cut(a,b,c): + def cut(a, b, c): return a*a+c*c > 2 sphinx_plot(P.add_condition(cut,40)) @@ -1067,7 +1067,7 @@ cdef class IndexFaceSet(PrimitiveObject): sage: P = plot3d(-sin(2*x*x+2*y*y)*exp(-x*x-y*y), (x,-2,2), (y,-2,2), # needs sage.symbolic ....: color='gold') - sage: def cut(x,y,z): + sage: def cut(x, y, z): ....: return x*x+y*y < 1 sage: Q = P.add_condition(cut);Q # needs sage.symbolic Graphics3d Object @@ -1076,7 +1076,7 @@ cdef class IndexFaceSet(PrimitiveObject): x,y,z = var('x,y,z') P = plot3d(-sin(2*x*x+2*y*y)*exp(-x*x-y*y),(x,-2,2),(y,-2,2),color='gold') - def cut(x,y,z): + def cut(x, y, z): return x*x+y*y < 1 sphinx_plot(P.add_condition(cut)) @@ -1087,7 +1087,7 @@ cdef class IndexFaceSet(PrimitiveObject): sage: # needs sage.symbolic sage: x,y,z = var('x,y,z') sage: P = plot3d(cos(x*y),(x,-2,2),(y,-2,2),color='red',opacity=0.1) - sage: def condi(x,y,z): + sage: def condi(x, y, z): ....: return not(x*x+y*y <= 1) sage: Q = P.add_condition(condi, 40) sage: L = Q.json_repr(Q.default_render_params()) @@ -1097,7 +1097,7 @@ cdef class IndexFaceSet(PrimitiveObject): A test that this works with polygons:: sage: p = polygon3d([[2,0,0], [0,2,0], [0,0,3]]) - sage: def f(x,y,z): + sage: def f(x, y, z): ....: return bool(x*x+y*y+z*z<=5) sage: cut = p.add_condition(f,60,1.0e-12); cut.face_list() # needs sage.symbolic [[(0.556128491210302, 0.0, 2.165807263184547), diff --git a/src/sage/plot/plot3d/parametric_plot3d.py b/src/sage/plot/plot3d/parametric_plot3d.py index fa8a69a805e..6a3da2b830f 100644 --- a/src/sage/plot/plot3d/parametric_plot3d.py +++ b/src/sage/plot/plot3d/parametric_plot3d.py @@ -166,7 +166,7 @@ def parametric_plot3d(f, urange, vrange=None, plot_points='automatic', values in the interval [0,1]. :: sage: u,v = var('u,v') - sage: def cf(u,v): return sin(u+v/2)**2 + sage: def cf(u, v): return sin(u+v/2)**2 sage: P = parametric_plot3d((cos(u), sin(u)+cos(v), sin(v)), ....: (u,0,2*pi), (v,-pi,pi), color=(cf,colormaps.PiYG), plot_points=[60,60]) sage: P.show(viewer='tachyon') @@ -174,7 +174,7 @@ def parametric_plot3d(f, urange, vrange=None, plot_points='automatic', .. PLOT:: u,v = var('u,v') - def cf(u,v): return sin(u+v/2)**2 + def cf(u, v): return sin(u+v/2)**2 P = parametric_plot3d((cos(u), sin(u)+cos(v), sin(v)), (u,0,2*pi), (v,-pi,pi), color=(cf,colormaps.PiYG), plot_points=[60,60]) sphinx_plot(P) @@ -182,7 +182,7 @@ def cf(u,v): return sin(u+v/2)**2 Another example, a colored Möbius band:: sage: cm = colormaps.ocean - sage: def c(x,y): return sin(x*y)**2 + sage: def c(x, y): return sin(x*y)**2 sage: from sage.plot.plot3d.parametric_surface import MoebiusStrip sage: MoebiusStrip(5, 1, plot_points=200, color=(c,cm)) Graphics3d Object @@ -190,7 +190,7 @@ def cf(u,v): return sin(u+v/2)**2 .. PLOT:: cm = colormaps.ocean - def c(x,y): return sin(x*y)**2 + def c(x, y): return sin(x*y)**2 from sage.plot.plot3d.parametric_surface import MoebiusStrip sphinx_plot(MoebiusStrip(5, 1, plot_points=200, color=(c,cm))) @@ -198,8 +198,8 @@ def c(x,y): return sin(x*y)**2 sage: from sage.plot.plot3d.parametric_surface import ParametricSurface sage: cm = colormaps.autumn - sage: def c(x,y): return sin(x*y)**2 - sage: def g(x,y): return x, y+sin(y), x**2 + y**2 + sage: def c(x, y): return sin(x*y)**2 + sage: def g(x, y): return x, y+sin(y), x**2 + y**2 sage: ParametricSurface(g, (srange(-10,10,0.1), srange(-5,5.0,0.1)), color=(c,cm)) Graphics3d Object @@ -207,8 +207,8 @@ def c(x,y): return sin(x*y)**2 from sage.plot.plot3d.parametric_surface import ParametricSurface cm = colormaps.autumn - def c(x,y): return sin(x*y)**2 - def g(x,y): return x, y+sin(y), x**2 + y**2 + def c(x, y): return sin(x*y)**2 + def g(x, y): return x, y+sin(y), x**2 + y**2 sphinx_plot(ParametricSurface(g, (srange(-10,10,0.1), srange(-5,5.0,0.1)), color=(c,cm))) We call the space curve function but with polynomials instead of diff --git a/src/sage/plot/plot3d/parametric_surface.pyx b/src/sage/plot/plot3d/parametric_surface.pyx index dab78e762a5..efff00af83b 100644 --- a/src/sage/plot/plot3d/parametric_surface.pyx +++ b/src/sage/plot/plot3d/parametric_surface.pyx @@ -18,14 +18,14 @@ AUTHORS: EXAMPLES:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface, MoebiusStrip - sage: def f(x,y): return x+y, sin(x)*sin(y), x*y + sage: def f(x, y): return x+y, sin(x)*sin(y), x*y sage: P = ParametricSurface(f, (srange(0,10,0.1), srange(-5,5.0,0.1))) sage: show(P) .. PLOT:: from sage.plot.plot3d.parametric_surface import ParametricSurface - def f(x,y): return x+y, sin(x)*sin(y), x*y + def f(x, y): return x+y, sin(x)*sin(y), x*y sphinx_plot(ParametricSurface(f, (srange(0,10,0.1), srange(-5,5.0,0.1)))) :: @@ -50,13 +50,13 @@ By default, the surface is colored with one single color. :: .. PLOT:: from sage.plot.plot3d.parametric_surface import ParametricSurface - def f(x,y): return x+y, sin(x)*sin(y), x*y + def f(x, y): return x+y, sin(x)*sin(y), x*y sphinx_plot(ParametricSurface(f, (srange(0,10,0.1), srange(-5,5.0,0.1)), color='red')) One can instead provide a coloring function and a colormap:: - sage: def f(x,y): return x+y, x-y, x*y - sage: def c(x,y): return sin((x+y)/2)**2 + sage: def f(x, y): return x+y, x-y, x*y + sage: def c(x, y): return sin((x+y)/2)**2 sage: cm = colormaps.RdYlGn sage: P = ParametricSurface(f, (srange(-5,5,0.1), srange(-5,5.0,0.1)), color=(c,cm)) sage: P.show(viewer='tachyon') @@ -64,8 +64,8 @@ One can instead provide a coloring function and a colormap:: .. PLOT:: from sage.plot.plot3d.parametric_surface import ParametricSurface - def f(x,y): return x+y, x-y, x*y - def c(x,y): return sin((x+y)/2)**2 + def f(x, y): return x+y, x-y, x*y + def c(x, y): return sin((x+y)/2)**2 cm = colormaps.RdYlGn sphinx_plot(ParametricSurface(f, (srange(-5,5,0.1), srange(-5,5.0,0.1)), color=(c,cm))) @@ -75,7 +75,7 @@ This value is passed to the chosen colormap. Another colored example:: sage: colm = colormaps.autumn - sage: def g(x,y): return x, y, x**2 + y**2 + sage: def g(x, y): return x, y, x**2 + y**2 sage: P = ParametricSurface(g, (srange(-10,10,0.1), srange(-5,5.0,0.1)), color=(c,colm)) sage: P.show(viewer='tachyon') @@ -83,8 +83,8 @@ Another colored example:: from sage.plot.plot3d.parametric_surface import ParametricSurface colm = colormaps.autumn - def g(x,y): return x, y, x**2 + y**2 - def c(x,y): return sin((x+y)/2)**2 + def g(x, y): return x, y, x**2 + y**2 + def c(x, y): return sin((x+y)/2)**2 sphinx_plot(ParametricSurface(g, (srange(-10,10,0.1), srange(-5,5.0,0.1)), color=(c,colm))) .. NOTE:: @@ -161,7 +161,7 @@ cdef class ParametricSurface(IndexFaceSet): EXAMPLES:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface - sage: def f(x,y): return cos(x)*sin(y), sin(x)*sin(y), cos(y)+log(tan(y/2))+0.2*x + sage: def f(x, y): return cos(x)*sin(y), sin(x)*sin(y), cos(y)+log(tan(y/2))+0.2*x sage: S = ParametricSurface(f, (srange(0,12.4,0.1), srange(0.1,2,0.1))) sage: show(S) @@ -171,14 +171,14 @@ cdef class ParametricSurface(IndexFaceSet): .. PLOT:: from sage.plot.plot3d.parametric_surface import ParametricSurface - def f(x,y): return cos(x)*sin(y), sin(x)*sin(y), cos(y)+log(tan(y/2))+0.2*x + def f(x, y): return cos(x)*sin(y), sin(x)*sin(y), cos(y)+log(tan(y/2))+0.2*x sphinx_plot(ParametricSurface(f, (srange(0,12.4,0.1), srange(0.1,2,0.1)))) The Hessenberg surface: :: - sage: def f(u,v): + sage: def f(u, v): ....: a = 1 ....: from math import cos, sin, sinh, cosh ....: x = cos(a)*(cos(u)*sinh(v)-cos(3*u)*sinh(3*v)/3) + sin(a)*( @@ -194,7 +194,7 @@ cdef class ParametricSurface(IndexFaceSet): .. PLOT:: - def f(u,v): + def f(u, v): a = 1 from math import cos, sin, sinh, cosh x = cos(a)*(cos(u)*sinh(v)-cos(3*u)*sinh(3*v)/3) + sin(a)*(sin(u)*cosh(v)-sin(3*u)*cosh(3*v)/3) @@ -207,8 +207,8 @@ cdef class ParametricSurface(IndexFaceSet): A colored example using the ``color`` keyword:: - sage: def g(x,y): return x, y, - x**2 + y**2 - sage: def c(x,y): return sin((x-y/2)*y/4)**2 + sage: def g(x, y): return x, y, - x**2 + y**2 + sage: def c(x, y): return sin((x-y/2)*y/4)**2 sage: cm = colormaps.gist_rainbow sage: P = ParametricSurface(g, (srange(-10,10,0.1), ....: srange(-5,5.0,0.1)),color=(c,cm)) @@ -217,8 +217,8 @@ cdef class ParametricSurface(IndexFaceSet): .. PLOT:: from sage.plot.plot3d.parametric_surface import ParametricSurface - def g(x,y): return x, y, - x**2 + y**2 - def c(x,y): return sin((x-y/2)*y/4)**2 + def g(x, y): return x, y, - x**2 + y**2 + def c(x, y): return sin((x-y/2)*y/4)**2 cm = colormaps.gist_rainbow sphinx_plot(ParametricSurface(g, (srange(-10,10,0.1), srange(-5,5.0,0.1)),color=(c,cm))) """ @@ -231,7 +231,7 @@ cdef class ParametricSurface(IndexFaceSet): EXAMPLES:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface - sage: def f(x,y): return x+y, sin(x)*sin(y), x*y + sage: def f(x, y): return x+y, sin(x)*sin(y), x*y sage: S = ParametricSurface(f, (srange(0,12.4,0.1), srange(0.1,2,0.1))) """ if isinstance(f, list): @@ -489,7 +489,7 @@ cdef class ParametricSurface(IndexFaceSet): TESTS:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface, MoebiusStrip - sage: def f(x,y): return x+y, sin(x)*sin(y), x*y # indirect doctests + sage: def f(x, y): return x+y, sin(x)*sin(y), x*y # indirect doctests sage: P = ParametricSurface(f, (srange(0,10,0.1), srange(-5,5.0,0.1))) # indirect doctests sage: P.show() # indirect doctests sage: S = MoebiusStrip(1, .2) # indirect doctests @@ -638,7 +638,7 @@ cdef class ParametricSurface(IndexFaceSet): TESTS:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface - sage: def f(x,y): return x+y,x-y,x*y + sage: def f(x, y): return x+y,x-y,x*y sage: P = ParametricSurface(f) sage: P.get_grid(.1) Traceback (most recent call last): @@ -763,7 +763,7 @@ cdef class ParametricSurface(IndexFaceSet): TESTS:: sage: from sage.plot.plot3d.parametric_surface import ParametricSurface - sage: def f(x,y): return x+y,x-y,x*y + sage: def f(x, y): return x+y,x-y,x*y sage: P = ParametricSurface(f,(srange(0,1,0.1),srange(0,1,0.1))) sage: P.eval(0,0) Traceback (most recent call last): diff --git a/src/sage/plot/plot3d/plot3d.py b/src/sage/plot/plot3d/plot3d.py index ac3dbf15316..9f5b9a8d94d 100644 --- a/src/sage/plot/plot3d/plot3d.py +++ b/src/sage/plot/plot3d/plot3d.py @@ -19,7 +19,7 @@ :: - sage: def f(x,y): + sage: def f(x, y): ....: return math.sin(y^2 + x^2)/math.sqrt(x^2 + y^2 + 0.0001) sage: P = plot3d(f, (-3, 3),(-3, 3), adaptive=True, ....: color=rainbow(60, 'rgbtuple'), max_bend=.1, max_depth=15) @@ -27,13 +27,13 @@ .. PLOT:: - def f(x,y): return math.sin(y**2 + x**2)/math.sqrt(x**2 + y**2 + 0.0001) + def f(x, y): return math.sin(y**2 + x**2)/math.sqrt(x**2 + y**2 + 0.0001) P = plot3d(f, (-3, 3), (-3, 3), adaptive=True, color=rainbow(60, 'rgbtuple'), max_bend=.1, max_depth=15) sphinx_plot(P) :: - sage: def f(x,y): + sage: def f(x, y): ....: return math.exp(x/5)*math.sin(y) ....: sage: P = plot3d(f, (-5, 5), (-5, 5), adaptive=True, color=['red', 'yellow']) @@ -43,7 +43,7 @@ def f(x,y): return math.sin(y**2 + x**2)/math.sqrt(x**2 + y**2 + 0.0001) .. PLOT:: - def f(x,y): return math.exp(x/5)*math.sin(y) + def f(x, y): return math.exp(x/5)*math.sin(y) P = plot3d(f, (-5, 5), (-5, 5), adaptive=True, color=['red', 'yellow']) from sage.plot.plot3d.plot3d import axes S = P + axes(6, color='black') @@ -82,7 +82,7 @@ def c(x, y): return float((x + y + x*y)/15) % 1 sage: S += sphere((.45, .1, .15), size=.1, color='white') sage: S += sphere((.51, .1,.17), size=.05, color='black') sage: S += sphere((.5, 0, -.2), size=.1, color='yellow') - sage: def f(x,y): return math.exp(x/5)*math.cos(y) + sage: def f(x, y): return math.exp(x/5)*math.cos(y) sage: P = plot3d(f, (-5, 5), (-5, 5), adaptive=True, ....: color=['red','yellow'], max_depth=10) sage: cape_man = P.scale(.2) + S.translate(1, 0, 0) @@ -96,7 +96,7 @@ def c(x, y): return float((x + y + x*y)/15) % 1 S += sphere((.45, -.1, .15), size=.1, color='white') + sphere((.51,-.1,.17), size=.05, color='black') S += sphere((.45, .1, .15), size=.1, color='white') + sphere((.51, .1,.17), size=.05, color='black') S += sphere((.5, 0, -.2), size=.1, color='yellow') - def f(x,y): return math.exp(x/5)*math.cos(y) + def f(x, y): return math.exp(x/5)*math.cos(y) P = plot3d(f, (-5, 5), (-5, 5), adaptive=True, color=['red','yellow'], max_depth=10) cape_man = P.scale(.2) + S.translate(1, 0, 0) cape_man.aspect_ratio([1, 1, 1]) @@ -272,7 +272,7 @@ def to_cartesian(self, func, params=None): FullArgSpec(args=['a', 'b'], varargs=None, varkw=None, defaults=None, kwonlyargs=[], kwonlydefaults=None, annotations={}) - sage: def g(a,b): return 2*a+b + sage: def g(a, b): return 2*a+b sage: t1,t2,t3=T.to_cartesian(g) sage: sage_getargspec(t1) FullArgSpec(args=['a', 'b'], varargs=None, varkw=None, defaults=None, @@ -389,12 +389,12 @@ def _find_arguments_for_callable(func): sage: from sage.plot.plot3d.plot3d import _find_arguments_for_callable sage: _find_arguments_for_callable(lambda x,y: x+y) ['x', 'y'] - sage: def f(a,b,c): return a+b+c + sage: def f(a, b, c): return a+b+c sage: _find_arguments_for_callable(f) ['a', 'b', 'c'] sage: _find_arguments_for_callable(lambda x,y,z=2: x+y+z) ['x', 'y'] - sage: def f(a,b,c,d=2,e=1): return a+b+c+d+e + sage: def f(a, b, c, d=2, e=1): return a+b+c+d+e sage: _find_arguments_for_callable(f) ['a', 'b', 'c'] sage: g(w,r,t)=w+r+t diff --git a/src/sage/plot/plot3d/revolution_plot3d.py b/src/sage/plot/plot3d/revolution_plot3d.py index 6c16263d971..721573516a5 100644 --- a/src/sage/plot/plot3d/revolution_plot3d.py +++ b/src/sage/plot/plot3d/revolution_plot3d.py @@ -27,7 +27,7 @@ @rename_keyword(alpha='opacity') -def revolution_plot3d(curve,trange,phirange=None,parallel_axis='z',axis=(0,0),print_vector=False,show_curve=False,**kwds): +def revolution_plot3d(curve, trange, phirange=None, parallel_axis='z', axis=(0, 0), print_vector=False, show_curve=False, **kwds): r""" Return a plot of a revolved curve. @@ -196,7 +196,7 @@ def revolution_plot3d(curve,trange,phirange=None,parallel_axis='z',axis=(0,0),pr function must take values in the interval `[0,1]`. :: sage: u, phi = var('u,phi') - sage: def cf(u,phi): return sin(phi+u) ^ 2 + sage: def cf(u, phi): return sin(phi+u) ^ 2 sage: curve = (1+u^2/4, 0, u) sage: revolution_plot3d(curve, (u,-2,2), (0,2*pi), parallel_axis='z', ....: color=(cf, colormaps.PiYG)).show(aspect_ratio=(1,1,1)) diff --git a/src/sage/plot/plot3d/tachyon.py b/src/sage/plot/plot3d/tachyon.py index 83315e33368..adb1d80b7be 100644 --- a/src/sage/plot/plot3d/tachyon.py +++ b/src/sage/plot/plot3d/tachyon.py @@ -559,7 +559,7 @@ def show(self, **kwds): sage: h = Tachyon(xres=512, yres=512, camera_position=(4,-4,3), ....: viewdir=(-4,4,-3), raydepth=4) sage: h.light((4.4,-4.4,4.4), 0.2, (1,1,1)) - sage: def f(x,y): return float(sin(x*y)) + sage: def f(x, y): return float(sin(x*y)) sage: h.