adds sgb tests

Author: RafaelDavidMohr

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

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