From 6491bc4a3662662eab6878d39c941aa03b2d4be6 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 13 Nov 2024 18:40:46 +0100
Subject: [PATCH 01/11] fix conversion of module orderings from Oscar to
 Singular

---
 src/Rings/orderings.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Rings/orderings.jl b/src/Rings/orderings.jl
index 6f4ab817af08..7b6b18371a2e 100644
--- a/src/Rings/orderings.jl
+++ b/src/Rings/orderings.jl
@@ -2154,8 +2154,8 @@ function _try_singular_easy(Q::order_conversion_ctx, o::Orderings.ModOrdering)
   Q.has_c_or_C && return (false, Q.def)
   Q.has_c_or_C = true
   o.gens == 1:length(o.gens) || return (false, Q.def)
-  return o.ord == :lex    ? (true, Singular.ordering_C(length(o.gens))) :
-         o.ord == :invlex ? (true, Singular.ordering_c(length(o.gens))) :
+  return o.ord == :lex    ? (true, Singular.ordering_c(length(o.gens))) :
+         o.ord == :invlex ? (true, Singular.ordering_C(length(o.gens))) :
                             (false, Q.def)
 end
 

From 557b1856742458a091a702a84ee2e9a80256cf78 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Thu, 14 Nov 2024 09:02:03 +0100
Subject: [PATCH 02/11] added Test

---
 test/Modules/UngradedModules.jl | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/test/Modules/UngradedModules.jl b/test/Modules/UngradedModules.jl
index dc7223e275c7..468cd27cd63e 100644
--- a/test/Modules/UngradedModules.jl
+++ b/test/Modules/UngradedModules.jl
@@ -431,6 +431,29 @@ end
   @test_throws ArgumentError groebner_basis(M)
 end
 
+#issue 4303
+@testset "module ordering conversion to Singular" begin
+  R, (x,y) = polynomial_ring(QQ, [:x, :y])
+  F = free_module(R, 4)
+  g = F[1] + x*F[2] + x*F[3] + F[4]
+  M = SubquoModule(F, [g])
+  
+  ord = lex(F)*deglex(R)
+  @test leading_term(g, ordering=ord) == F[1]              #ordering is applied in Oscar
+  @test leading_module(M, ord) == SubquoModule(F, [F[1]])  #ordering is applied after conversion to Singular
+
+  ord = deglex(R)*lex(F)
+  @test leading_term(g, ordering=ord) == x*F[2]              
+  @test leading_module(M, ord) == SubquoModule(F, [x*F[2]])
+
+  ord = deglex(R)*invlex(F)
+  @test leading_term(g, ordering=ord) == x*F[3]              
+  @test leading_module(M, ord) == SubquoModule(F, [x*F[3]])
+  
+  ord = invlex(F)*deglex(R)
+  @test leading_term(g, ordering=ord) == F[4]              
+  @test leading_module(M, ord) == SubquoModule(F, [F[4]])
+end
 
 @testset "Test kernel" begin
   Oscar.set_seed!(235)

From 478e95d8c2965415b7fd608b1f13d67341248ebe Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 20 Nov 2024 22:01:04 +0100
Subject: [PATCH 03/11] experimenting

Changed default ModuleOrdering to match the default ordering on the Singular side
---
 src/Modules/UngradedModules/Methods.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Modules/UngradedModules/Methods.jl b/src/Modules/UngradedModules/Methods.jl
index 822b9036ea85..30f06b810f03 100644
--- a/src/Modules/UngradedModules/Methods.jl
+++ b/src/Modules/UngradedModules/Methods.jl
@@ -233,9 +233,9 @@ ring_map(f::SubQuoHom) = f.ring_map
 function default_ordering(F::FreeMod)
   if !isdefined(F, :default_ordering)
     if iszero(F)
-      F.default_ordering = default_ordering(base_ring(F))*ModuleOrdering(F, Orderings.ModOrdering(Vector{Int}(), :lex))
+      F.default_ordering = default_ordering(base_ring(F))*ModuleOrdering(F, Orderings.ModOrdering(Vector{Int}(), :invlex))
     else
-      F.default_ordering = default_ordering(base_ring(F))*lex(gens(F))
+      F.default_ordering = default_ordering(base_ring(F))*invlex(gens(F))
     end
   end
   return F.default_ordering::ModuleOrdering{typeof(F)}