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1, ....: opacity=1.0, color=(1.0,0,0)) sage: h.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3, # needs sage.symbolic @@ -577,7 +577,7 @@ def show(self, **kwds): sage: s = Tachyon(xres=512, yres=512, camera_position=(4,-4,3), ....: viewdir=(-4,4,-3), raydepth=4) sage: s.light((4.4,-4.4,4.4), 0.2, (1,1,1)) - sage: def f(x,y): return float(sin(x*y)) + sage: def f(x, y): return float(sin(x*y)) sage: s.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1, ....: opacity=1.0, color=(1.0,0,0)) sage: s.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3, # needs sage.symbolic @@ -600,7 +600,7 @@ def show(self, **kwds): sage: d = Tachyon(xres=512, yres=512, camera_position=(4,-4,3), ....: viewdir=(-4,4,-3), raydepth=4) sage: d.light((4.4,-4.4,4.4), 0.2, (1,1,1)) - sage: def f(x,y): return float(sin(x*y)) + sage: def f(x, y): return float(sin(x*y)) sage: d.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1, ....: opacity=1.0, color=(1.0,0,0)) sage: d.plot(f,(-4,4),(-4,4),"t0",max_depth=5,initial_depth=3, # needs sage.symbolic @@ -1004,7 +1004,7 @@ def plot(self, f, xmin_xmax, ymin_ymax, texture, grad_f=None, sage: t = Tachyon(xres=512, yres=512, camera_position=(4,-4,3), ....: viewdir=(-4,4,-3), raydepth=4) sage: t.light((4.4,-4.4,4.4), 0.2, (1,1,1)) - sage: def f(x,y): return float(sin(x*y)) + sage: def f(x, y): return float(sin(x*y)) sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1, ....: opacity=1.0, color=(1.0,0,0)) sage: t.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3, # needs sage.symbolic @@ -1020,8 +1020,8 @@ def plot(self, f, xmin_xmax, ymin_ymax, texture, grad_f=None, sage: t = Tachyon(xres=512, yres=512, camera_position=(4,-4,3), ....: viewdir=(-4,4,-3), raydepth=4) sage: t.light((4.4,-4.4,4.4), 0.2, (1,1,1)) - sage: def f(x,y): return float(sin(x*y)) - sage: def g(x,y): return (float(y*cos(x*y)), float(x*cos(x*y)), 1) + sage: def f(x, y): return float(sin(x*y)) + sage: def g(x, y): return (float(y*cos(x*y)), float(x*cos(x*y)), 1) sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1, ....: opacity=1.0, color=(1.0,0,0)) sage: t.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3, # needs sage.symbolic diff --git a/src/sage/plot/plot3d/tri_plot.py b/src/sage/plot/plot3d/tri_plot.py index 4453d8c574c..a2e843778eb 100644 --- a/src/sage/plot/plot3d/tri_plot.py +++ b/src/sage/plot/plot3d/tri_plot.py @@ -30,7 +30,7 @@ class Triangle: """ A graphical triangle class. """ - def __init__(self,a,b,c,color=0): + def __init__(self, a, b, c, color=0): """ a, b, c : triples (x,y,z) representing corners on a triangle in 3-space. @@ -101,7 +101,7 @@ class SmoothTriangle(Triangle): """ A class for smoothed triangles. """ - def __init__(self,a,b,c,da,db,dc,color=0): + def __init__(self, a, b, c, da, db, dc, color=0): """ a, b, c : triples (x,y,z) representing corners on a triangle in 3-space da, db, dc : triples (dx,dy,dz) representing the normal vector at each point a,b,c @@ -265,10 +265,10 @@ def __init__(self, triangle_factory, f, min_x__max_x, min_y__max_y, g=None, raise ValueError('plot rectangle is really a line; make sure min_x != max_x and min_y != max_y') self._num_colors = num_colors if g is None: - def fcn(x,y): + def fcn(x, y): return [self._f(x,y)] else: - def fcn(x,y): + def fcn(x, y): return [self._f(x,y), self._g(x,y)] self._fcn = fcn @@ -541,7 +541,7 @@ def extrema(self, list): self._max = max(list+[self._max]) -def crossunit(u,v): +def crossunit(u, v): """ This function computes triangle normal unit vectors by taking the cross-products of the midpoint-to-corner vectors. It always goes diff --git a/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py b/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py index 0e447f982dd..3922767e870 100644 --- a/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py +++ b/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py @@ -25,7 +25,7 @@ # TO DO -- Add second argument -# def __call__(self,v,w=None): +# def __call__(self, v, w=None): # if w is None: # return half(v * self._matrix_() * v) # else: diff --git a/src/sage/rings/bernmm.pyx b/src/sage/rings/bernmm.pyx index 492181f1f22..f3af4355bd0 100644 --- a/src/sage/rings/bernmm.pyx +++ b/src/sage/rings/bernmm.pyx @@ -39,7 +39,7 @@ cdef extern from "bernmm/bern_modp.h": from sage.rings.rational cimport Rational -def bernmm_bern_rat(long k, int num_threads = 1): +def bernmm_bern_rat(long k, int num_threads=1): r""" Compute `k`-th Bernoulli number using a multimodular algorithm. (Wrapper for bernmm library.) diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx index d6e5a7d05b1..98477e0dd72 100644 --- a/src/sage/rings/complex_double.pyx +++ b/src/sage/rings/complex_double.pyx @@ -2601,7 +2601,7 @@ cdef class ComplexToCDF(Morphism): cdef ComplexDoubleField_class _CDF _CDF = ComplexDoubleField_class() CDF = _CDF # external interface -cdef ComplexDoubleElement I = ComplexDoubleElement(0,1) +cdef ComplexDoubleElement I = ComplexDoubleElement(0, 1) def ComplexDoubleField(): diff --git a/src/sage/rings/complex_interval.pyx b/src/sage/rings/complex_interval.pyx index e8e528e1453..60bc5b5abff 100644 --- a/src/sage/rings/complex_interval.pyx +++ b/src/sage/rings/complex_interval.pyx @@ -321,7 +321,7 @@ cdef class ComplexIntervalFieldElement(FieldElement): g = polygon2d([(x0, y0), (x1, y0), (x1, y1), (x0, y1), (x0, y0)], thickness=pointsize/4, **kwds) # Nearly empty polygons don't show up. - g += self.center().plot(pointsize= pointsize, **kwds) + g += self.center().plot(pointsize=pointsize, **kwds) return g def _latex_(self): diff --git a/src/sage/rings/finite_rings/element_base.pyx b/src/sage/rings/finite_rings/element_base.pyx index aa0a66b4748..a9c54232163 100755 --- a/src/sage/rings/finite_rings/element_base.pyx +++ b/src/sage/rings/finite_rings/element_base.pyx @@ -202,7 +202,7 @@ cdef class FinitePolyExtElement(FiniteRingElement): f = Cx([base_map(c) for c in f]) return codomain(f(im_gens[0])) - def minpoly(self,var='x',algorithm='pari'): + def minpoly(self, var='x', algorithm='pari'): """ Return the minimal polynomial of this element (over the corresponding prime subfield). @@ -822,7 +822,7 @@ cdef class FinitePolyExtElement(FiniteRingElement): """ return self.square_root(extend=extend, all=all) - def nth_root(self, n, extend = False, all = False, algorithm=None, cunningham=False): + def nth_root(self, n, extend=False, all=False, algorithm=None, cunningham=False): r""" Return an `n`-th root of ``self``. @@ -941,7 +941,7 @@ cdef class FinitePolyExtElement(FiniteRingElement): n = Integer(n) return self._nth_root_common(n, all, algorithm, cunningham) - def pth_power(self, int k = 1): + def pth_power(self, int k=1): """ Return the `(p^k)`-th power of self, where `p` is the characteristic of the field. @@ -975,7 +975,7 @@ cdef class FinitePolyExtElement(FiniteRingElement): frobenius = pth_power - def pth_root(self, int k = 1): + def pth_root(self, int k=1): """ Return the `(p^k)`-th root of self, where `p` is the characteristic of the field. diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx index 085ce14ce87..b5234146c03 100644 --- a/src/sage/rings/finite_rings/finite_field_base.pyx +++ b/src/sage/rings/finite_rings/finite_field_base.pyx @@ -846,7 +846,7 @@ cdef class FiniteField(Field): """ return 1 - def is_field(self, proof = True): + def is_field(self, proof=True): """ Return whether or not the finite field is a field, i.e., always returns ``True``. diff --git a/src/sage/rings/finite_rings/integer_mod.pyx b/src/sage/rings/finite_rings/integer_mod.pyx index 0b220e81a1e..cf2d43ca59a 100644 --- a/src/sage/rings/finite_rings/integer_mod.pyx +++ b/src/sage/rings/finite_rings/integer_mod.pyx @@ -1350,7 +1350,7 @@ cdef class IntegerMod_abstract(FiniteRingElement): square_root = sqrt - def nth_root(self, n, extend = False, all = False, algorithm = None, cunningham = False): + def nth_root(self, n, extend=False, all=False, algorithm=None, cunningham=False): r""" Return an `n`-th root of ``self``. diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx index 3146f7fd764..be83c5165f6 100644 --- a/src/sage/rings/finite_rings/residue_field.pyx +++ b/src/sage/rings/finite_rings/residue_field.pyx @@ -307,7 +307,7 @@ class ResidueFieldFactory(UniqueFactory): sage: K.residue_field(K.ideal(3)) # needs sage.rings.number_field Residue field of Fractional ideal (3) """ - def create_key_and_extra_args(self, p, names = None, check=True, impl=None, **kwds): + def create_key_and_extra_args(self, p, names=None, check=True, impl=None, **kwds): """ Return a tuple containing the key (uniquely defining data) and any extra arguments. diff --git a/src/sage/rings/fraction_field_element.pyx b/src/sage/rings/fraction_field_element.pyx index 3d14ab66134..bd8718da968 100644 --- a/src/sage/rings/fraction_field_element.pyx +++ b/src/sage/rings/fraction_field_element.pyx @@ -263,7 +263,7 @@ cdef class FractionFieldElement(FieldElement): """ return self._denominator - def is_square(self,root=False): + def is_square(self, root=False): """ Return whether or not ``self`` is a perfect square. diff --git a/src/sage/rings/function_field/constructor.py b/src/sage/rings/function_field/constructor.py index 098da7b59da..fa5a31cb683 100644 --- a/src/sage/rings/function_field/constructor.py +++ b/src/sage/rings/function_field/constructor.py @@ -89,7 +89,7 @@ def create_key(self, F, names): names = (names,) return (F, names) - def create_object(self, version, key,**extra_args): + def create_object(self, version, key, **extra_args): """ Create the object from the key and extra arguments. This is only called if the object was not found in the cache. @@ -143,7 +143,7 @@ class FunctionFieldExtensionFactory(UniqueFactory): sage: L is M # needs sage.rings.function_field True """ - def create_key(self,polynomial,names): + def create_key(self, polynomial, names): """ Given the arguments and keywords, create a key that uniquely determines this object. @@ -175,7 +175,7 @@ def create_key(self,polynomial,names): names = (names,) return (polynomial,names,polynomial.base_ring()) - def create_object(self,version,key,**extra_args): + def create_object(self, version, key, **extra_args): """ Create the object from the key and extra arguments. This is only called if the object was not found in the cache. diff --git a/src/sage/rings/function_field/divisor.py b/src/sage/rings/function_field/divisor.py index 8c72b4cdb98..94f3ff2bce3 100644 --- a/src/sage/rings/function_field/divisor.py +++ b/src/sage/rings/function_field/divisor.py @@ -922,7 +922,7 @@ def pivot(v): if e != 0: return (i,e.numerator().degree() - e.denominator().degree()) - def greater(v,w): # v and w are not equal + def greater(v, w): # v and w are not equal return v[0] < w[0] or v[0] == w[0] and v[1] > w[1] # collate rows by their pivot position diff --git a/src/sage/rings/function_field/order_polymod.py b/src/sage/rings/function_field/order_polymod.py index 16ff2d8f2ae..ed2223fcdab 100644 --- a/src/sage/rings/function_field/order_polymod.py +++ b/src/sage/rings/function_field/order_polymod.py @@ -1372,7 +1372,7 @@ def mul(Ib, Jb): h = matrix(m).echelon_form() return cut_last_zero_rows(h) - def add(Ib,Jb): + def add(Ib, Jb): m = block_matrix([[Ib], [Jb]]) h = m.echelon_form() return cut_last_zero_rows(h) diff --git a/src/sage/rings/integer.pxd b/src/sage/rings/integer.pxd index 1165895729e..c113d562835 100644 --- a/src/sage/rings/integer.pxd +++ b/src/sage/rings/integer.pxd @@ -23,8 +23,8 @@ cdef class Integer(EuclideanDomainElement): cdef _or(Integer self, Integer other) cdef _xor(Integer self, Integer other) - cpdef size_t _exact_log_log2_iter(self,Integer m) noexcept - cpdef size_t _exact_log_mpfi_log(self,m) noexcept + cpdef size_t _exact_log_log2_iter(self, Integer m) noexcept + cpdef size_t _exact_log_mpfi_log(self, m) noexcept cpdef RingElement _valuation(Integer self, Integer p) cdef object _val_unit(Integer self, Integer p) cdef Integer _divide_knowing_divisible_by(Integer self, Integer right) diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx index 9616e7946bc..206c4c458d8 100644 --- a/src/sage/rings/integer.pyx +++ b/src/sage/rings/integer.pyx @@ -215,7 +215,7 @@ cdef set_from_Integer(Integer self, Integer other): mpz_set(self.value, other.value) -cdef _digits_naive(mpz_t v,l,int offset,Integer base,digits): +cdef _digits_naive(mpz_t v, l, int offset, Integer base, digits): """ This method fills in digit entries in the list, l, using the most basic digit algorithm -- repeat division by base. @@ -262,7 +262,7 @@ cdef _digits_naive(mpz_t v,l,int offset,Integer base,digits): mpz_clear(mpz_value) -cdef _digits_internal(mpz_t v,l,int offset,int power_index,power_list,digits): +cdef _digits_internal(mpz_t v, l, int offset, int power_index, power_list, digits): """ INPUT: @@ -1131,7 +1131,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): sage: "{0:#x}; {0:#b}; {0:+05d}".format(ZZ(17)) '0x11; 0b10001; +0017' """ - return int(self).__format__(*args,**kwargs) + return int(self).