first small step in fixing the orderings

src/Modules/missing_functionality.jl

@@ -42,7 +42,7 @@ function lift(f::MPolyElem, I::MPolyIdeal, o::MonomialOrdering)
   iszero(f) && return zero(MatrixSpace(base_ring(I), 1, ngens(I)))
   R = parent(f)
   R == base_ring(I) || error("polynomial does not belong to the base ring of the ideal")
-  Rsing = singular_poly_ring(R, o.o)
+  Rsing = singular_poly_ring(R, o)
   fsing = Singular.Ideal(Rsing, [Rsing(f)])
   gsing = Singular.Ideal(Rsing, Rsing.(gens(I)))
   a_s, rem_s, u_s = lift(gsing, fsing, false, false, false)

src/Rings/mpoly-graded.jl

@@ -780,7 +780,7 @@ end
 
 function singular_poly_ring(R::MPolyRing_dec; keep_ordering::Bool = false)
   if !keep_ordering
-    return singular_poly_ring(R.R, default_ordering(R).o)
+    return singular_poly_ring(R.R, default_ordering(R))
   end
   return singular_poly_ring(R.R, keep_ordering = keep_ordering)
 end

src/Rings/mpoly.jl

@@ -474,7 +474,7 @@ end
 singular(ord::MonomialOrdering) = singular(ord.o)
 singular(ord::ModuleOrdering) = singular(ord.o)
 
-function singular_poly_ring(Rx::MPolyRing{T}, ord::Orderings.AbsOrdering) where {T <: RingElem}
+function singular_poly_ring(Rx::MPolyRing{T}, ord::MonomialOrdering) where {T <: RingElem}
   return Singular.PolynomialRing(singular_coeff_ring(base_ring(Rx)),
               [string(x) for x = Nemo.symbols(Rx)],
               ordering = singular(ord),
@@ -571,7 +571,7 @@ end
 function singular_assure(I::BiPolyArray, ordering::MonomialOrdering)
     if !isdefined(I, :S) 
         I.ord = ordering.o
-        I.Sx = singular_poly_ring(I.Ox, ordering.o)
+        I.Sx = singular_poly_ring(I.Ox, ordering)
         I.S = Singular.Ideal(I.Sx, elem_type(I.Sx)[I.Sx(x) for x = I.O])
         if I.isGB
             I.S.isGB = true
@@ -581,7 +581,7 @@ function singular_assure(I::BiPolyArray, ordering::MonomialOrdering)
          = attached, thus we have to create a new singular ring and map the ideal. =#
         if !isdefined(I, :ord) || I.ord != ordering.o
             I.ord = ordering.o
-            SR    = singular_poly_ring(I.Ox, ordering.o)
+            SR    = singular_poly_ring(I.Ox, ordering)
             f     = Singular.AlgebraHomomorphism(I.Sx, SR, gens(SR))
             I.S   = Singular.map_ideal(f, I.S)
             I.Sx  = SR

src/Rings/orderings.jl

@@ -144,7 +144,7 @@ function weights(a::GenOrdering)
   end
   if a.ord == :negdeglex || a.ord == Symbol("Singular(Ds)")
     return [-matrix(ZZ, 1, length(a.vars), ones(fmpz, length(a.vars)));
-            -identity_matrix(ZZ, length(a.vars)-1) zero_matrix(ZZ, length(a.vars)-1, 1)]
+            identity_matrix(ZZ, length(a.vars)-1) zero_matrix(ZZ, length(a.vars)-1, 1)]
   end
   if a.ord == :negdegrevlex || a.ord == Symbol("Singular(ds)")
     return [-matrix(ZZ, 1, length(a.vars), ones(fmpz, length(a.vars))) ;
@@ -155,7 +155,7 @@ function weights(a::GenOrdering)
   end
   if a.ord == :negwdeglex || a.ord == Symbol("Singular(Ws)")
     return [-matrix(ZZ, 1, length(a.vars), a.w);
-            -identity_matrix(ZZ, length(a.vars)-1) zero_matrix(ZZ, length(a.vars)-1, 1)]
+            identity_matrix(ZZ, length(a.vars)-1) zero_matrix(ZZ, length(a.vars)-1, 1)]
   end
   if a.ord == :negwdegrevlex || a.ord == Symbol("Singular(ws)")
     return [-matrix(ZZ, 1, length(a.vars), a.w);

test/Rings/orderings-test.jl

@@ -87,6 +87,12 @@ end
    @test negdeglex([x, y, z]) == negwdeglex([x, y, z], [1, 1, 1])
    @test negdegrevlex([x, y, z]) == negwdegrevlex([x, y, z], [1, 1, 1])
    @test neglex([z])*neglex([y])*neglex([x]) == negrevlex([x, y, z])
+
+   m = matrix(ZZ, [-1 -1 -1; 1 0 0; 0 1 0; 0 0 1])
+   @test negdeglex(gens(R)) == matrix_ordering(gens(R), m)
+
+   m = matrix(ZZ, [-2 -3 -4; 1 0 0; 0 1 0; 0 0 1])
+   @test negwdeglex(gens(R), [2, 3, 4]) == matrix_ordering(gens(R), m)
  end
 
  @testset "Polynomial Orderings sorting" begin
@@ -110,7 +116,6 @@ end
    o = negrevlex([x1, x2])*wdegrevlex([x3, x4], [1, 2])
    @test collect(monomials(f, o)) == M
 
-   # currently fails
    M = [one(R), x3, x3^2, x4, x3^3, x3*x4, x3^2*x4, x4^2, x3*x4^2,
         x4^3, x2, x2*x3, x2*x3^2, x2*x4, x2*x3*x4, x2*x4^2, x2^2, x2^2*x3,
         x2^2*x4, x2^3, x1, x1*x3, x1*x3^2, x1*x4, x1*x3*x4, x1*x4^2, x1*x2,