Merge pull request #27 from RafaelDavidMohr/f5

Adds tests for `sig_groebner_basis`

Author: ederc

src/siggb/linear_algebra.jl

@@ -100,7 +100,6 @@ function echelonize!(matrix::MacaulayMatrix,
     if !iszero(arit_ops)
         @info "$(arit_ops) submul's"
     end
-    @assert is_triangular(matrix)
 end
 
 # subtract mult

src/siggb/siggb.jl

@@ -63,7 +63,7 @@ function sig_groebner_basis(sys::Vector{T}; info_level::Int=0, degbound::Int=0)
     Rchar = characteristic(R)
 
     # check if input is ok
-    if Rchar > 2^31
+    if Rchar > 2^31 || iszero(Rchar)
         error("At the moment we only support finite fields up to prime characteristic < 2^31.")
     end
     sysl = length(sys)
@@ -242,3 +242,15 @@ function _homogenize(F::Vector{P}) where {P <: MPolyRingElem}
     end
     return res
 end
+
+# test against msolve
+function _is_gb(gb::Vector{Tuple{Tuple{Int, P}, P}}) where {P <: MPolyRingElem}
+    gb_pols = [p[2] for p in gb]
+    gb_msolve = groebner_basis(Ideal(gb_pols), complete_reduction = true)
+    
+    lms_gb = (Nemo.leading_monomial).(gb_pols)
+    lms_msolve = (Nemo.leading_monomial).(gb_msolve)
+    res1 = all(u -> any(v -> divides(u, v)[1], lms_gb), lms_msolve)
+    res2 = all(u -> any(v -> divides(u, v)[1], lms_msolve), lms_gb)
+    return res1 && res2
+end

src/siggb/symbolic_pp.jl

@@ -110,14 +110,14 @@ function select_normal!(pairset::Pairset{N},
 
                 add_cond = !iszero(reducer_ind)
                 if add_cond
-                    resize_pivots!(matrix, symbol_ht)
                     mult = divide(monomial(reducer_sig),
                                   monomial(basis.sigs[reducer_ind]))
                     lead_idx = write_to_matrix_row!(matrix, basis,
                                                     reducer_ind,
                                                     symbol_ht, ht, mult,
                                                     reducer_sig)
                     # set pivot
+                    resize_pivots!(matrix, symbol_ht)
                     matrix.pivots[lead_idx] = matrix.nrows
                 end
             end

test/algorithms/groebner-bases.jl

@@ -26,3 +26,32 @@
     @test L == H
     @test I.gb[2] == H
 end
+
+@testset "Algorithms -> Sig Gröbner bases" begin
+    R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex)
+    F = [x^2+1-3, x*y-z, x*z^2-3*y^2]
+    #= not a finite field =#
+    @test_throws ErrorException sig_groebner_basis(F)
+    R, (x,y,z) = polynomial_ring(GF(17),["x","y","z"], ordering=:degrevlex)
+    F = [x^2+1-3, x*y-z, x*z^2-3*y^2]
+    #= not homogeneous =#
+    @test_throws ErrorException sig_groebner_basis(F)
+
+    #= GB test 1 =#
+    Fhom = AlgebraicSolving._homogenize(F)
+    sgb = sig_groebner_basis(Fhom)
+    @test AlgebraicSolving._is_gb(sgb)
+
+    #= GB test 2 =#
+    R, (x,y,z,w) = polynomial_ring(GF(65521),["x","y","z","w"], ordering=:degrevlex)
+    F = cyclic(R).gens
+    Fhom = AlgebraicSolving._homogenize(F)
+    sgb = sig_groebner_basis(Fhom)
+    @test AlgebraicSolving._is_gb(sgb)
+
+    #= GB test 3 =#
+    F = katsura(R).gens
+    Fhom = AlgebraicSolving._homogenize(F)
+    sgb = sig_groebner_basis(Fhom)
+    @test AlgebraicSolving._is_gb(sgb)
+end