def test_sdm_nf_mora(): f = sdm_from_dict({(1, 2, 1, 1): QQ(1), (1, 1, 2, 1): QQ(1), (1, 0, 2, 1): QQ(1), (1, 0, 0, 3): QQ(1), (1, 1, 1, 0): QQ(1)}, grlex) f1 = sdm_from_dict({(1, 1, 1, 0): QQ(1), (1, 0, 2, 0): QQ(1), (1, 0, 0, 0): QQ(-1)}, grlex) f2 = sdm_from_dict({(1, 1, 1, 0): QQ(1)}, grlex) (id0, id1, id2) = [sdm_from_dict({(i, 0, 0, 0): QQ(1)}, grlex) for i in range(3)] assert sdm_nf_mora(f, [f1, f2], grlex, QQ, phantom=(id0, [id1, id2])) == \ ([((1, 0, 2, 1), QQ(1)), ((1, 0, 0, 3), QQ(1)), ((1, 1, 1, 0), QQ(1)), ((1, 1, 0, 1), QQ(1))], [((1, 1, 0, 1), QQ(-1)), ((0, 0, 0, 0), QQ(1))]) assert sdm_nf_mora(f, [f2, f1], grlex, QQ, phantom=(id0, [id2, id1])) == \ ([((1, 0, 2, 1), QQ(1)), ((1, 0, 0, 3), QQ(1)), ((1, 1, 1, 0), QQ(1))], [((2, 1, 0, 1), QQ(-1)), ((2, 0, 1, 1), QQ(-1)), ((0, 0, 0, 0), QQ(1))]) f = sdm_from_vector([x*z, y**2 + y*z - z, y], lex, QQ, gens=[x, y, z]) f1 = sdm_from_vector([x, y, 1], lex, QQ, gens=[x, y, z]) f2 = sdm_from_vector([x*y, z, z**2], lex, QQ, gens=[x, y, z]) assert sdm_nf_mora(f, [f1, f2], lex, QQ) == \ sdm_nf_mora(f, [f2, f1], lex, QQ) == \ [((1, 0, 1, 1), QQ(1)), ((1, 0, 0, 1), QQ(-1)), ((0, 1, 1, 0), QQ(-1)), ((0, 1, 0, 1), QQ(1))]
def test_uncovered_line(): gens = [x, y] f1 = sdm_zero() f2 = sdm_from_vector([x, 0], lex, QQ, gens=gens) f3 = sdm_from_vector([0, y], lex, QQ, gens=gens) assert sdm_spoly(f1, f2, lex, QQ) == sdm_zero() assert sdm_spoly(f3, f2, lex, QQ) == sdm_zero()
def test_conversion(): f = [x**2 + y**2, 2*z] g = [((1, 0, 0, 1), QQ(2)), ((0, 2, 0, 0), QQ(1)), ((0, 0, 2, 0), QQ(1))] assert sdm_to_vector(g, [x, y, z], QQ) == f assert sdm_from_vector(f, lex, QQ) == g assert sdm_from_vector( [x, 1], lex, QQ) == [((1, 0), QQ(1)), ((0, 1), QQ(1))] assert sdm_to_vector([((1, 1, 0, 0), 1)], [x, y, z], QQ, n=3) == [0, x, 0] assert sdm_from_vector([0, 0], lex, QQ, gens=[x, y]) == sdm_zero()
def test_chain_criterion(): gens = [x] f1 = sdm_from_vector([1, x], grlex, QQ, gens=gens) f2 = sdm_from_vector([0, x - 2], grlex, QQ, gens=gens) assert len(sdm_groebner([f1, f2], sdm_nf_mora, grlex, QQ)) == 2
def contains(I, f): S = [sdm_from_vector([g], igrlex, QQ, gens=gens) for g in I] G = sdm_groebner(S, sdm_nf_mora, igrlex, QQ) return sdm_nf_mora(sdm_from_vector([f], lex, QQ, gens=gens), G, lex, QQ) == sdm_zero()