__format__(*args, **kwargs) def ordinal_str(self): """ @@ -2439,7 +2439,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): raise ValueError("%s is not a %s power" % (self, integer_ring.ZZ(n).ordinal_str())) - cpdef size_t _exact_log_log2_iter(self,Integer m) noexcept: + cpdef size_t _exact_log_log2_iter(self, Integer m) noexcept: r""" This is only for internal use only. You should expect it to crash and burn for negative or other malformed input. In particular, if @@ -2517,7 +2517,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): sig_off() return l_min - cpdef size_t _exact_log_mpfi_log(self,m) noexcept: + cpdef size_t _exact_log_mpfi_log(self, m) noexcept: """ This is only for internal use only. You should expect it to crash and burn for negative or other malformed input. @@ -5993,7 +5993,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): if mpz_cmp_ui(self.value, 2) < 0: return smallInteger(2) - cdef mp_bitcnt_t bit_index = mpz_sizeinbase(self.value,2) + cdef mp_bitcnt_t bit_index = mpz_sizeinbase(self.value, 2) cdef Integer n = PY_NEW(Integer) mpz_add_ui(n.value, self.value, 1 if mpz_even_p(self.value) else 2) @@ -6066,7 +6066,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): cdef Integer n = PY_NEW(Integer) mpz_sub_ui(n.value, self.value, 1) - cdef mp_bitcnt_t bit_index = mpz_sizeinbase(n.value,2)-1 + cdef mp_bitcnt_t bit_index = mpz_sizeinbase(n.value, 2)-1 if mpz_even_p(n.value): mpz_sub_ui(n.value, n.value, 1) diff --git a/src/sage/rings/integer_ring.pyx b/src/sage/rings/integer_ring.pyx index 2b2ec33294c..346a67481e1 100644 --- a/src/sage/rings/integer_ring.pyx +++ b/src/sage/rings/integer_ring.pyx @@ -876,7 +876,7 @@ cdef class IntegerRing_class(CommutativeRing): return True return super()._repr_option(key) - def is_field(self, proof = True): + def is_field(self, proof=True): """ Return ``False`` since the integers are not a field. @@ -1158,7 +1158,7 @@ cdef class IntegerRing_class(CommutativeRing): """ return True - def completion(self, p, prec, extras = {}): + def completion(self, p, prec, extras={}): r""" Return the metric completion of the integers at the prime `p`. diff --git a/src/sage/rings/invariants/invariant_theory.py b/src/sage/rings/invariants/invariant_theory.py index fb953f98813..836dc8dd249 100644 --- a/src/sage/rings/invariants/invariant_theory.py +++ b/src/sage/rings/invariants/invariant_theory.py @@ -3498,7 +3498,7 @@ def syzygy(self, Delta, Theta, Theta_prime, Delta_prime, S, S_prime, F, J): sage: R. = QQ[] sage: monomials = [x^2, x*y, y^2, x*z, y*z, z^2] - sage: def q_rnd(): return sum(randint(-1000,1000)*m for m in monomials) + sage: def q_rnd(): return sum(randint(-1000, 1000)*m for m in monomials) sage: biquadratic = invariant_theory.ternary_biquadratic(q_rnd(), q_rnd(), [x,y,z]) sage: Delta = biquadratic.Delta_invariant() sage: Theta = biquadratic.Theta_invariant() @@ -3880,7 +3880,7 @@ def syzygy(self, Delta, Theta, Phi, Theta_prime, Delta_prime, U, V, T, T_prime, sage: R. = QQ[] sage: monomials = [x^2, x*y, y^2, x*z, y*z, z^2, x*w, y*w, z*w, w^2] - sage: def q_rnd(): return sum(randint(-1000,1000)*m for m in monomials) + sage: def q_rnd(): return sum(randint(-1000, 1000)*m for m in monomials) sage: biquadratic = invariant_theory.quaternary_biquadratic(q_rnd(), q_rnd()) sage: Delta = biquadratic.Delta_invariant() sage: Theta = biquadratic.Theta_invariant() diff --git a/src/sage/rings/multi_power_series_ring.py b/src/sage/rings/multi_power_series_ring.py index 35c4d4beb32..3a30b89b9e9 100644 --- a/src/sage/rings/multi_power_series_ring.py +++ b/src/sage/rings/multi_power_series_ring.py @@ -1047,7 +1047,7 @@ def prec_ideal(self): """ return self._poly_ring().ideal(self._poly_ring().gens()) - def bigoh(self,prec): + def bigoh(self, prec): """ Return big oh with precision ``prec``. The function ``O`` does the same thing. @@ -1062,7 +1062,7 @@ def bigoh(self,prec): """ return self.zero().O(prec) - def O(self,prec): + def O(self, prec): """ Return big oh with precision ``prec``. This function is an alias for ``bigoh``. @@ -1077,7 +1077,7 @@ def O(self,prec): """ return self.bigoh(prec) - def _send_to_bg(self,f): + def _send_to_bg(self, f): """ Send an element of the foreground polynomial ring to the background power series ring. @@ -1100,7 +1100,7 @@ def _send_to_bg(self,f): raise TypeError("Cannot coerce input to polynomial ring.") return self._bg_ps_ring(f.homogeneous_components()) - def _send_to_fg(self,f): + def _send_to_fg(self, f): """ Send an element of the background univariate power series ring to the foreground multivariate polynomial ring. diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py index 8e1789d5672..9c27ba678bb 100644 --- a/src/sage/rings/multi_power_series_ring_element.py +++ b/src/sage/rings/multi_power_series_ring_element.py @@ -671,7 +671,7 @@ def _im_gens_(self, codomain, im_gens, base_map=None): else: return codomain(self._subs_formal(*im_gens, base_map=base_map)) - def __getitem__(self,n): + def __getitem__(self, n): """ Return summand of total degree ``n``. @@ -2130,7 +2130,7 @@ class MO: sage: w^2 1 + 2*a + O(a, b, c)^2 """ - def __init__(self,x): + def __init__(self, x): """ Initialize ``self``. diff --git a/src/sage/rings/number_field/selmer_group.py b/src/sage/rings/number_field/selmer_group.py index 5204cfc80b6..283db17c84e 100644 --- a/src/sage/rings/number_field/selmer_group.py +++ b/src/sage/rings/number_field/selmer_group.py @@ -133,7 +133,7 @@ def _coords_in_C_p(I, C, p): raise ValueError("The {} power of {} is not principal".format(p.ordinal_str(),I)) -def _coords_in_C_mod_p(I,C,p): +def _coords_in_C_mod_p(I, C, p): r""" Return coordinates of the ideal ``I`` with respect to a basis of the `p`-cotorsion of the ideal class group ``C``. diff --git a/src/sage/rings/padics/CA_template.pxi b/src/sage/rings/padics/CA_template.pxi index 0e6a10b67d9..9a274d6d81e 100644 --- a/src/sage/rings/padics/CA_template.pxi +++ b/src/sage/rings/padics/CA_template.pxi @@ -684,7 +684,7 @@ cdef class CAElement(pAdicTemplateElement): """ return ciszero(self.value, self.prime_pow) - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): r""" Determine whether this element is zero modulo `\pi^{\mbox{absprec}}`. diff --git a/src/sage/rings/padics/CR_template.pxi b/src/sage/rings/padics/CR_template.pxi index 853a3c3df79..f6f3bc8a632 100644 --- a/src/sage/rings/padics/CR_template.pxi +++ b/src/sage/rings/padics/CR_template.pxi @@ -992,7 +992,7 @@ cdef class CRElement(pAdicTemplateElement): """ return self.relprec == 0 and not exactzero(self.ordp) - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): r""" Determine whether this element is zero modulo `\pi^{\mbox{absprec}}`. diff --git a/src/sage/rings/padics/FM_template.pxi b/src/sage/rings/padics/FM_template.pxi index c05930fb0af..07a091a9313 100644 --- a/src/sage/rings/padics/FM_template.pxi +++ b/src/sage/rings/padics/FM_template.pxi @@ -533,7 +533,7 @@ cdef class FMElement(pAdicTemplateElement): """ return ciszero(self.value, self.prime_pow) - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): r""" Return whether ``self`` is zero modulo `\pi^{\mbox{absprec}}`. diff --git a/src/sage/rings/padics/FP_template.pxi b/src/sage/rings/padics/FP_template.pxi index 654c3d6b6a3..69454eeb842 100644 --- a/src/sage/rings/padics/FP_template.pxi +++ b/src/sage/rings/padics/FP_template.pxi @@ -862,7 +862,7 @@ cdef class FPElement(pAdicTemplateElement): """ return very_pos_val(self.ordp) - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): r""" Return whether ``self`` is zero modulo `\pi^{\mbox{absprec}}`. diff --git a/src/sage/rings/padics/local_generic_element.pyx b/src/sage/rings/padics/local_generic_element.pyx index 84143902e86..e3f1db454ff 100644 --- a/src/sage/rings/padics/local_generic_element.pyx +++ b/src/sage/rings/padics/local_generic_element.pyx @@ -194,7 +194,7 @@ cdef class LocalGenericElement(CommutativeRingElement): """ raise TypeError("this local element is not iterable") - def slice(self, i, j, k = 1, lift_mode='simple'): + def slice(self, i, j, k=1, lift_mode='simple'): r""" Return the sum of the `pi^{i + l \cdot k}` terms of the series expansion of this element, where pi is the uniformizer, @@ -815,7 +815,7 @@ cdef class LocalGenericElement(CommutativeRingElement): """ return self.square_root(extend, all) - #def square_root(self, extend = True, all = False): + #def square_root(self, extend=True, all=False): # raise NotImplementedError #def unit_part(self): diff --git a/src/sage/rings/padics/morphism.pyx b/src/sage/rings/padics/morphism.pyx index d4684f9649d..6f0d501bc86 100644 --- a/src/sage/rings/padics/morphism.pyx +++ b/src/sage/rings/padics/morphism.pyx @@ -28,7 +28,7 @@ cdef class FrobeniusEndomorphism_padics(RingHomomorphism): """ A class implementing Frobenius endomorphisms on `p`-adic fields. """ - def __init__ (self,domain,n=1): + def __init__ (self, domain, n=1): """ INPUT: @@ -218,7 +218,7 @@ cdef class FrobeniusEndomorphism_padics(RingHomomorphism): """ return self._power - def __pow__(self,n,modulus): + def __pow__(self, n, modulus): """ Return the `n`-th iterate of this endomorphism. diff --git a/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx index 7efcfc5a047..0e826c40db8 100644 --- a/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx +++ b/src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx @@ -196,7 +196,7 @@ from sage.rings.infinity import infinity cdef long maxordp = (1L << (sizeof(long) * 8 - 2)) -1 cdef class pAdicZZpXCAElement(pAdicZZpXElement): - def __init__(self, parent, x, absprec = infinity, relprec = infinity, empty = False): + def __init__(self, parent, x, absprec=infinity, relprec=infinity, empty=False): """ Create an element of a capped absolute precision, unramified or Eisenstein extension of Zp or Qp. @@ -1769,7 +1769,7 @@ cdef class pAdicZZpXCAElement(pAdicZZpXElement): """ return ZZ_pX_ConstTerm(self.value) - def is_equal_to(self, right, absprec = None): + def is_equal_to(self, right, absprec=None): """ Return whether ``self`` is equal to ``right`` modulo ``self.uniformizer()^absprec``. @@ -1995,7 +1995,7 @@ cdef class pAdicZZpXCAElement(pAdicZZpXElement): ZZ_pX_MulMod_pre(cur.x, cur.x, x, m[0]) return matrix(R, n, n, L) -# def matrix(self, base = None): +# def matrix(self, base=None): # """ # If base is None, return the matrix of right multiplication by # the element on the power basis `1, x, x^2, \ldots, x^{d-1}` @@ -2034,7 +2034,7 @@ cdef class pAdicZZpXCAElement(pAdicZZpXElement): # """ # raise NotImplementedError - def teichmuller_expansion(self, n = None): + def teichmuller_expansion(self, n=None): r""" Return a list [`a_0`, `a_1`,..., `a_n`] such that: @@ -2164,7 +2164,7 @@ cdef class pAdicZZpXCAElement(pAdicZZpXElement): else: self.prime_pow.teichmuller_set_c(&self.value, &self.value, self.absprec) -# def padded_list(self, n, lift_mode = 'simple'): +# def padded_list(self, n, lift_mode='simple'): # """ # Returns a list of coefficients of pi starting with `pi^0` up to # `pi^n` exclusive (padded with zeros if needed) diff --git a/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx index 82d04980363..5db54020fb2 100644 --- a/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx +++ b/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx @@ -223,7 +223,7 @@ cdef inline int check_ordp(long a) except -1: cdef class pAdicZZpXCRElement(pAdicZZpXElement): - def __init__(self, parent, x, absprec = infinity, relprec = infinity, empty = False): + def __init__(self, parent, x, absprec=infinity, relprec=infinity, empty=False): r""" Create an element of a capped relative precision, unramified or Eisenstein extension of `\ZZ_p` or `\QQ_p`. @@ -2327,7 +2327,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): ZZ_to_mpz(ans.value, &tmp_z) return ans - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): r""" Return whether the valuation of this element is at least ``absprec``. If ``absprec`` is ``None``, checks if this element @@ -2585,7 +2585,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): """ return ZZ_pX_ConstTerm((self).unit) - def is_equal_to(self, right, absprec = None): + def is_equal_to(self, right, absprec=None): """ Return whether this element is equal to ``right`` modulo ``self.uniformizer()^absprec``. @@ -2703,7 +2703,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): ZZ_pX_conv_modulus(ans.unit, self.unit, self.prime_pow.get_context_capdiv(rprec).x) return ans - def expansion(self, n = None, lift_mode = 'simple'): + def expansion(self, n=None, lift_mode='simple'): """ Return a list giving a series representation of ``self``. @@ -2877,7 +2877,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): ZZ_pX_MulMod_pre(cur.x, cur.x, x, m[0]) return matrix(R, n, n, L) -# def matrix(self, base = None): +# def matrix(self, base=None): # """ # If base is None, return the matrix of right multiplication by # the element on the power basis `1, x, x^2, \ldots, x^{d-1}` @@ -2915,7 +2915,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): # """ # raise NotImplementedError - def teichmuller_expansion(self, n = None): + def teichmuller_expansion(self, n=None): r""" Return a list [`a_0`, `a_1`,..., `a_n`] such that: @@ -3060,7 +3060,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): else: self.prime_pow.teichmuller_set_c(&self.unit, &self.unit, self.relprec) -# def padded_list(self, n, lift_mode = 'simple'): +# def padded_list(self, n, lift_mode='simple'): # """ # Return a list of coefficients of pi starting with `pi^0` up to # `pi^n` exclusive (padded with zeros if needed) @@ -3130,7 +3130,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement): mpz_set_ui(ans.value, self.relprec) return ans -# def residue(self, n = 1): +# def residue(self, n=1): # """ # Reduces this element modulo pi^n. # """ diff --git a/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx index a3dcd42b3d6..de3df469423 100644 --- a/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx +++ b/src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx @@ -879,7 +879,7 @@ cdef class pAdicZZpXFMElement(pAdicZZpXElement): ans.value = self.value # does this actually copy correctly return ans - def is_zero(self, absprec = None): + def is_zero(self, absprec=None): """ Return whether the valuation of ``self`` is