From d80a5d3e68bc090728bc63652a9d654b11ecb5cc Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 20 Nov 2024 22:30:46 +0100
Subject: [PATCH 04/11] Fixed wrong conversion test for ModuleOrderings

---
 test/Rings/orderings.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/Rings/orderings.jl b/test/Rings/orderings.jl
index 8fac041a8e28..c47a081dc195 100644
--- a/test/Rings/orderings.jl
+++ b/test/Rings/orderings.jl
@@ -360,14 +360,14 @@ end
    O5 = invlex(gens(K))*degrevlex(gens(R))
    @test monomial_ordering(R, singular(O5)) == degrevlex(gens(R))
    @test length(string(O5)) > 2
-   @test string(singular(O5)) == "ordering_c() * ordering_dp(5)"
+   @test string(singular(O5)) == "ordering_C() * ordering_dp(5)"
 
    a = matrix_ordering([x, y], matrix(ZZ, 2, 2, [1 2; 3 4]))
    b = wdeglex([s, t, u], [1, 2, 3])
    O6 = a * lex(gens(K)) * b
    @test monomial_ordering(R, singular(O6)) == a * b
    @test length(string(O6)) > 2
-   @test string(singular(O6)) == "ordering_M([1 2; 3 4]) * ordering_C() * ordering_Wp([1, 2, 3])"
+   @test string(singular(O6)) == "ordering_M([1 2; 3 4]) * ordering_c() * ordering_Wp([1, 2, 3])"
 
    O7 = weight_ordering([-1,2,0,2,0], degrevlex(gens(R)))
    @test monomial_ordering(R, singular(O7)) == O7

From 57af1da4babb89154c2fe38797c261e194d0c930 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 20 Nov 2024 22:38:32 +0100
Subject: [PATCH 05/11] adapt doctest to experimenting

---
 docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
index 382c07afd0fc..f7109041e8d3 100644
--- a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
+++ b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
@@ -70,7 +70,7 @@ julia> F = free_module(R, 2)
 Free module of rank 2 over R
 
 julia> default_ordering(F)
-degrevlex([x, y, z])*lex([gen(1), gen(2)])
+degrevlex([x, y, z])*invlex([gen(1), gen(2)])
 
 julia> S, _ = grade(R, [1, 2, 3])
 (Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])

From 64e3048d6b1194b1970ab7f0d5bf7f4d90b6b67f Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 20 Nov 2024 23:38:54 +0100
Subject: [PATCH 06/11] adapt doctest to experimenting part 2

---
 docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
index f7109041e8d3..53689f4f121c 100644
--- a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
+++ b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
@@ -153,7 +153,7 @@ julia> f = (5*x*y^2-y^10+3)*F[1]+(4*x^3+2*y) *F[2]+16*x*F[3]
 (5*x*y^2 - y^10 + 3)*e[1] + (4*x^3 + 2*y)*e[2] + 16*x*e[3]
 
 julia> default_ordering(F)
-degrevlex([x, y])*lex([gen(1), gen(2), gen(3)])
+degrevlex([x, y])*invlex([gen(1), gen(2), gen(3)])
 
 julia> collect(terms(f))
 6-element Vector{FreeModElem{QQMPolyRingElem}}:

From c3f29bb8a8dc5ee1034579d259776599f9916565 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Fri, 22 Nov 2024 10:25:41 +0100
Subject: [PATCH 07/11] Fixes minimal_generating_set

---
 src/Rings/mpolyquo-localizations.jl       | 2 +-
 test/AlgebraicGeometry/Schemes/Tjurina.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 633652679a38..ecf76f2ac0ce 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -2510,7 +2510,7 @@ Note: This is only available for localizations at rational points.
   F = free_module(R, length(Jlist))
   Imax = ideal(R,gens(R))
   M = sub(F,[F(syz_mod[i]) for i=1:Singular.ngens(syz_mod)])[1] + (Imax*F)[1]
-  oF =  negdegrevlex(R)*invlex(F)
+  oF =  negdegrevlex(R)*lex(F)
   res_vec = typeof(gen(I,1))[]
 
