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 _vector_to_sdm_helper(v, order):
"""Helper method for common code in Global and Local poly rings."""
from diofant.polys.distributedmodules import sdm_from_dict
d = {}
for i, e in enumerate(v):
for key, value in e.to_dict().items():
d[(i,) + key] = value
return sdm_from_dict(d, order)
def test_sdm_from_dict():
dic = {
(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)
}
assert sdm_from_dict(dic, grlex) == \
[((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))]
def test_sdm_LT():
dic = {(1, 2, 3): QQ(1), (4, 0, 0): QQ(2), (4, 0, 1): QQ(3)}
assert sdm_LT(sdm_from_dict(dic, lex)) == ((4, 0, 1), QQ(3))
def test_sdm_LM():
dic = {(1, 2, 3): QQ(1), (4, 0, 0): QQ(1), (4, 0, 1): QQ(1)}
assert sdm_LM(sdm_from_dict(dic, lex)) == (4, 0, 1)