at least ``absprec``; if ``absprec`` is ``None``, return whether @@ -1038,7 +1038,7 @@ cdef class pAdicZZpXFMElement(pAdicZZpXElement): ZZ_pX_MulMod_pre(cur.x, cur.x, x, m[0]) return matrix(R, n, n, L) -# def matrix(self, base = None): +# def matrix(self, base=None): # """ # If base is None, return the matrix of right multiplication by # the element on the power basis `1, x, x^2, \ldots, x^{d-1}` @@ -1380,7 +1380,7 @@ cdef class pAdicZZpXFMElement(pAdicZZpXElement): return zero return [zero] * ordp + ulist - def teichmuller_expansion(self, n = None): + def teichmuller_expansion(self, n=None): r""" Return a list `[a_0, a_1, \ldots, a_n]` such that. @@ -1532,7 +1532,7 @@ cdef class pAdicZZpXFMElement(pAdicZZpXElement): # """ # raise NotImplementedError -# def padded_list(self, n, lift_mode = 'simple'): +# def padded_list(self, n, lift_mode='simple'): # """ # Returns a list of coefficients of pi starting with `pi^0` up to # `pi^n` exclusive (padded with zeros if needed) diff --git a/src/sage/rings/padics/padic_ZZ_pX_element.pyx b/src/sage/rings/padics/padic_ZZ_pX_element.pyx index b2d6267503e..9e907b25899 100644 --- a/src/sage/rings/padics/padic_ZZ_pX_element.pyx +++ b/src/sage/rings/padics/padic_ZZ_pX_element.pyx @@ -291,7 +291,7 @@ cdef class pAdicZZpXElement(pAdicExtElement): cdef ZZ_pX_c shifter = (self._ntl_rep()).x #cdef ntl_ZZ_pContext_class cup = self.prime_pow.get_context(self.prime_pow.prec_cap + (self.prime_pow).low_length) - #cdef ntl_ZZ_pX printer = ntl_ZZ_pX([],cup) + #cdef ntl_ZZ_pX printer = ntl_ZZ_pX([], cup) #printer.x = ((self.prime_pow).low_shifter[0]).val() #print(printer) @@ -429,7 +429,7 @@ cdef class pAdicZZpXElement(pAdicExtElement): norm_of_uniformizer = (-1)**self.parent().degree() * self.parent().defining_polynomial()[0] return self.parent().ground_ring()(self.unit_part().matrix_mod_pn().det()) * norm_of_uniformizer**self.valuation() - def trace(self, base = None): + def trace(self, base=None): r""" Return the absolute or relative trace of this element. diff --git a/src/sage/rings/padics/padic_extension_generic.py b/src/sage/rings/padics/padic_extension_generic.py index e3e97906be2..d3ca159a5fc 100644 --- a/src/sage/rings/padics/padic_extension_generic.py +++ b/src/sage/rings/padics/padic_extension_generic.py @@ -475,7 +475,7 @@ def polynomial_ring(self): """ return self._given_poly.parent() - #def teichmuller(self, x, prec = None): + #def teichmuller(self, x, prec=None): # if prec is None: # prec = self.precision_cap() # x = self(x, prec) @@ -652,7 +652,7 @@ def free_module(self, base=None, basis=None, map=True): #def principal_unit_group(self): # raise NotImplementedError - #def zeta(self, n = None): + #def zeta(self, n=None): # raise NotImplementedError #def zeta_order(self): diff --git a/src/sage/rings/padics/padic_generic.py b/src/sage/rings/padics/padic_generic.py index 3f041a5e146..39d1fb43006 100644 --- a/src/sage/rings/padics/padic_generic.py +++ b/src/sage/rings/padics/padic_generic.py @@ -198,7 +198,7 @@ def __richcmp__(self, other, op): # def ngens(self): # return 1 - # def gen(self, n = 0): + # def gen(self, n=0): # if n != 0: # raise IndexError, "only one generator" # return self(self.prime()) diff --git a/src/sage/rings/padics/padic_generic_element.pyx b/src/sage/rings/padics/padic_generic_element.pyx index ec3b1848416..073a3d98f5f 100644 --- a/src/sage/rings/padics/padic_generic_element.pyx +++ b/src/sage/rings/padics/padic_generic_element.pyx @@ -1877,7 +1877,7 @@ cdef class pAdicGenericElement(LocalGenericElement): #def log_artin_hasse(self): # raise NotImplementedError - def multiplicative_order(self, prec = None): + def multiplicative_order(self, prec=None): r""" Return the multiplicative order of ``self``, where ``self`` is considered to be one if it is one modulo `p^{\mbox{prec}}`. @@ -1975,7 +1975,7 @@ cdef class pAdicGenericElement(LocalGenericElement): return order return infinity - def valuation(self, p = None): + def valuation(self, p=None): r""" Return the valuation of this element. @@ -2099,7 +2099,7 @@ cdef class pAdicGenericElement(LocalGenericElement): """ raise NotImplementedError - def ordp(self, p = None): + def ordp(self, p=None): r""" Return the valuation of ``self``, normalized so that the valuation of `p` is 1. @@ -4056,7 +4056,7 @@ cdef class pAdicGenericElement(LocalGenericElement): """ raise NotImplementedError - def _polylog_res_1(self, n, p_branch = 0): + def _polylog_res_1(self, n, p_branch=0): r""" Return `Li_n(`self`)`, the `n`-th `p`-adic polylogarithm of ``self``, assuming that ``self`` is congruent to `1 \pmod p`. diff --git a/src/sage/rings/padics/padic_printing.pyx b/src/sage/rings/padics/padic_printing.pyx index c0988388066..634e6d64115 100644 --- a/src/sage/rings/padics/padic_printing.pyx +++ b/src/sage/rings/padics/padic_printing.pyx @@ -76,7 +76,7 @@ class pAdicPrinterDefaults(SageObject): """ This class stores global defaults for `p`-adic printing. """ - def __init__(self, mode = 'series', pos = True, max_ram_terms = -1, max_unram_terms = -1, max_terse_terms = -1, sep = "|", alphabet = None): + def __init__(self, mode='series', pos=True, max_ram_terms=-1, max_unram_terms=-1, max_terse_terms=-1, sep="|", alphabet=None): r""" Instances of this class store global defaults used in determining printing options during the creation of `p`-adic @@ -150,7 +150,7 @@ class pAdicPrinterDefaults(SageObject): else: raise ValueError("invalid printing mode") - def allow_negatives(self, neg = None): + def allow_negatives(self, neg=None): r""" Controls whether or not to display a balanced representation. @@ -172,7 +172,7 @@ class pAdicPrinterDefaults(SageObject): else: self._pos = not neg - def max_series_terms(self, max = None): + def max_series_terms(self, max=None): r""" Controls the maximum number of terms shown when printing in ``'series'``, ``'digits'`` or ``'bars'`` mode. @@ -197,7 +197,7 @@ class pAdicPrinterDefaults(SageObject): else: self._max_ram_terms = int(max) - def max_unram_terms(self, max = None): + def max_unram_terms(self, max=None): r""" For rings with non-prime residue fields, controls how many terms appear in the coefficient of each ``pi^n`` when printing in @@ -222,7 +222,7 @@ class pAdicPrinterDefaults(SageObject): else: self._max_unram_terms = int(max) - def max_poly_terms(self, max = None): + def max_poly_terms(self, max=None): r""" Controls the number of terms appearing when printing polynomial representations in ``'terse'`` or ``'val-unit'`` modes. @@ -248,7 +248,7 @@ class pAdicPrinterDefaults(SageObject): else: self._max_terse_terms = int(max) - def sep(self, sep = None): + def sep(self, sep=None): r""" Controls the separator used in ``'bars'`` mode. @@ -271,7 +271,7 @@ class pAdicPrinterDefaults(SageObject): else: self._sep = str(sep) - def alphabet(self, alphabet = None): + def alphabet(self, alphabet=None): r""" Controls the alphabet used to translate `p`-adic digits into strings (so that no separator need be used in ``'digits'`` mode). @@ -832,7 +832,7 @@ cdef class pAdicPrinter_class(SageObject): else: return trim_zeros(list(value.unit_part().expansion(lift_mode='smallest'))) - def repr_gen(self, elt, do_latex, pos = None, mode = None, ram_name = None): + def repr_gen(self, elt, do_latex, pos=None, mode=None, ram_name=None): """ The entry point for printing an element. diff --git a/src/sage/rings/padics/padic_template_element.pxi b/src/sage/rings/padics/padic_template_element.pxi index c842d9934cd..381887d6a5b 100644 --- a/src/sage/rings/padics/padic_template_element.pxi +++ b/src/sage/rings/padics/padic_template_element.pxi @@ -383,7 +383,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement): """ raise NotImplementedError - def expansion(self, n = None, lift_mode = 'simple', start_val = None): + def expansion(self, n=None, lift_mode='simple', start_val=None): r""" Return the coefficients in a `\pi`-adic expansion. If this is a field element, start at @@ -560,7 +560,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement): else: return expansion[n] - def teichmuller_expansion(self, n = None): + def teichmuller_expansion(self, n=None): r""" Return an iterator over coefficients `a_0, a_1, \dots, a_n` such that diff --git a/src/sage/rings/padics/pow_computer.pyx b/src/sage/rings/padics/pow_computer.pyx index 9719dfa1efe..cbd0118b455 100644 --- a/src/sage/rings/padics/pow_computer.pyx +++ b/src/sage/rings/padics/pow_computer.pyx @@ -638,7 +638,7 @@ cdef PowComputer_base PowComputer_c(Integer m, Integer cache_limit, Integer prec # To speed up the creation of PowComputers with the same m, we might eventually want to copy over data from an existing PowComputer. -def PowComputer(m, cache_limit, prec_cap, in_field = False, prec_type=None): +def PowComputer(m, cache_limit, prec_cap, in_field=False, prec_type=None): r""" Return a ``PowComputer`` that caches the values `1, m, m^2, \ldots, m^{C}`, where `C` is ``cache_limit``. diff --git a/src/sage/rings/padics/pow_computer_ext.pyx b/src/sage/rings/padics/pow_computer_ext.pyx index 389bd0bb20d..13d60f11f28 100644 --- a/src/sage/rings/padics/pow_computer_ext.pyx +++ b/src/sage/rings/padics/pow_computer_ext.pyx @@ -201,7 +201,7 @@ cdef int ZZ_pX_Eis_init(PowComputer_ZZ_pX prime_pow, ntl_ZZ_pX shift_seed) excep #ZZ_div(a, ZZ_p_rep(ZZ_pX_ConstTerm(modup)), prime_pow.small_powers[1]) #ZZ_InvMod(a, a, prime_pow.pow_ZZ_tmp(prime_pow.prec_cap + low_length)[0]) #ZZ_negate(a, a) - ##cdef ntl_ZZ_pX printer = ntl_ZZ_pX([],prime_pow.get_context(prime_pow.prec_cap)) + ##cdef ntl_ZZ_pX printer = ntl_ZZ_pX([], prime_pow.get_context(prime_pow.prec_cap)) ##printer.x = modup # Note that we're losing one digit of precision here. # This is correct because right shifting does not preserve precision. @@ -728,7 +728,7 @@ cdef class PowComputer_ext(PowComputer_class): return self.ram_prec_cap cdef class PowComputer_ZZ_pX(PowComputer_ext): - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Initialization. @@ -1221,7 +1221,7 @@ cdef class PowComputer_ZZ_pX_FM(PowComputer_ZZ_pX): and unramified extensions of `\ZZ_p`. """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Caches a context and modulus for ``prime^prec_cap``. @@ -1316,7 +1316,7 @@ cdef class PowComputer_ZZ_pX_FM_Eis(PowComputer_ZZ_pX_FM): This class computes and stores ``low_shifter`` and ``high_shifter``, which aid in right shifting elements. """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Call ``Eis_init``, which initializes ``high_shifter`` and ``low_shifter``. @@ -1545,7 +1545,7 @@ cdef class PowComputer_ZZ_pX_small(PowComputer_ZZ_pX): extensions of the base `p`-adic fields. """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Caches contexts and moduli densely between 1 and cache_limit. @@ -1745,7 +1745,7 @@ cdef class PowComputer_ZZ_pX_small_Eis(PowComputer_ZZ_pX_small): This class computes and stores ``low_shifter`` and ``high_shifter``, which aid in right shifting elements. These are only stored at maximal precision: in order to get lower precision versions just reduce mod p^n. """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Initialization. @@ -1907,7 +1907,7 @@ cdef class PowComputer_ZZ_pX_big(PowComputer_ZZ_pX): a dictionary of contexts and moduli of """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Caches contexts and moduli densely between 1 and cache_limit. Caches a context and modulus for prec_cap. Also creates the dictionaries. @@ -2178,7 +2178,7 @@ cdef class PowComputer_ZZ_pX_big_Eis(PowComputer_ZZ_pX_big): These are only stored at maximal precision: in order to get lower precision versions just reduce mod p^n. """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly, shift_seed=None): """ Initialization. @@ -2335,7 +2335,7 @@ cdef class PowComputer_ZZ_pX_big_Eis(PowComputer_ZZ_pX_big): return ZZ_pX_eis_shift_p(self, x, a, n, finalprec) -def PowComputer_ext_maker(prime, cache_limit, prec_cap, ram_prec_cap, in_field, poly, prec_type = "small", ext_type = "u", shift_seed = None): +def PowComputer_ext_maker(prime, cache_limit, prec_cap, ram_prec_cap, in_field, poly, prec_type="small", ext_type="u", shift_seed=None): r""" Return a ``PowComputer`` that caches the values `1, p, p^2, \ldots, p^C`, where `C` is ``cache_limit``. diff --git a/src/sage/rings/padics/pow_computer_flint.pyx b/src/sage/rings/padics/pow_computer_flint.pyx index cac2d70d758..6f316b05e2a 100644 --- a/src/sage/rings/padics/pow_computer_flint.pyx +++ b/src/sage/rings/padics/pow_computer_flint.pyx @@ -33,7 +33,7 @@ cdef class PowComputer_flint(PowComputer_class): sage: PowComputer_flint(5, 20, 20, 20, False) FLINT PowComputer for 5 """ - def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None, shift_seed = None): + def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None, shift_seed=None): """ Memory initialization. diff --git a/src/sage/rings/polynomial/multi_polynomial.pyx b/src/sage/rings/polynomial/multi_polynomial.pyx index ca25adc23f0..a906ffce164 100644 --- a/src/sage/rings/polynomial/multi_polynomial.pyx +++ b/src/sage/rings/polynomial/multi_polynomial.pyx @@ -1391,7 +1391,7 @@ cdef class MPolynomial(CommutativePolynomial): v = [self] + [self.map_coefficients(k.hom([k.gen()**(p**i)])) for i in range(1,e)] return prod(v).change_ring(k.prime_subfield()) - def sylvester_matrix(self, right, variable = None): + def sylvester_matrix(self, right, variable=None): r""" Given two nonzero polynomials ``self`` and ``right``, return the Sylvester matrix of the polynomials with respect to a given variable. @@ -1545,7 +1545,7 @@ cdef class MPolynomial(CommutativePolynomial): return M - def discriminant(self,variable): + def discriminant(self, variable): r""" Return the discriminant of ``self`` with respect to the given variable. diff --git a/src/sage/rings/polynomial/multi_polynomial_element.py b/src/sage/rings/polynomial/multi_polynomial_element.py index 6c4ec02c1b1..ca1f1c538a4 100644 --- a/src/sage/rings/polynomial/multi_polynomial_element.py +++ b/src/sage/rings/polynomial/multi_polynomial_element.py @@ -1657,7 +1657,7 @@ def variables(self): """ return tuple([self.parent().gen(index) for index in self.degrees().nonzero_positions()]) - def variable(self,i): + def variable(self, i): """ Return the `i`-th variable occurring in this polynomial. @@ -2200,7 +2200,7 @@ def factor(self, proof=None): return F @handle_AA_and_QQbar - def lift(self,I): + def lift(self, I): """ Given an ideal `I = (f_1,...,f_r)` and some `g` (= ``self``) in `I`, find `s_1,...,s_r` such that `g = s_1 f_1 + ... + s_r f_r`. diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py index 8e358652be3..04fcc867d40 100644 --- a/src/sage/rings/polynomial/multi_polynomial_ideal.py +++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py @@ -3726,7 +3726,7 @@ def _groebner_strategy(self): from sage.libs.singular.groebner_strategy import NCGroebnerStrategy return NCGroebnerStrategy(self.std()) - def reduce(self,p): + def reduce(self, p): """ Reduce an element modulo a Groebner basis for this ideal. @@ -3761,7 +3761,7 @@ def reduce(self,p): """ return self._groebner_strategy().normal_form(p) - def _contains_(self,p): + def _contains_(self, p): """ EXAMPLES: @@ -4741,7 +4741,7 @@ def groebner_basis(self, algorithm='', deg_bound=None, mult_bound=None, prot=Fal gb = self._groebner_basis_ginv(*args, **kwds) elif ":" in algorithm: ginv,alg = algorithm.split(":") - gb = self._groebner_basis_ginv(algorithm=alg,*args, **kwds) + gb = self._groebner_basis_ginv(algorithm=alg, *args, **kwds) else: raise NameError("Algorithm '%s' unknown." % algorithm) elif algorithm == 'giac:gbasis': diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx index d05760d84cd..cb692c6e4cc 100644 --- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx +++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx @@ -1702,7 +1702,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base): sage: P.monomial_lcm(x,P(1)) x """ - cdef poly *m = p_ISet(1,self._ring) + cdef poly *m = p_ISet(1, self._ring) if self is not f._parent: f = self.coerce(f) @@ -2884,7 +2884,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): cdef poly *_degrees = 0 cdef poly *p = self._poly cdef ring *r = self._parent_ring - cdef poly *newp = p_ISet(0,r) + cdef poly *newp = p_ISet(0, r) cdef poly *newptemp cdef int i cdef int flag @@ -3146,7 +3146,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): return -2 return result - def __getitem__(self,x): + def __getitem__(self, x): """ Same as ``self.monomial_coefficient`` but for exponent vectors. @@ -4576,7 +4576,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): """ global errorreported - cdef ideal *fI = idInit(1,1) + cdef ideal *fI = idInit(1, 1) cdef ideal *_I cdef MPolynomialRing_libsingular parent = self._parent cdef int i = 0 @@ -4888,7 +4888,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): if n_GetChar(_ring.cf) > 1<<29: raise NotImplementedError("GCD of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.") - cdef int count = singular_polynomial_length_bounded(self._poly,20) \ + cdef int count = singular_polynomial_length_bounded(self._poly, 20) \ + singular_polynomial_length_bounded(_right._poly,20) if count >= 20: sig_on() @@ -4964,7 +4964,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): if n_GetChar(_ring.cf) > 1<<29: raise NotImplementedError("LCM of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.") - cdef int count = singular_polynomial_length_bounded(self._poly,20) \ + cdef int count = singular_polynomial_length_bounded(self._poly, 20) \ + singular_polynomial_length_bounded(_g._poly,20) if count >= 20: sig_on() @@ -5044,7 +5044,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base): if n_GetChar(r.cf) > 1<<29: raise NotImplementedError("Division of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.") - cdef int count = singular_polynomial_length_bounded(self._poly,15) + cdef int count = singular_polynomial_length_bounded(self._poly, 15) if count >= 15: # note that _right._poly must be of shorter length than self._poly for us to care about this call sig_on() if r!=currRing: rChangeCurrRing(r) # singclap_pdivide diff --git a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx index 19c2ddac7b1..ac5e445908d 100644 --- a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx +++ b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx @@ -392,21 +392,21 @@ cdef class MPolynomialRing_base(CommutativeRing): EXAMPLES:: - sage: def F(a,b,c): + sage: def F(a, b, c): ....: return a^3*b + b + c^2 + 25 ....: sage: R. = PolynomialRing(QQ) sage: R.interpolation(4, F) # needs sage.modules x^3*y + z^2 + y + 25 - sage: def F(a,b,c): + sage: def F(a, b, c): ....: return a^3*b + b + c^2 + 25 ....: sage: R. = PolynomialRing(QQ) sage: R.interpolation([3,1,2], F) # needs sage.modules x^3*y + z^2 + y + 25 - sage: def F(a,b,c): + sage: def F(a, b, c): ....: return a^3*b + b + c^2 + 25 ....: sage: R. = PolynomialRing(QQ) @@ -444,7 +444,7 @@ cdef class MPolynomialRing_base(CommutativeRing): as well. So if you give wrong bounds, you will get a wrong answer without any warning. :: - sage: def F(a,b,c): + sage: def F(a, b, c): ....: return a^3*b + b + c^2 + 25 ....: sage: R. = PolynomialRing(QQ) diff --git a/src/sage/rings/polynomial/multi_polynomial_sequence.py b/src/sage/rings/polynomial/multi_polynomial_sequence.py index ff1ec275633..db276a75c25 100644 --- a/src/sage/rings/polynomial/multi_polynomial_sequence.py +++ b/src/sage/rings/polynomial/multi_polynomial_sequence.py @@ -857,7 +857,7 @@ def subs(self, *args, **kwargs): sage: F = F.subs(s); F # needs sage.rings.polynomial.pbori Polynomial Sequence with 40 Polynomials in 16 Variables """ - return PolynomialSequence(self._ring, [tuple([f.subs(*args,**kwargs) for f in r]) for r in self._parts]) + return PolynomialSequence(self._ring, [tuple([f.subs(*args, **kwargs) for f in r]) for r in self._parts]) def _singular_(self): """ diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx index 35de7feefe5..0751068f27a 100644 --- a/src/sage/rings/polynomial/plural.pyx +++ b/src/sage/rings/polynomial/plural.pyx @@ -335,7 +335,7 @@ cdef class NCPolynomialRing_plural(Ring): from sage.libs.singular.function import singular_function ncalgebra = singular_function('nc_algebra') - cdef RingWrap rw = ncalgebra(self._c, self._d, ring = P) + cdef RingWrap rw = ncalgebra(self._c, self._d, ring=P) # rw._output() self._ring = singular_ring_reference(rw._ring) @@ -1184,7 +1184,7 @@ cdef class NCPolynomialRing_plural(Ring): sage: P.monomial_lcm(x,P(1)) x """ - cdef poly *m = p_ISet(1,self._ring) + cdef poly *m = p_ISet(1, self._ring) if self is not f._parent: f = self.coerce(f) @@ -2091,7 +2091,7 @@ cdef class NCPolynomial_plural(RingElement): cdef poly *_degrees = 0 cdef poly *p = self._poly cdef ring *r = (self._parent)._ring - cdef poly *newp = p_ISet(0,r) + cdef poly *newp = p_ISet(0, r) cdef poly *newptemp cdef int i cdef int flag @@ -2353,7 +2353,7 @@ cdef class NCPolynomial_plural(RingElement): return -2 return result - def __getitem__(self,x): + def __getitem__(self, x): """ Same as :meth:`monomial_coefficient` but for exponent vectors. @@ -3117,7 +3117,7 @@ def SCA(base_ring, names, alt_vars, order='degrevlex'): return H.quotient(I) -def ExteriorAlgebra(base_ring, names,order='degrevlex'): +def ExteriorAlgebra(base_ring, names, order='degrevlex'): """ Return the exterior algebra on some generators. diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx index 7c1ca199ced..837b8bb5908 100644 --- a/src/sage/rings/polynomial/polynomial_element.pyx +++ b/src/sage/rings/polynomial/polynomial_element.pyx @@ -208,7 +208,7 @@ cdef class Polynomial(CommutativePolynomial): .. automethod:: _mul_trunc_ """ - def __init__(self, parent, is_gen = False, construct=False): + def __init__(self, parent, is_gen=False, construct=False): """ The following examples illustrate creation of elements of polynomial rings, and some basic arithmetic. @@ -3528,7 +3528,7 @@ cdef class Polynomial(CommutativePolynomial): @cython.boundscheck(False) @cython.wraparound(False) @cython.overflowcheck(False) - def _mul_karatsuba(self, right, K_threshold = None): + def _mul_karatsuba(self, right, K_threshold=None): r""" Compute the product of two polynomials using the Karatsuba divide and conquer multiplication algorithm. This is only used over a @@ -4323,7 +4323,7 @@ cdef class Polynomial(CommutativePolynomial): """ return [self.diff()] - def integral(self,var=None): + def integral(self, var=None): """ Return the integral of this polynomial. @@ -5314,7 +5314,7 @@ cdef class Polynomial(CommutativePolynomial): raise NotImplementedError("splitting_field() is only implemented over number fields and finite fields") - def pseudo_quo_rem(self,other): + def pseudo_quo_rem(self, other): r""" Compute the pseudo-division of two polynomials. @@ -5831,7 +5831,7 @@ cdef class Polynomial(CommutativePolynomial): return R.fraction_field()[self._parent.variable_name()].quotient(self, names) - def sylvester_matrix(self, right, variable = None): + def sylvester_matrix(self, right, variable=None): """ Return the Sylvester matrix of ``self`` and ``right``. @@ -11805,7 +11805,7 @@ cdef list do_karatsuba_different_size(list left, list right, Py_ssize_t K_thresh @cython.boundscheck(False) @cython.wraparound(False) @cython.overflowcheck(False) -cdef list do_karatsuba(list left, list right, Py_ssize_t K_threshold,Py_ssize_t start_l, Py_ssize_t start_r,Py_ssize_t num_elts): +cdef list do_karatsuba(list left, list right, Py_ssize_t K_threshold, Py_ssize_t start_l, Py_ssize_t start_r, Py_ssize_t num_elts): """ Core routine for Karatsuba multiplication. This function works for two polynomials of the same degree. diff --git a/src/sage/rings/polynomial/polynomial_rational_flint.pyx b/src/sage/rings/polynomial/polynomial_rational_flint.pyx index ceaa9d7b2d5..c11592cf2d6 100644 --- a/src/sage/rings/polynomial/polynomial_rational_flint.pyx +++ b/src/sage/rings/polynomial/polynomial_rational_flint.pyx @@ -1495,7 +1495,7 @@ cdef class Polynomial_rational_flint(Polynomial): fmpz_get_mpz(den.value, fmpq_poly_denref(self._poly)) return den - def _derivative(self, var = None): + def _derivative(self, var=None): """ Return the derivative of this polynomial with respect to ``var``. diff --git a/src/sage/rings/polynomial/real_roots.pyx b/src/sage/rings/polynomial/real_roots.pyx index a91a95a1d55..bf294c3c398 100644 --- a/src/sage/rings/polynomial/real_roots.pyx +++ b/src/sage/rings/polynomial/real_roots.pyx @@ -1248,7 +1248,7 @@ def de_casteljau_intvec(Vector_integer_dense c, int c_bitsize, Rational x, int u # An ULP is a "unit in the last place"; it is the (varying) unit for # how much adjacent floating-point numbers differ from each other. # A half-ULP is half this amount; it is the maximum rounding error -# in the basic operations (+,-,*,/) in a correctly-operating IEEE +# in the basic operations (+, -, *, /) in a correctly-operating IEEE # floating-point unit. # (Note that by default, the x86 does not use IEEE double precision; # instead, it uses extra precision, which can (counterintuitively) diff --git a/src/sage/rings/polynomial/skew_polynomial_finite_field.pyx b/src/sage/rings/polynomial/skew_polynomial_finite_field.pyx index 0c8c660c18c..8193108d25a 100644 --- a/src/sage/rings/polynomial/skew_polynomial_finite_field.pyx +++ b/src/sage/rings/polynomial/skew_polynomial_finite_field.pyx @@ -842,7 +842,7 @@ cdef class SkewPolynomial_finite_field_dense(SkewPolynomial_finite_order_dense): cdef list indices = sample(range(1, m+1), m) cdef unit = self.leading_coefficient() - cdef SkewPolynomial_finite_field_dense left = self._new_c(self._coeffs[:],skew_ring) + cdef SkewPolynomial_finite_field_dense left = self._new_c(self._coeffs[:], skew_ring) left = left.right_monic() cdef SkewPolynomial_finite_field_dense right = skew_ring.one() cdef SkewPolynomial_finite_field_dense L, R diff --git a/src/sage/rings/polynomial/skew_polynomial_finite_order.pyx b/src/sage/rings/polynomial/skew_polynomial_finite_order.pyx index f90484cba62..e92cca63198 100644 --- a/src/sage/rings/polynomial/skew_polynomial_finite_order.pyx +++ b/src/sage/rings/polynomial/skew_polynomial_finite_order.pyx @@ -94,7 +94,7 @@ cdef class SkewPolynomial_finite_order_dense(SkewPolynomial_generic_dense): else: col = 0 exp = r - cdef SkewPolynomial_finite_order_dense powx = self._new_c([zero,one], parent) + cdef SkewPolynomial_finite_order_dense powx = self._new_c([zero, one], parent) cdef SkewPolynomial_finite_order_dense v if (exp % 2 == 1): v = self._new_c([zero,one], parent) diff --git a/src/sage/rings/polynomial/term_order.py b/src/sage/rings/polynomial/term_order.py index cd5cad00f8f..a88568248ce 100644 --- a/src/sage/rings/polynomial/term_order.py +++ b/src/sage/rings/polynomial/term_order.py @@ -1211,7 +1211,7 @@ def sortkey_block(self, f): n += len(block) return key - def greater_tuple_matrix(self,f,g): + def greater_tuple_matrix(self, f, g): """ Return the greater exponent tuple with respect to the matrix term order. @@ -1240,7 +1240,7 @@ def greater_tuple_matrix(self,f,g): return g return g - def greater_tuple_lex(self,f,g): + def greater_tuple_lex(self, f, g): """ Return the greater exponent tuple with respect to the lexicographical term order. @@ -1262,7 +1262,7 @@ def greater_tuple_lex(self,f,g): """ return f > g and f or g - def greater_tuple_invlex(self,f,g): + def greater_tuple_invlex(self, f, g): """ Return the greater exponent tuple with respect to the inversed lexicographical term order. @@ -1286,7 +1286,7 @@ def greater_tuple_invlex(self,f,g): """ return f.reversed() > g.reversed() and f or g - def greater_tuple_deglex(self,f,g): + def greater_tuple_deglex(self, f, g): """ Return the greater exponent tuple with respect to the total degree lexicographical term order. @@ -1312,7 +1312,7 @@ def greater_tuple_deglex(self,f,g): sg = sum(g.nonzero_values(sort=False)) return ( sf > sg or ( sf == sg and f > g )) and f or g - def greater_tuple_degrevlex(self,f,g): + def greater_tuple_degrevlex(self, f, g): """ Return the greater exponent tuple