add divrem2 (#774)

* add divrem2 * Update src/ideal/ideal.jl Co-authored-by: ederc <ederc@mathematik.uni-kl.de> * Update src/ideal/ideal.jl Co-authored-by: ederc <ederc@mathematik.uni-kl.de> * compatibily * Update src/ideal/ideal.jl Co-authored-by: Max Horn <max@quendi.de> * Update test/ideal/sideal-test.jl Co-authored-by: Max Horn <max@quendi.de> * fix: test --------- Co-authored-by: ederc <ederc@mathematik.uni-kl.de> Co-authored-by: Max Horn <max@quendi.de>
oscar-system · Feb 13, 2024 · a7a0749 · a7a0749
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Showing 3 changed files with 26 additions and 3 deletions.
diff --git a/deps/src/ideals.cpp b/deps/src/ideals.cpp
@@ -473,9 +473,10 @@ void singular_define_ideals(jlcxx::Module & Singular)
  rChangeCurrRing(o);
  ideal factors;
  ideal unit;
- ideal res = idDivRem(sm, m, factors, &unit, flag);
+ ideal rest = idDivRem(m, sm, factors, &unit, flag);
+ rest->rank = m->rank;
  rChangeCurrRing(origin);
- return std::make_tuple(res, factors, unit);
+ return std::make_tuple(rest,factors, unit);
  });
 
  Singular.method("id_Lift", [](ideal m, ideal sm, ring o) {

diff --git a/src/ideal/ideal.jl b/src/ideal/ideal.jl
@@ -5,7 +5,7 @@ export sideal, IdealSet, syz, lead, normalize!, is_constant, is_zerodim, fglm,
  intersection, homogenize_ideal, homogenize_ideal_with_weights,
  quotient, reduce, eliminate, kernel, equal, contains, is_var_generated,
  saturation, saturation2, satstd, slimgb, std, vdim, interreduce, degree, mult,
- hilbert_series, std_hilbert, is_homogeneous, division, divrem, mstd
+ hilbert_series, std_hilbert, is_homogeneous, division, divrem, divrem2, mstd
 
 ###############################################################################
 #
@@ -840,6 +840,25 @@ function divrem(I::sideal{S}, G::sideal{S}; complete_reduction::Bool = false) wh
  return (smodule{S}(R,ptr_T), sideal{S}(R,ptr_Rest), smodule{S}(R,ptr_U))
 end
 
+@doc raw"""
+ divrem2(I::sideal{S}, G::sideal{S}; complete_reduction::Bool = false) where S <: SPolyUnion
+
+Computes a normal form of the generators of `I` by the generators of `G`,
+keeping track of the reduction. Returns a tuple (Quo, Rem, U) where
+`Matrix(I)*Matrix(U) = Matrix(G)*Matrix(Quo) + Matrix(Rem)`
+and `Rem = reduce(I, G; complete_reduction)`. `U` is a diagonal matrix of units differing
+from the identity matrix only for local monomial orderings.
+Leading terms of `Matrix(G)*Matrix(Quo)` are less or equal to the corresponding terms of `I`.
+No term of `Rem` is divisible by any leading term of `G`.
+`divrem2` is identical to `divrem` if G is given by a Groebner basis.
+"""
+function divrem2(I::sideal{S}, G::sideal{S}; complete_reduction::Bool = false) where S <: SPolyUnion
+ check_parent(I, G)
+ R = base_ring(I)
+ ptr_Rest,ptr_T,ptr_U = GC.@preserve I G R libSingular.id_DivRem_Unit(I.ptr, G.ptr, R.ptr, 0)
+ return (smodule{S}(R,ptr_T), sideal{S}(R,ptr_Rest),smodule{S}(R,ptr_U))
+end
+
 ###############################################################################
 #
 # Eliminate

diff --git a/test/ideal/sideal-test.jl b/test/ideal/sideal-test.jl
@@ -713,4 +713,7 @@ end
  @test Singular.Matrix(a)*Singular.Matrix(u) == Singular.Matrix(b)*Singular.Matrix(q)+Singular.Matrix(r)
  @test gens(reduce(a, b, complete_reduction=false))[1] ==y^3+x*y
  @test gens(reduce(a, b, complete_reduction=true))[1] == y^3
+ q2,r2,u2 = divrem2(a, b)
+ @test Singular.Matrix(a)*Singular.Matrix(u2) == Singular.Matrix(b)*Singular.Matrix(q2)+Singular.Matrix(r2)
+ @test isequal(r2, reduce(a, b))
 end