sagemathgh-38907: Format function headers around = and ,

    
A PEP8 sweep mostly of function headers around equal signs and commas.

An illustration of the type of changes:
From
```
def f(x = 0,y):
```
to
```
def f(x=0, y):
```

I am in the awkward position of announcing the abundance of such
PEP8-malformations, thousands of which remain in functions calls. I may
do a follow-up PR addressing those.
    
URL: sagemath#38907
Reported by: gmou3
Reviewer(s): Martin Rubey

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``.
 

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):

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`.
 

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 \

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`.
 

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)`.
 

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``.
 

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):
         ...

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

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

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`

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()):

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)

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}

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
         ....:

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::
 

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]]])

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):
             """

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

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.

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

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.
 

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.

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::

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'>

src/sage/categories/morphism.pyx

@@ -619,7 +619,7 @@ cdef class SetMorphism(Morphism):
 
             sage: from sage.categories.morphism import SetMorphism
             sage: R.<x> = 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)