with respect to the total degree reversed lexicographical term order. @@ -1338,7 +1338,7 @@ def greater_tuple_degrevlex(self,f,g): sg = sum(g.nonzero_values(sort=False)) return ( sf > sg or ( sf == sg and f.reversed() < g.reversed() )) and f or g - def greater_tuple_negdegrevlex(self,f,g): + def greater_tuple_negdegrevlex(self, f, g): """ Return the greater exponent tuple with respect to the negative degree reverse lexicographical term order. @@ -1367,7 +1367,7 @@ def greater_tuple_negdegrevlex(self,f,g): sg = sum(g.nonzero_values(sort=False)) return ( sf < sg or ( sf == sg and f.reversed() < g.reversed() )) and f or g - def greater_tuple_negdeglex(self,f,g): + def greater_tuple_negdeglex(self, f, g): """ Return the greater exponent tuple with respect to the negative degree lexicographical term order. @@ -1396,7 +1396,7 @@ def greater_tuple_negdeglex(self,f,g): sg = sum(g.nonzero_values(sort=False)) return ( sf < sg or ( sf == sg and f > g )) and f or g - def greater_tuple_degneglex(self,f,g): + def greater_tuple_degneglex(self, f, g): """ Return the greater exponent tuple with respect to the degree negative lexicographical term order. @@ -1422,7 +1422,7 @@ def greater_tuple_degneglex(self,f,g): sg = sum(g.nonzero_values(sort=False)) return ( sf > sg or ( sf == sg and f < g )) and f or g - def greater_tuple_neglex(self,f,g): + def greater_tuple_neglex(self, f, g): """ Return the greater exponent tuple with respect to the negative lexicographical term order. @@ -1447,7 +1447,7 @@ def greater_tuple_neglex(self,f,g): """ return (f < g) and f or g - def greater_tuple_wdeglex(self,f,g): + def greater_tuple_wdeglex(self, f, g): """ Return the greater exponent tuple with respect to the weighted degree lexicographical term order. @@ -1474,7 +1474,7 @@ def greater_tuple_wdeglex(self,f,g): sg = sum(l*r for (l,r) in zip(g,self._weights)) return (sf > sg or ( sf == sg and f > g )) and f or g - def greater_tuple_wdegrevlex(self,f,g): + def greater_tuple_wdegrevlex(self, f, g): """ Return the greater exponent tuple with respect to the weighted degree reverse lexicographical term order. @@ -1501,7 +1501,7 @@ def greater_tuple_wdegrevlex(self,f,g): sg = sum(l*r for (l,r) in zip(g,self._weights)) return (sf > sg or ( sf == sg and f.reversed() < g.reversed())) and f or g - def greater_tuple_negwdeglex(self,f,g): + def greater_tuple_negwdeglex(self, f, g): """ Return the greater exponent tuple with respect to the negative weighted degree lexicographical term order. @@ -1531,7 +1531,7 @@ def greater_tuple_negwdeglex(self,f,g): sg = sum(l*r for (l,r) in zip(g,self._weights)) return (sf < sg or ( sf == sg and f > g )) and f or g - def greater_tuple_negwdegrevlex(self,f,g): + def greater_tuple_negwdegrevlex(self, f, g): """ Return the greater exponent tuple with respect to the negative weighted degree reverse lexicographical term order. @@ -1561,7 +1561,7 @@ def greater_tuple_negwdegrevlex(self,f,g): sg = sum(l*r for (l,r) in zip(g,self._weights)) return (sf < sg or ( sf == sg and f.reversed() < g.reversed() )) and f or g - def greater_tuple_block(self, f,g): + def greater_tuple_block(self, f, g): """ Return the greater exponent tuple with respect to the block order as specified when constructing this element. diff --git a/src/sage/rings/power_series_poly.pyx b/src/sage/rings/power_series_poly.pyx index 309d72c8f6a..39b05cce069 100644 --- a/src/sage/rings/power_series_poly.pyx +++ b/src/sage/rings/power_series_poly.pyx @@ -874,7 +874,7 @@ cdef class PowerSeries_poly(PowerSeries): return PowerSeries_poly(self._parent, self.__f._derivative(), self.prec()-1, check=False) - def integral(self,var=None): + def integral(self, var=None): """ Return the integral of this power series. diff --git a/src/sage/rings/power_series_ring_element.pyx b/src/sage/rings/power_series_ring_element.pyx index b1ca6ea4ab1..1d24794eb37 100644 --- a/src/sage/rings/power_series_ring_element.pyx +++ b/src/sage/rings/power_series_ring_element.pyx @@ -839,7 +839,7 @@ cdef class PowerSeries(AlgebraElement): v = [a[i] for i in range(min(prec, len(a)))] return self._parent(v, prec) - def __getitem__(self,n): + def __getitem__(self, n): r""" Return the coefficient of `t^n` in this power series, where `t` is the indeterminate of the power series ring. @@ -2317,7 +2317,7 @@ cdef class PowerSeries(AlgebraElement): coeffs = self[:prec] return self._parent(coeffs, prec) - def solve_linear_de(self, prec = infinity, b = None, f0 = None): + def solve_linear_de(self, prec=infinity, b=None, f0=None): r""" Obtain a power series solution to an inhomogeneous linear differential equation of the form: diff --git a/src/sage/rings/quotient_ring.py b/src/sage/rings/quotient_ring.py index f98322c2183..c867ba41bbc 100644 --- a/src/sage/rings/quotient_ring.py +++ b/src/sage/rings/quotient_ring.py @@ -35,7 +35,7 @@ ....: self._power = n ....: self._power = n ....: Ideal_nc.__init__(self, R, [R.prod(m) for m in product(R.gens(), repeat=n)]) - ....: def reduce(self,x): + ....: def reduce(self, x): ....: R = self.ring() ....: return add([c*R(m) for m,c in x if len(m) = FreeAlgebra(QQ, 3) # needs sage.combinat sage.modules @@ -793,7 +793,7 @@ def lift(self, x=None): return self.lifting_map() return self.lifting_map()(x) - def retract(self,x): + def retract(self, x): """ The image of an element of the cover ring under the quotient map. diff --git a/src/sage/rings/ring.pyx b/src/sage/rings/ring.pyx index f92aa7c0d27..28f272a18f0 100644 --- a/src/sage/rings/ring.pyx +++ b/src/sage/rings/ring.pyx @@ -1217,7 +1217,7 @@ cdef class Field(CommutativeRing): """ return self - def is_field(self, proof = True): + def is_field(self, proof=True): """ Return ``True`` since this is a field. diff --git a/src/sage/rings/ring_extension_element.pyx b/src/sage/rings/ring_extension_element.pyx index e3184503d77..a23ab11d328 100644 --- a/src/sage/rings/ring_extension_element.pyx +++ b/src/sage/rings/ring_extension_element.pyx @@ -384,7 +384,7 @@ cdef class RingExtensionElement(CommutativeAlgebraElement): """ return left._backend._richcmp_(backend_element(right), op) - cpdef _add_(self,other): + cpdef _add_(self, other): r""" Return the sum of this element and ``other``. @@ -424,7 +424,7 @@ cdef class RingExtensionElement(CommutativeAlgebraElement): ans._backend = -self._backend return ans - cpdef _sub_(self,other): + cpdef _sub_(self, other): r""" Return the difference of this element and ``other``. @@ -444,7 +444,7 @@ cdef class RingExtensionElement(CommutativeAlgebraElement): ans._backend = self._backend - (other)._backend return ans - cpdef _mul_(self,other): + cpdef _mul_(self, other): r""" Return the product of this element and ``other``. @@ -464,7 +464,7 @@ cdef class RingExtensionElement(CommutativeAlgebraElement): ans._backend = self._backend * (other)._backend return ans - cpdef _div_(self,other): + cpdef _div_(self, other): r""" Return the quotient of this element by ``other``, considered as an element of the fraction field. diff --git a/src/sage/schemes/elliptic_curves/cm.py b/src/sage/schemes/elliptic_curves/cm.py index 6760719e789..e02a117ee3c 100755 --- a/src/sage/schemes/elliptic_curves/cm.py +++ b/src/sage/schemes/elliptic_curves/cm.py @@ -288,7 +288,7 @@ def is_HCP(f, check_monic_irreducible=True): return D if f == hilbert_class_polynomial(D) else zero -def OrderClassNumber(D0,h0,f): +def OrderClassNumber(D0, h0, f): r""" Return the class number h(f**2 * D0), given h(D0)=h0. diff --git a/src/sage/schemes/elliptic_curves/constructor.py b/src/sage/schemes/elliptic_curves/constructor.py index 831ee47e280..5a97d2eda9b 100755 --- a/src/sage/schemes/elliptic_curves/constructor.py +++ b/src/sage/schemes/elliptic_curves/constructor.py @@ -1271,7 +1271,7 @@ def EllipticCurve_from_cubic(F, P=None, morphism=True): C, E, fwd_defining_poly, fwd_post, inv_defining_poly, inv_post) -def tangent_at_smooth_point(C,P): +def tangent_at_smooth_point(C, P): r"""Return the tangent at the smooth point `P` of projective curve `C`. INPUT: diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py index eea2e5cc243..8af221880b6 100755 --- a/src/sage/schemes/elliptic_curves/ell_number_field.py +++ b/src/sage/schemes/elliptic_curves/ell_number_field.py @@ -541,7 +541,7 @@ def is_local_integral_model(self, *P): return all(self.is_local_integral_model(x) for x in P) return all(x.valuation(P) >= 0 for x in self.ainvs()) - def local_integral_model(self,*P): + def local_integral_model(self, *P): r""" Return a model of ``self`` which is integral at the prime ideal `P`. @@ -1898,7 +1898,7 @@ def global_minimal_model(self, proof=None, semi_global=False): raise ValueError("%s has no global minimal model! For a semi-global minimal model use semi_global=True" % self) - def reduction(self,place): + def reduction(self, place): r""" Return the reduction of the elliptic curve at a place of good reduction. diff --git a/src/sage/schemes/elliptic_curves/ell_point.py b/src/sage/schemes/elliptic_curves/ell_point.py index 507930474c1..1bb0f1de8a4 100755 --- a/src/sage/schemes/elliptic_curves/ell_point.py +++ b/src/sage/schemes/elliptic_curves/ell_point.py @@ -4264,7 +4264,7 @@ def discrete_log(self, Q): ' methods in Sage uniform. Please update your code.') return Q.log(self) - def padic_elliptic_logarithm(self,Q, p): + def padic_elliptic_logarithm(self, Q, p): r""" Return the discrete logarithm of `Q` to base `P` = ``self``, that is, an integer `x` such that `xP = Q` only for anomalous curves. diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py index d00187d49a2..41e5ea3a9eb 100755 --- a/src/sage/schemes/elliptic_curves/ell_rational_field.py +++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py @@ -4116,7 +4116,7 @@ def cremona_label(self, space=False): label = cremona_label - def reduction(self,p): + def reduction(self, p): r""" Return the reduction of the elliptic curve at a prime of good reduction. @@ -5945,7 +5945,7 @@ def antilogarithm(self, z, max_denominator=None): except TypeError: raise ValueError("approximated point not on the curve") - def integral_x_coords_in_interval(self,xmin,xmax): + def integral_x_coords_in_interval(self, xmin, xmax): r""" Return the set of integers `x` with `xmin\le x\le xmax` which are `x`-coordinates of rational points on this curve. @@ -6136,7 +6136,7 @@ def integral_points(self, mw_base='auto', both_signs=False, verbose=False): # INTERNAL FUNCTIONS ################################################ ############################## begin ################################ - def point_preprocessing(free,tor): + def point_preprocessing(free, tor): r""" Transform the mw_basis ``free`` into a `\ZZ`-basis for `E(\QQ)\cap E^0(`\RR)`. If there is a torsion point on the diff --git a/src/sage/schemes/elliptic_curves/ell_wp.py b/src/sage/schemes/elliptic_curves/ell_wp.py index 5c8e7930830..622f8fed5f3 100755 --- a/src/sage/schemes/elliptic_curves/ell_wp.py +++ b/src/sage/schemes/elliptic_curves/ell_wp.py @@ -167,7 +167,7 @@ def weierstrass_p(E, prec=20, algorithm=None): return wp(z*u) * u**2 -def compute_wp_pari(E,prec): +def compute_wp_pari(E, prec): r""" Compute the Weierstrass `\wp`-function with the ``ellwp`` function from PARI. diff --git a/src/sage/schemes/elliptic_curves/gal_reps.py b/src/sage/schemes/elliptic_curves/gal_reps.py index b9360acdf56..8f0e0ed9a60 100755 --- a/src/sage/schemes/elliptic_curves/gal_reps.py +++ b/src/sage/schemes/elliptic_curves/gal_reps.py @@ -203,7 +203,7 @@ def __repr__(self): """ return "Compatible family of Galois representations associated to the " + repr(self._E) - def __eq__(self,other): + def __eq__(self, other): r""" Compare two Galois representations. We define tho compatible families of representations @@ -1081,7 +1081,7 @@ def image_type(self, p): self.__image_type[p] = "The image could not be determined. Sorry." return self.__image_type[p] - def image_classes(self,p,bound=10000): + def image_classes(self, p, bound=10000): r""" This function returns, given the representation `\rho` a list of `p` values that add up to 1, representing the @@ -1228,7 +1228,7 @@ def image_classes(self,p,bound=10000): # ell-adic reps - def is_unramified(self,p,ell): + def is_unramified(self, p, ell): r""" Return true if the Galois representation to `GL_2(\ZZ_p)` is unramified at `\ell`, i.e. if the inertia group at a place above `\ell` in `\text{Gal}(\bar\QQ/\QQ)` has trivial image in @@ -1262,7 +1262,7 @@ def is_unramified(self,p,ell): raise ValueError('ell (=%s) must be prime' % ell) return (ell != p) and self._E.has_good_reduction(ell) - def is_unipotent(self,p,ell): + def is_unipotent(self, p, ell): r""" Return true if the Galois representation to `GL_2(\ZZ_p)` is unipotent at `\ell\neq p`, i.e. if the inertia group at a place above `\ell` in `\text{Gal}(\bar\QQ/\QQ)` maps into a Borel subgroup. @@ -1301,7 +1301,7 @@ def is_unipotent(self,p,ell): raise ValueError("unipotent is not defined for l = p, use semistable instead.") return not self._E.has_additive_reduction(ell) - def is_quasi_unipotent(self,p,ell): + def is_quasi_unipotent(self, p, ell): r""" Return true if the Galois representation to `GL_2(\ZZ_p)` is quasi-unipotent at `\ell\neq p`, i.e. if there is a finite extension `K/\QQ` such that the inertia group at a place above `\ell` in `\text{Gal}(\bar\QQ/K)` maps into a Borel subgroup. @@ -1330,7 +1330,7 @@ def is_quasi_unipotent(self,p,ell): # p-adic reps - def is_ordinary(self,p): + def is_ordinary(self, p): r""" Return true if the `p`-adic Galois representation to `GL_2(\ZZ_p)` is ordinary, i.e. if the image of the decomposition group in `\text{Gal}(\bar\QQ/\QQ)` above he prime `p` maps into @@ -1360,7 +1360,7 @@ def is_ordinary(self,p): raise NotImplementedError('is_ordinary is only implemented for semi-stable representations') return self._E.has_multiplicative_reduction(p) or (self._E.has_good_reduction(p) and self._E.ap(p) % p != 0) - def is_crystalline(self,p): + def is_crystalline(self, p): r""" Return true is the `p`-adic Galois representation to `GL_2(\ZZ_p)` is crystalline. @@ -1384,7 +1384,7 @@ def is_crystalline(self,p): raise ValueError('p (=%s) must be prime' % p) return self._E.has_good_reduction(p) - def is_potentially_crystalline(self,p): + def is_potentially_crystalline(self, p): r""" Return true is the `p`-adic Galois representation to `GL_2(\ZZ_p)` is potentially crystalline, i.e. if there is a finite extension `K/\QQ_p` such that the `p`-adic representation becomes crystalline. @@ -1409,7 +1409,7 @@ def is_potentially_crystalline(self,p): raise ValueError('p (=%s) must be prime' % p) return self._E.j_invariant().valuation(p) >= 0 - def is_semistable(self,p): + def is_semistable(self, p): r""" Return true if the `p`-adic Galois representation to `GL_2(\ZZ_p)` is semistable. @@ -1435,7 +1435,7 @@ def is_semistable(self,p): raise ValueError('p (=%s) must be prime' % p) return not self._E.has_additive_reduction(p) - def is_potentially_semistable(self,p): + def is_potentially_semistable(self, p): r""" Return true if the `p`-adic Galois representation to `GL_2(\ZZ_p)` is potentially semistable. diff --git a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py index a4eb66a6df7..7824893b05f 100755 --- a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py +++ b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py @@ -132,7 +132,7 @@ def __repr__(self): else: return "Compatible family of Galois representations associated to the " + repr(self.E) - def __eq__(self,other): + def __eq__(self, other): r""" Compare two Galois representations. @@ -1191,7 +1191,7 @@ def Billerey_P_l(E, l): return P -def Billerey_B_l(E,l,B=0): +def Billerey_B_l(E, l, B=0): r""" Return Billerey's `B_l`, adapted from the definition in [Bil2011]_, after (9). diff --git a/src/sage/schemes/elliptic_curves/heegner.py b/src/sage/schemes/elliptic_curves/heegner.py index 1bff085023c..f0a7087d7ea 100755 --- a/src/sage/schemes/elliptic_curves/heegner.py +++ b/src/sage/schemes/elliptic_curves/heegner.py @@ -1177,7 +1177,7 @@ def __getitem__(self, i): """ EXAMPLES:: - sage: E = EllipticCurve('389a'); F= E.heegner_point(-7,5).ring_class_field() + sage: E = EllipticCurve('389a'); F = E.heegner_point(-7,5).ring_class_field() sage: G = F.galois_group(F.quadratic_field()) sage: G[0] Class field automorphism defined by x^2 + x*y + 44*y^2 @@ -1666,7 +1666,7 @@ def ideal(self): EXAMPLES:: - sage: E = EllipticCurve('389a'); F= E.heegner_point(-20,3).ring_class_field() + sage: E = EllipticCurve('389a'); F = E.heegner_point(-20,3).ring_class_field() sage: G = F.galois_group(F.quadratic_field()) sage: G[1].ideal() Fractional ideal (2, 1/2*sqrt_minus_20 + 1) @@ -4283,7 +4283,7 @@ def plot(self, prec=53, *args, **kwds): if not P: # point at infinity return Graphics() - return point((P[0].real(), P[1].real()),*args, **kwds) + return point((P[0].real(), P[1].real()), *args, **kwds) else: raise NotImplementedError diff --git a/src/sage/schemes/elliptic_curves/kraus.py b/src/sage/schemes/elliptic_curves/kraus.py index 49dff06b493..5e749a0448d 100755 --- a/src/sage/schemes/elliptic_curves/kraus.py +++ b/src/sage/schemes/elliptic_curves/kraus.py @@ -798,7 +798,7 @@ def check_Kraus_global(c4, c6, assume_nonsingular=False, debug=False): sage: E = EllipticCurve([a, 0, 1, 2*a^2 + 5*a + 3, -a^2 - 3*a - 2]) sage: assert E.conductor().norm() == 8 sage: G = K.galois_group(names='b') - sage: def conj_curve(E,sigma): return EllipticCurve([sigma(a) for a in E.ainvs()]) + sage: def conj_curve(E, sigma): return EllipticCurve([sigma(a) for a in E.ainvs()]) sage: EL = conj_curve(E,G[0]) sage: L = EL.base_field() sage: assert L.class_number() == 2 diff --git a/src/sage/schemes/elliptic_curves/padic_lseries.py b/src/sage/schemes/elliptic_curves/padic_lseries.py index 1fcc30764b2..6cb54115933 100755 --- a/src/sage/schemes/elliptic_curves/padic_lseries.py +++ b/src/sage/schemes/elliptic_curves/padic_lseries.py @@ -1640,7 +1640,7 @@ def bernardi_sigma_function(self, prec=20): return sigma_of_z - def Dp_valued_height(self,prec=20): + def Dp_valued_height(self, prec=20): r""" Return the canonical `p`-adic height with values in the Dieudonné module `D_p(E)`. @@ -1674,7 +1674,7 @@ def Dp_valued_height(self,prec=20): n = _multiple_to_make_good_reduction(E) n = LCM(n, E.Np(p)) # allowed here because E has good reduction at p - def height(P,check=True): + def height(P, check=True): if P.is_finite_order(): return Qp(p,prec)(0) if check: @@ -1755,7 +1755,7 @@ def regv(vec): return M.determinant() - def Dp_pairing(vec1,vec2): + def Dp_pairing(vec1, vec2): return (vec1[0]*vec2[1]-vec1[1]*vec2[0]) omega_vec = vector([K(1),K(0)]) diff --git a/src/sage/schemes/generic/divisor.py b/src/sage/schemes/generic/divisor.py index 441efbf36e7..0099a74b86c 100755 --- a/src/sage/schemes/generic/divisor.py +++ b/src/sage/schemes/generic/divisor.py @@ -53,7 +53,7 @@ lazy_import('sage.schemes.generic.morphism', 'SchemeMorphism') -def CurvePointToIdeal(C,P): +def CurvePointToIdeal(C, P): r""" Return the vanishing ideal of a point on a curve. diff --git a/src/sage/schemes/generic/morphism.py b/src/sage/schemes/generic/morphism.py index 56bfb8da197..51906d804eb 100755 --- a/src/sage/schemes/generic/morphism.py +++ b/src/sage/schemes/generic/morphism.py @@ -246,7 +246,7 @@ def __call__(self, x, *args, **kwds): converter = D._internal_coerce_map_from(P) if converter is None: try: - return self.pushforward(x,*args,**kwds) + return self.pushforward(x, *args, **kwds) except (AttributeError, TypeError, NotImplementedError): pass # raise TypeError, "%s must be coercible into %s"%(x, self.domain()) # Here, we would like to do diff --git a/src/sage/schemes/hyperelliptic_curves/jacobian_morphism.py b/src/sage/schemes/hyperelliptic_curves/jacobian_morphism.py index c0cbccd84ea..8194f25f45c 100755 --- a/src/sage/schemes/hyperelliptic_curves/jacobian_morphism.py +++ b/src/sage/schemes/hyperelliptic_curves/jacobian_morphism.py @@ -211,7 +211,7 @@ def cantor_reduction(a, b, f, h, genus): return (a, b) -def cantor_composition_simple(D1,D2,f,genus): +def cantor_composition_simple(D1, D2, f, genus): r""" Given `D_1` and `D_2` two reduced Mumford divisors on the Jacobian of the curve `y^2 = f(x)`, @@ -270,7 +270,7 @@ def cantor_composition_simple(D1,D2,f,genus): return (a, b) -def cantor_composition(D1,D2,f,h,genus): +def cantor_composition(D1, D2, f, h, genus): r""" EXAMPLES:: @@ -808,7 +808,7 @@ def __neg__(self): D = (polys[0],-polys[1]-(h+polys[0]) % (polys[0])) return JacobianMorphism_divisor_class_field(X, D, check=False) - def _add_(self,other): + def _add_(self, other): r""" Return a Mumford representative of the divisor ``self + other``. diff --git a/src/sage/schemes/projective/projective_point.py b/src/sage/schemes/projective/projective_point.py index 7f941ec6726..c5d6b02c05a 100755 --- a/src/sage/schemes/projective/projective_point.py +++ b/src/sage/schemes/projective/projective_point.py @@ -625,7 +625,7 @@ def normalize_coordinates(self): self.scale_by(-ZZ.one()) self._normalized = True - def dehomogenize(self,n): + def dehomogenize(self, n): r""" Dehomogenizes at the `n`-th coordinate. diff --git a/src/sage/schemes/toric/divisor.py b/src/sage/schemes/toric/divisor.py index 1da707e0cb6..fe043e5dbb0 100755 --- a/src/sage/schemes/toric/divisor.py +++ b/src/sage/schemes/toric/divisor.py @@ -954,7 +954,7 @@ def is_ample(self): sage: fan = Fan(cones=[(0,1), (1,2), (2,3), (3,0)], ....: rays=[(-1,2), (0,1), (1,0), (0,-1)]) sage: F2 = ToricVariety(fan,'u1, u2, u3, u4') - sage: def D(a,b): return a*F2.divisor(2) + b*F2.divisor(3) + sage: def D(a, b): return a*F2.divisor(2) + b*F2.divisor(3) sage: [ (a,b) for a,b in product(range(-3,3), repeat=2) ....: if D(a,b).is_ample() ] [(1, 1), (1, 2), (2, 1), (2, 2)] @@ -1031,7 +1031,7 @@ def is_nef(self): sage: fan = Fan(cones=[(0,1), (1,2), (2,3), (3,0)], ....: rays=[(-1,2), (0,1), (1,0), (0,-1)]) sage: F2 = ToricVariety(fan,'u1, u2, u3, u4') - sage: def D(a,b): return a*F2.divisor(2) + b*F2.divisor(3) + sage: def D(a, b): return a*F2.divisor(2) + b*F2.divisor(3) sage: [ (a,b) for a,b in product(range(-3,3), repeat=2) ....: if D(a,b).is_ample() ] [(1, 1), (1, 2), (2, 1), (2, 2)] diff --git a/src/sage/sets/set_from_iterator.py b/src/sage/sets/set_from_iterator.py index 6f68f1245b8..19d11c7ad85 100644 --- a/src/sage/sets/set_from_iterator.py +++ b/src/sage/sets/set_from_iterator.py @@ -39,7 +39,7 @@ sage: from sage.sets.set_from_iterator import set_from_method sage: class A: ....: @set_from_method - ....: def f(self,n): + ....: def f(self, n): ....: return xsrange(n) sage: a = A() sage: a.f(3) @@ -776,7 +776,7 @@ def __call__(self, *args, **kwds): sage: from sage.sets.set_from_iterator import set_from_method sage: class A: ....: @set_from_method(name = lambda self,n: str(self)*n) - ....: def f(self,n): + ....: def f(self, n): ....: return xsrange(n) ....: def __repr__(self): ....: return "A" diff --git a/src/sage/stats/time_series.pyx b/src/sage/stats/time_series.pyx index 0baad597dde..28318238a25 100644 --- a/src/sage/stats/time_series.pyx +++ b/src/sage/stats/time_series.pyx @@ -557,7 +557,7 @@ cdef class TimeSeries: memcpy(v._values + i*T._length, T._values, sizeof(double)*T._length) return v - def autoregressive_fit(self,M): + def autoregressive_fit(self, M): r""" This method fits the time series to an autoregressive process of order ``M``. That is, we assume the process is given by @@ -782,7 +782,7 @@ cdef class TimeSeries: t._values[i] = self._values[i] if self._values[i] >= 0 else -self._values[i] return t - def diffs(self, Py_ssize_t k = 1): + def diffs(self, Py_ssize_t k=1): r""" Return the new time series got by taking the differences of successive terms in the time series. So if ``self`` is the time diff --git a/src/sage/structure/category_object.pyx b/src/sage/structure/category_object.pyx index a72d3fcd887..e0c217a0e3b 100644 --- a/src/sage/structure/category_object.pyx +++ b/src/sage/structure/category_object.pyx @@ -78,7 +78,7 @@ cdef class CategoryObject(SageObject): """ An object in some category. """ - def __init__(self, category = None, base = None): + def __init__(self, category=None, base=None): """ Initialize an object in a category. @@ -722,7 +722,7 @@ cdef class CategoryObject(SageObject): return d - def __setstate__(self,d): + def __setstate__(self, d): try: version = d['_pickle_version'] except KeyError: diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx index 18a58f46103..14cae09d6f0 100644 --- a/src/sage/structure/element.pyx +++ b/src/sage/structure/element.pyx @@ -4699,7 +4699,7 @@ def coerce_binop(method): sage: from sage.structure.element import coerce_binop sage: class MyRational(Rational): - ....: def __init__(self,value): + ....: def __init__(self, value): ....: self.v = value ....: @coerce_binop ....: def test_add(self, other, keyword='z'): diff --git a/src/sage/structure/parent_base.pyx b/src/sage/structure/parent_base.pyx index 7cef8f692c5..a9c5e80a1a9 100644 --- a/src/sage/structure/parent_base.pyx +++ b/src/sage/structure/parent_base.pyx @@ -28,7 +28,7 @@ cdef class ParentWithBase(Parent_old): Parent_old.__init__(self, *args, **kwds) self._base = base - cdef _coerce_c_impl(self,x): + cdef _coerce_c_impl(self, x): check_old_coerce(self) from sage.misc.superseded import deprecation deprecation(33497, "_coerce_c_impl is deprecated, use coerce instead") diff --git a/src/sage/structure/unique_representation.py b/src/sage/structure/unique_representation.py index c7bb3783658..d5208beb1ea 100644 --- a/src/sage/structure/unique_representation.py +++ b/src/sage/structure/unique_representation.py @@ -763,7 +763,7 @@ class CachedRepresentation(WithPicklingByInitArgs): implementation does not work:: sage: class MyClass3(CachedRepresentation): - ....: def __init__(self, value = 3): + ....: def __init__(self, value=3): ....: self.value = value sage: MyClass3(3) is MyClass3() False @@ -772,7 +772,7 @@ class CachedRepresentation(WithPicklingByInitArgs): sage: class MyClass3(UniqueRepresentation): ....: @staticmethod - ....: def __classcall__(cls, value = 3): + ....: def __classcall__(cls, value=3): ....: return super().__classcall__(cls, value) ....: ....: def __init__(self, value): @@ -1130,7 +1130,7 @@ def _clear_cache_(cls): sage: class B(A): ....: @staticmethod ....: def __classcall__(cls, *args, **kwds): - ....: return super().__classcall__(cls,*args,**kwds) + ....: return super().__classcall__(cls, *args, **kwds) sage: class C(B): pass sage: a = A(1) sage: b = B(2) @@ -1163,7 +1163,7 @@ def _clear_cache_(cls): ....: @staticmethod ....: def __classcall_private__(cls, *args, **kwds): ....: print("Private B") - ....: return super().__classcall__(cls,*args,**kwds) + ....: return super().__classcall__(cls, *args, **kwds) sage: class C(B): pass sage: a = A(1) sage: b = B(2) diff --git a/src/sage/symbolic/benchmark.py b/src/sage/symbolic/benchmark.py index 89a62a422c6..b8b98948c04 100644 --- a/src/sage/symbolic/benchmark.py +++ b/src/sage/symbolic/benchmark.py @@ -19,7 +19,7 @@ Problem R2:: - sage: def hermite(n,y): + sage: def hermite(n, y): ....: if n == 1: return 2*y ....: if n == 0: return 1 ....: return expand(2*y*hermite(n-1,y) - 2*(n-1)*hermite(n-2,y)) @@ -37,7 +37,7 @@ Problem R5:: - sage: def blowup(L,n): + sage: def blowup(L, n): ....: for i in [0..n]: ....: L.append( (L[i] + L[i+1]) * L[i+2] ) sage: L = list(var('x,y,z')) diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx index f221fd64de0..52da8232dc6 100644 --- a/src/sage/symbolic/expression.pyx +++ b/src/sage/symbolic/expression.pyx @@ -10010,7 +10010,7 @@ cdef class Expression(Expression_abc): sig_off() return new_Expression_from_GEx(self._parent, r) - def numerator(self, bint normalize = True): + def numerator(self, bint normalize=True): """ Return the numerator of this symbolic expression. @@ -11018,7 +11018,7 @@ cdef class Expression(Expression_abc): trig_simplify = simplify_trig - def simplify_rational(self,algorithm='full', map=False): + def simplify_rational(self, algorithm='full', map=False): r""" Simplify rational expressions. @@ -11604,7 +11604,7 @@ cdef class Expression(Expression_abc): log_simplify = simplify_log - def expand_log(self,algorithm='products'): + def expand_log(self, algorithm='products'): r""" Simplify symbolic expression, which can contain logs. diff --git a/src/sage/symbolic/function.pyx b/src/sage/symbolic/function.pyx index 362d01ea297..86860237d5b 100644 --- a/src/sage/symbolic/function.pyx +++ b/src/sage/symbolic/function.pyx @@ -1294,7 +1294,7 @@ cdef class SymbolicFunction(Function): sage: t(x, y) foo(x, y) - sage: def ev(self, x,y): return 2*x + sage: def ev(self, x, y): return 2*x sage: foo = function("foo", nargs=2, eval_func=ev) # needs sage.symbolic sage: foo.