def _groebner(self, extended=False):
"""Returns a standard basis in sdm form."""
from diofant.polys.distributedmodules import sdm_groebner, sdm_nf_mora
if self._gbe is None and extended:
gb, gbe = sdm_groebner(
[self.ring._vector_to_sdm(x, self.order) for x in self.gens],
sdm_nf_mora,
self.order,
self.ring.domain,
extended=True)
self._gb, self._gbe = tuple(gb), tuple(gbe)
if self._gb is None:
self._gb = tuple(
sdm_groebner([
self.ring._vector_to_sdm(x, self.order) for x in self.gens
], sdm_nf_mora, self.order, self.ring.domain))
if extended:
return self._gb, self._gbe
else:
return self._gb
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()