def test_InverseOrder():
ilex = InverseOrder(lex)
igrlex = InverseOrder(grlex)
assert ilex((1, 2, 3)) > ilex((2, 0, 3))
assert igrlex((1, 2, 3)) < igrlex((0, 2, 3))
assert str(ilex) == "ilex"
assert str(igrlex) == "igrlex"
assert ilex.is_global is False
assert igrlex.is_global is False
assert ilex != igrlex
assert ilex == InverseOrder(LexOrder())
def test_pickling_polys_orderings():
from sympy.polys.orderings import (
LexOrder,
GradedLexOrder,
ReversedGradedLexOrder,
InverseOrder,
)
# from sympy.polys.orderings import ProductOrder
for c in (LexOrder, LexOrder()):
check(c)
for c in (GradedLexOrder, GradedLexOrder()):
check(c)
for c in (ReversedGradedLexOrder, ReversedGradedLexOrder()):
check(c)
# TODO: Argh, Python is so naive. No lambdas nor inner function support in
# pickling module. Maybe someone could figure out what to do with this.
#
# for c in (ProductOrder, ProductOrder((LexOrder(), lambda m: m[:2]),
# (GradedLexOrder(), lambda m: m[2:]))):
# check(c)
for c in (InverseOrder, InverseOrder(LexOrder())):
check(c)
def test_local():
igrlex = InverseOrder(grlex)
gens = [x, y, z]
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()
assert contains([x, y], x)
assert contains([x, y], x + y)
assert not contains([x, y], 1)
assert not contains([x, y], z)
assert contains([x**2 + y, x**2 + x], x - y)
assert not contains([x + y + z, x*y + x*z + y*z, x*y*z], x**2)
assert contains([x*(1 + x + y), y*(1 + z)], x)
assert contains([x*(1 + x + y), y*(1 + z)], x + y)