   ## select by Nakayama
diff --git a/test/AlgebraicGeometry/Schemes/Tjurina.jl b/test/AlgebraicGeometry/Schemes/Tjurina.jl
index a9014b53b246..ef60b00817d5 100644
--- a/test/AlgebraicGeometry/Schemes/Tjurina.jl
+++ b/test/AlgebraicGeometry/Schemes/Tjurina.jl
@@ -194,7 +194,7 @@ end
   @test is_contact_equivalent(L(x^5+y^4), L(x^5*y^4-3*x^5+y^5-y^4))
   @test is_contact_equivalent(L(x^5+y^4), L(x^5-y^4))
   @test is_contact_equivalent(L(x*y), L(x^2-y^2*(x-3)))
-  @test is_contact_equivalent(L(x^5+y^2), L(x^2-(x-y)^5))
+  @test is_contact_equivalent(L(x^5+y^2), L(x^2-(x-y)^5))     # if this test fails minimal_generating_set could be broken
   
   ## pos. char.
   R, (x,y) = GF(5)[:x, :y]
@@ -223,7 +223,7 @@ end
   R, (x,y,z) = QQ[:x, :y, :z]
   L,_  = localization(R, complement_of_point_ideal(R, [0, 0, 0]))  
   @test is_contact_equivalent(zero(L), L(0//(x+1)))
-  @test is_contact_equivalent(L(x^2+y^2), L(y^2+z^2)) 
+  @test is_contact_equivalent(L(x^2+y^2), L(y^2+z^2))      # if this test fails minimal_generating_set is probably broken
   @test !is_contact_equivalent(L(z^2), L(x^2+y^2))
   @test !is_contact_equivalent(L(x^2+y^2), L(x^2+y^2-z^2))
 end

From df45b4c7c44d6899314a5fd924ad79bffac75ed7 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Fri, 22 Nov 2024 12:04:25 +0100
Subject: [PATCH 08/11] Adapted present_finite_extension_ring to conversion fix

---
 experimental/IntersectionTheory/src/blowup.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/experimental/IntersectionTheory/src/blowup.jl b/experimental/IntersectionTheory/src/blowup.jl
index d21404c040fc..31733da8ca62 100644
--- a/experimental/IntersectionTheory/src/blowup.jl
+++ b/experimental/IntersectionTheory/src/blowup.jl
@@ -207,7 +207,7 @@ function  present_finite_extension_ring(F::Oscar.AffAlgHom)
   gJ = elem_type(FM)[FM([j==i ? x : R() for j in 1:g]) for x in gens(V) for i in 1:g]
   U  = vcat(gB, gJ)
   S, _ = sub(FM, U)
-  P = groebner_basis(S, ordering = default_ordering(R)*lex(FM))
+  P = groebner_basis(S, ordering = default_ordering(R)*invlex(FM))
   Rw, _ = grade(R, vcat(repeat([1], b), repeat([0], a)))
   RtoRw = hom(R, Rw, gens(Rw))
   inA = x -> x == zero(Rw) ?  true : (degree(Int, leading_term(RtoRw(x)))) <= 0

From 6261b37b3ca59ec7b2b170bb5f7f348057cd2423 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Mon, 25 Nov 2024 11:19:48 +0100
Subject: [PATCH 09/11] Revert experimenting (default ordering for modules)

---
 docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md | 4 ++--
 src/Modules/UngradedModules/Methods.jl                      | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
index 53689f4f121c..382c07afd0fc 100644
--- a/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
+++ b/docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md
@@ -70,7 +70,7 @@ julia> F = free_module(R, 2)
 Free module of rank 2 over R
 
 julia> default_ordering(F)
-degrevlex([x, y, z])*invlex([gen(1), gen(2)])
+degrevlex([x, y, z])*lex([gen(1), gen(2)])
 
 julia> S, _ = grade(R, [1, 2, 3])
 (Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
@@ -153,7 +153,7 @@ julia> f = (5*x*y^2-y^10+3)*F[1]+(4*x^3+2*y) *F[2]+16*x*F[3]
 (5*x*y^2 - y^10 + 3)*e[1] + (4*x^3 + 2*y)*e[2] + 16*x*e[3]
 
 julia> default_ordering(F)
-degrevlex([x, y])*invlex([gen(1), gen(2), gen(3)])
+degrevlex([x, y])*lex([gen(1), gen(2), gen(3)])
 
