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 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()
def _contains(self, x):
from diofant.polys.distributedmodules import sdm_zero, sdm_nf_mora
return sdm_nf_mora(self.ring._vector_to_sdm(x, self.order),
self._groebner(), self.order, self.ring.domain) == \
sdm_zero()