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_sdm_zero():
assert sdm_zero() == []
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()