__getstate__() # needs sage.symbolic (2, 'foo', 2, None, {}, True, diff --git a/src/sage/symbolic/function_factory.py b/src/sage/symbolic/function_factory.py index 057d1e07811..1918e166443 100644 --- a/src/sage/symbolic/function_factory.py +++ b/src/sage/symbolic/function_factory.py @@ -270,7 +270,7 @@ def function(s, **kwds) -> SymbolicFunction | list[SymbolicFunction]: sage: foo(x).conjugate() 2*x - sage: def deriv(self, *args,**kwds): + sage: def deriv(self, *args, **kwds): ....: print("{} {}".format(args, kwds)) ....: return args[kwds['diff_param']]^2 sage: foo = function("foo", nargs=2, derivative_func=deriv) diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx index 32afe8d3a62..65fccee5324 100644 --- a/src/sage/symbolic/ring.pyx +++ b/src/sage/symbolic/ring.pyx @@ -675,7 +675,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing): Simple definition of a functional derivative:: - sage: def functional_derivative(expr,f,x): + sage: def functional_derivative(expr, f, x): ....: with SR.temp_var() as a: ....: return expr.subs({f(x):a}).diff(a).subs({a:f(x)}) sage: f = function('f') @@ -686,7 +686,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing): Contrast this to a similar implementation using SR.var(), which gives a wrong result in our example:: - sage: def functional_derivative(expr,f,x): + sage: def functional_derivative(expr, f, x): ....: a = SR.var('a') ....: return expr.subs({f(x):a}).diff(a).subs({a:f(x)}) sage: f = function('f') diff --git a/src/sage/tensor/modules/tensor_with_indices.py b/src/sage/tensor/modules/tensor_with_indices.py index e65277935a7..be7c88a859c 100644 --- a/src/sage/tensor/modules/tensor_with_indices.py +++ b/src/sage/tensor/modules/tensor_with_indices.py @@ -937,7 +937,7 @@ def permute_indices(self, permutation): swap_params = list(combinations(range(self._tensor.tensor_rank()+1), 3)) # The associated permutation is as follows - def swap(param,N): + def swap(param, N): i,j,k = param L = list(range(1,N+1)) L = L[:i] + L[j:k] + L[i:j] + L[k:] diff --git a/src/sage/tests/book_schilling_zabrocki_kschur_primer.py b/src/sage/tests/book_schilling_zabrocki_kschur_primer.py index 69f1e2a1dca..2358c98039d 100644 --- a/src/sage/tests/book_schilling_zabrocki_kschur_primer.py +++ b/src/sage/tests/book_schilling_zabrocki_kschur_primer.py @@ -384,9 +384,9 @@ Sage example in ./kschurnotes/notes-mike-anne.tex, line 2487:: sage: Sym = SymmetricFunctions(QQ) - sage: ks = Sym.kschur(3,t=1) + sage: ks = Sym.kschur(3, t=1) sage: h = Sym.homogeneous() - sage: for mu in Partitions(7, max_part =3): + sage: for mu in Partitions(7, max_part=3): ....: print(h(ks(mu))) h[3, 3, 1] h[3, 2, 2] - h[3, 3, 1] diff --git a/src/sage/tests/book_stein_ent.py b/src/sage/tests/book_stein_ent.py index a4b7632705f..970b377e962 100644 --- a/src/sage/tests/book_stein_ent.py +++ b/src/sage/tests/book_stein_ent.py @@ -206,9 +206,9 @@ ....: if gcd(e,phi_n) == 1: break ....: d = lift(Mod(e,phi_n)^(-1)) ....: return e, d, n -sage: def encrypt(m,e,n): +sage: def encrypt(m, e, n): ....: return lift(Mod(m,n)^e) -sage: def decrypt(c,d,n): +sage: def decrypt(c, d, n): ....: return lift(Mod(c,n)^d) sage: e,d,n = rsa(20) sage: c = encrypt(123, e, n) @@ -348,7 +348,7 @@ 1 sage: 1/zeta -zeta^3 - zeta^2 - zeta - 1 -sage: def gauss_sum(a,p): +sage: def gauss_sum(a, p): ....: K. = CyclotomicField(p) ....: return sum(legendre_symbol(n,p) * zeta^(a*n) for n in range(1,p)) sage: g2 = gauss_sum(2,5); g2 @@ -527,7 +527,7 @@ ....: y3^2 - (x3^3 + a*x3 + b)] ... sage: Q = R.quotient(rels) -sage: def op(P1,P2): +sage: def op(P1, P2): ....: x1,y1 = P1; x2,y2 = P2 ....: lam = (y1 - y2)/(x1 - x2); nu = y1 - lam*x1 ....: x3 = lam^2 - x1 - x2; y3 = -lam*x3 - nu diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/combinat_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/combinat_doctest.py index 08a76fd6dfb..aaa1ef87842 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/combinat_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/combinat_doctest.py @@ -704,7 +704,7 @@ Sage example in ./combinat.tex, line 2130:: - sage: def words(alphabet,l): + sage: def words(alphabet, l): ....: if l == 0: yield [] ....: else: ....: for word in words(alphabet, l-1): diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/float_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/float_doctest.py index 7b6587ecaf6..e283c56c74b 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/float_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/float_doctest.py @@ -188,7 +188,7 @@ Sage example in ./float.tex, line 1072:: - sage: def iter(y,delta,a,n): + sage: def iter(y, delta, a, n): ....: for i in range(0,n): ....: y += delta ....: delta *= a @@ -196,7 +196,7 @@ Sage example in ./float.tex, line 1087:: - sage: def exact(y,delta,a,n): + sage: def exact(y, delta, a, n): ....: return y+delta*(1-a^n)/(1-a) Sage example in ./float.tex, line 1106:: @@ -209,7 +209,7 @@ Sage example in ./float.tex, line 1128:: - sage: def sumcomp(y,delta,e,n,a): + sage: def sumcomp(y, delta, e, n, a): ....: for i in range(0,n): ....: b = y ....: e += delta @@ -357,7 +357,7 @@ Sage example in ./float.tex, line 1975:: - sage: def bisect(funct,x,tol,zeros): + sage: def bisect(funct, x, tol, zeros): ....: if 0 in funct(x): ....: if x.diameter()>tol: ....: x1,x2 = x.bisection() @@ -388,7 +388,7 @@ Sage example in ./float.tex, line 2022:: - sage: def NearlySingularMatrix(R,n): + sage: def NearlySingularMatrix(R, n): ....: M=matrix(R,n,n) ....: for i in range(0,n): ....: for j in range(0,n): @@ -408,7 +408,7 @@ Sage example in ./float.tex, line 2064:: - sage: def tryDet(R,n): + sage: def tryDet(R, n): ....: p = 53 ....: z = True ....: while z: diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/graphique_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/graphique_doctest.py index 0e79bd37093..8de427630d4 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/graphique_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/graphique_doctest.py @@ -153,7 +153,7 @@ sage: n = 11; L = srange(6, 18, 12 / n); R = srange(3, 9, 6 / n) sage: CI = list(zip(L, R)) # list of initial conditions - sage: def g(x,y): + sage: def g(x, y): ....: v = vector(dX_dt([x, y])) # for a nicer graph, we ....: return v/v.norm() # normalise the vector field sage: x, y = var('x, y') diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/integration_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/integration_doctest.py index bf0bb747282..5bcd8aa9de6 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/integration_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/integration_doctest.py @@ -226,12 +226,12 @@ Sage example in ./integration.tex, line 1244:: - sage: def f_1(t,y,params): return [y[1],params[0]*(1-y[0]^2)*y[1]-y[0]] + sage: def f_1(t, y, params): return [y[1],params[0]*(1-y[0]^2)*y[1]-y[0]] sage: T.function = f_1 Sage example in ./integration.tex, line 1266:: - sage: def j_1(t,y,params): + sage: def j_1(t, y, params): ....: return [[0, 1], ....: [-2*params[0]*y[0]*y[1]-1, params[0]*(1-y[0]^2)], ....: [0,0]] diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py index e5f90964e0c..00bcd8136a9 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/linsolve_doctest.py @@ -280,7 +280,7 @@ Sage example in ./linsolve.tex, line 2124:: - sage: def eval(P,x): + sage: def eval(P, x): ....: if len(P) == 0: ....: return 0 ....: else: @@ -288,12 +288,12 @@ Sage example in ./linsolve.tex, line 2133:: - sage: def pscal(P,Q,lx): + sage: def pscal(P, Q, lx): ....: return float(sum(eval(P,s)*eval(Q,s) for s in lx)) Sage example in ./linsolve.tex, line 2139:: - sage: def padd(P,a,Q): + sage: def padd(P, a, Q): ....: for i in range(0,len(Q)): ....: P[i] += a*Q[i] @@ -309,7 +309,7 @@ Sage example in ./linsolve.tex, line 2160:: - sage: def orthopoly(n,x): + sage: def orthopoly(n, x): ....: if n > len(x): ....: raise BadParamsforOrthop(n, len(x)) ....: orth = [[1./sqrt(float(len(x)))]] @@ -384,7 +384,7 @@ sage: from numpy.linalg import * sage: from numpy import array sage: from numpy.random import rand - sage: def power(A,x,N): # power iteration + sage: def power(A, x, N): # power iteration ....: for i in range(N): ....: y = A*x ....: z = y/norm(y) diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/numbertheory_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/numbertheory_doctest.py index c167763ae2c..486065812a9 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/numbertheory_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/numbertheory_doctest.py @@ -98,7 +98,7 @@ Sage example in ./numbertheory.tex, line 593:: - sage: def harmonic_mod(n,m): + sage: def harmonic_mod(n, m): ....: return add([1/x % m for x in range(1,n+1)]) sage: def harmonic2(n): ....: q = lcm(range(1,n+1)) diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/recequadiff_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/recequadiff_doctest.py index 8ac271ac7ca..97d2adb5c7a 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/recequadiff_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/recequadiff_doctest.py @@ -340,7 +340,7 @@ Sage example in ./recequadiff.tex, line 1582:: - sage: def cloud(u,n): + sage: def cloud(u, n): ....: L = [[0,u(0)]]; ....: for k in [1..n]: ....: L += [[k,u(k)]] @@ -352,7 +352,7 @@ Sage example in ./recequadiff.tex, line 1619:: - sage: def snail(f,x,u0,n,xmin,xmax): + sage: def snail(f, x, u0, n, xmin, xmax): ....: u = u0 ....: P = plot(x, x, xmin, xmax, color='gray') ....: for i in range(n): diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/float_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/float_doctest.py index ebec4373196..e762e6d2ca0 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/float_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/float_doctest.py @@ -75,7 +75,7 @@ Sage example in ./sol/float.tex, line 179:: - sage: def recur(x1,x0): + sage: def recur(x1, x0): ....: return 111 - 1130/x1 + 3000/(x0*x1) Sage example in ./sol/float.tex, line 190:: diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphique_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphique_doctest.py index 4871ae52f98..a999cc1fdf8 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphique_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphique_doctest.py @@ -61,7 +61,7 @@ Sage example in ./sol/graphique.tex, line 154:: sage: n = 10; L = srange(6, 18, 12 / n); R = srange(3, 9, 6 / n) - sage: def g(x,y): v = vector(f(x, y)); return v / v.norm() + sage: def g(x, y): v = vector(f(x, y)); return v / v.norm() sage: q = plot_vector_field(g(x, y), (x, 0, 60), (y, 0, 36)) sage: for j in range(n): ....: P = desolve_system_rk4(f(x,y), [x,y], @@ -76,7 +76,7 @@ sage: def dX_dt(X, t=0): return [X[1], 0.5*X[1] - X[0] - X[1]^3] sage: t = srange(0, 40, 0.01); x0 = srange(-2, 2, 0.1); y0 = 2.5 sage: CI = [[i, y0] for i in x0] + [[i, -y0] for i in x0] - sage: def g(x,y): v = vector(dX_dt([x, y])); return v / v.norm() + sage: def g(x, y): v = vector(dX_dt([x, y])); return v / v.norm() sage: x, y = var('x, y'); n = len(CI) sage: q = plot_vector_field(g(x, y), (x, -3, 3), (y, -y0, y0)) sage: for j in range(n): # long time diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphtheory_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphtheory_doctest.py index f32f65028af..d6e3834c495 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphtheory_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/graphtheory_doctest.py @@ -9,7 +9,7 @@ Sage example in ./sol/graphtheory.tex, line 5:: - sage: def circulant(n,d): + sage: def circulant(n, d): ....: g = Graph(n) ....: for u in range(n): ....: for c in range(d): @@ -18,7 +18,7 @@ Sage example in ./sol/graphtheory.tex, line 19:: - sage: def kneser(n,k): + sage: def kneser(n, k): ....: g = Graph() ....: g.add_vertices(Subsets(n,k)) ....: for u in g: @@ -29,7 +29,7 @@ Sage example in ./sol/graphtheory.tex, line 33:: - sage: def kneser(n,k): + sage: def kneser(n, k): ....: g = Graph() ....: sommets = Set(range(n)) ....: g.add_vertices(Subsets(sommets,k)) diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/nonlinear_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/nonlinear_doctest.py index a296d48d995..50bd9fd2d2f 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/nonlinear_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/nonlinear_doctest.py @@ -38,7 +38,7 @@ sage: from types import GeneratorType, FunctionType sage: def checklength(u, v, w, prec): ....: return abs(v - u) < 2 * prec - sage: def iterate(series,check=checklength,prec=10^-5,maxit=100): + sage: def iterate(series, check=checklength, prec=10^-5, maxit=100): ....: assert isinstance(series, GeneratorType) ....: assert isinstance(check, FunctionType) ....: niter = 2 diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/numbertheory_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/numbertheory_doctest.py index 3899766500d..8d4536d89a6 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/sol/numbertheory_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/sol/numbertheory_doctest.py @@ -26,7 +26,7 @@ Sage example in ./sol/numbertheory.tex, line 52:: - sage: def enum_carmichael_pq(n,a,m,p,q,verbose): + sage: def enum_carmichael_pq(n, a, m, p, q, verbose): ....: if (a-q) % gcd(m,q*(q-1)) != 0: return 0 ....: s = 0 ....: a = crt (a, q, m, q*(q-1)); m = lcm(m,q*(q-1))