 julia> collect(terms(f))
 6-element Vector{FreeModElem{QQMPolyRingElem}}:
diff --git a/src/Modules/UngradedModules/Methods.jl b/src/Modules/UngradedModules/Methods.jl
index 30f06b810f03..822b9036ea85 100644
--- a/src/Modules/UngradedModules/Methods.jl
+++ b/src/Modules/UngradedModules/Methods.jl
@@ -233,9 +233,9 @@ ring_map(f::SubQuoHom) = f.ring_map
 function default_ordering(F::FreeMod)
   if !isdefined(F, :default_ordering)
     if iszero(F)
-      F.default_ordering = default_ordering(base_ring(F))*ModuleOrdering(F, Orderings.ModOrdering(Vector{Int}(), :invlex))
+      F.default_ordering = default_ordering(base_ring(F))*ModuleOrdering(F, Orderings.ModOrdering(Vector{Int}(), :lex))
     else
-      F.default_ordering = default_ordering(base_ring(F))*invlex(gens(F))
+      F.default_ordering = default_ordering(base_ring(F))*lex(gens(F))
     end
   end
   return F.default_ordering::ModuleOrdering{typeof(F)}

From 4392c1daaf66979e8954cb70cc8bd1464adb3248 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 27 Nov 2024 10:21:58 +0100
Subject: [PATCH 10/11] Fix ordering conversion for free module over MPolyRing
 and MPolyDecRing

---
 src/Rings/mpoly-graded.jl | 5 ++++-
 src/Rings/mpoly.jl        | 9 ++++++---
 2 files changed, 10 insertions(+), 4 deletions(-)

diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl
index 40394f5d9b62..c7f6dd251f08 100644
--- a/src/Rings/mpoly-graded.jl
+++ b/src/Rings/mpoly-graded.jl
@@ -767,8 +767,11 @@ end
 end
 
 function singular_poly_ring(R::MPolyDecRing; keep_ordering::Bool = false)
+  @show "richtig verfolgt 1"
   if !keep_ordering
-    return singular_poly_ring(forget_decoration(R), default_ordering(R))
+    @show "richtig verfolgt 2"
+    return singular_poly_ring(forget_decoration(R), 
+    singular(default_ordering(R))*Singular.ordering_c())
   end
   return singular_poly_ring(forget_decoration(R); keep_ordering)
 end
diff --git a/src/Rings/mpoly.jl b/src/Rings/mpoly.jl
index ce2543562705..7f91f425d729 100644
--- a/src/Rings/mpoly.jl
+++ b/src/Rings/mpoly.jl
@@ -617,11 +617,13 @@ function singular_poly_ring(Rx::MPolyRing{T}; keep_ordering::Bool = false) where
   if keep_ordering
     return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)),
               _variables_for_singular(symbols(Rx)),
-              ordering = internal_ordering(Rx),
+              ordering = internal_ordering(Rx),              
+              ordering2 = :comp1max,
               cached = false)[1]
   else
     return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)),
               _variables_for_singular(symbols(Rx)),
+              ordering2 = :comp1max,
               cached = false)[1]
   end
 end
@@ -629,7 +631,8 @@ end
 function singular_poly_ring(Rx::MPolyRing{T}, ord::Symbol) where {T <: RingElem}
   return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)),
               _variables_for_singular(symbols(Rx)),
-              ordering = ord,
+              ordering = ord,              
+              ordering2 = :comp1max,
               cached = false)[1]
 end
 
@@ -643,7 +646,7 @@ end
 function singular_poly_ring(Rx::MPolyRing{T}, ord::MonomialOrdering) where {T <: RingElem}
   return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)),
               _variables_for_singular(symbols(Rx)),
-              ordering = singular(ord),
+              ordering = singular(ord)*Singular.ordering_c(),
               cached = false)[1]
 end
 

From 26fb5cae0d63e9e6d932d21d4dfae123d31b4f30 Mon Sep 17 00:00:00 2001
From: Syz-MS <125460956+Syz-MS@users.noreply.github.com>
Date: Wed, 27 Nov 2024 10:23:19 +0100
Subject: [PATCH 11/11] removed @show

---
 src/Rings/mpoly-graded.jl | 2 --
 1 file changed, 2 deletions(-)

diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl
index c7f6dd251f08..8798af5ff31a 100644
--- a/src/Rings/mpoly-graded.jl
+++ b/src/Rings/mpoly-graded.jl
@@ -767,9 +767,7 @@ end
 end
 
 function singular_poly_ring(R::MPolyDecRing; keep_ordering::Bool = false)
-  @show "richtig verfolgt 1"
   if !keep_ordering
-    @show "richtig verfolgt 2"
     return singular_poly_ring(forget_decoration(R), 
     singular(default_ordering(R))*Singular.ordering_c())
   end