def test_is_rewritable_or_comparable():
# from katsura4 with grlex
R, x, y, z, t = ring("x,y,z,t", QQ, grlex)
p = lbp(sig((0, 0, 2, 1), 2), R.zero, 2)
B = [
lbp(
sig((0, 0, 0, 1), 2),
QQ(2, 45) * y**2 + QQ(1, 5) * y * z + QQ(5, 63) * y * t +
z**2 * t + QQ(4, 45) * z**2 + QQ(76, 35) * z * t**2 -
QQ(32, 105) * z * t + QQ(13, 7) * t**3 - QQ(13, 21) * t**2, 6)
]
# rewritable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B) is True
p = lbp(sig((0, 1, 1, 0), 2), R.zero, 7)
B = [
lbp(
sig((0, 0, 0, 0), 3),
QQ(10, 3) * y * z + QQ(4, 3) * y * t - QQ(1, 3) * y + 4 * z**2 +
QQ(22, 3) * z * t - QQ(4, 3) * z + 4 * t**2 - QQ(4, 3) * t, 3)
]
# comparable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B) is True
def test_is_rewritable_or_comparable():
# from katsura4 with grlex
p = lbp(sig((0, 0, 2, 1), 2), [], 2)
B = [
lbp(sig((0, 0, 0, 1), 2), [((0, 0, 2, 1), QQ(1, 1)),
((0, 0, 1, 2), QQ(76, 35)),
((0, 0, 0, 3), QQ(13, 7)),
((0, 2, 0, 0), QQ(2, 45)),
((0, 1, 1, 0), QQ(1, 5)),
((0, 1, 0, 1), QQ(5, 63)),
((0, 0, 2, 0), QQ(4, 45)),
((0, 0, 1, 1), QQ(-32, 105)),
((0, 0, 0, 2), QQ(-13, 21))], 6)
]
# rewritable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B, 3, QQ) is True
p = lbp(sig((0, 1, 1, 0), 2), [], 7)
B = [
lbp(sig((0, 0, 0, 0), 3), [((0, 1, 1, 0), QQ(10, 3)),
((0, 1, 0, 1), QQ(4, 3)),
((0, 0, 2, 0), QQ(4, 1)),
((0, 0, 1, 1), QQ(22, 3)),
((0, 0, 0, 2), QQ(4, 1)),
((0, 1, 0, 0), QQ(-1, 3)),
((0, 0, 1, 0), QQ(-4, 3)),
((0, 0, 0, 1), QQ(-4, 3))], 3)
]
# comparable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B, 3, QQ) is True
def test_is_rewritable_or_comparable():
# from katsura4 with grlex
p = lbp(sig((0, 0, 2, 1), 2), [], 2)
B = [lbp(sig((0, 0, 0, 1), 2), [((0, 0, 2, 1), QQ(1,1)), ((0, 0, 1, 2), QQ(76,35)), ((0, 0, 0, 3), QQ(13,7)), ((0, 2, 0, 0), QQ(2,45)), ((0, 1, 1, 0), QQ(1,5)), ((0, 1, 0, 1), QQ(5,63)), ((0, 0, 2, 0), QQ(4,45)), ((0, 0, 1, 1), QQ(-32,105)), ((0, 0, 0, 2), QQ(-13,21))], 6)]
# rewritable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B, 3, QQ) == True
p = lbp(sig((0, 1, 1, 0), 2), [], 7)
B = [lbp(sig((0, 0, 0, 0), 3), [((0, 1, 1, 0), QQ(10,3)), ((0, 1, 0, 1), QQ(4,3)), ((0, 0, 2, 0), QQ(4,1)), ((0, 0, 1, 1), QQ(22,3)), ((0, 0, 0, 2), QQ(4,1)), ((0, 1, 0, 0), QQ(-1,3)), ((0, 0, 1, 0), QQ(-4,3)), ((0, 0, 0, 1), QQ(-4,3))], 3)]
# comparable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B, 3, QQ) == True
def test_is_rewritable_or_comparable():
# from katsura4 with grlex
R, x,y,z,t = ring("x,y,z,t", QQ, grlex)
p = lbp(sig((0, 0, 2, 1), 2), R.zero, 2)
B = [lbp(sig((0, 0, 0, 1), 2), QQ(2,45)*y**2 + QQ(1,5)*y*z + QQ(5,63)*y*t + z**2*t + QQ(4,45)*z**2 + QQ(76,35)*z*t**2 - QQ(32,105)*z*t + QQ(13,7)*t**3 - QQ(13,21)*t**2, 6)]
# rewritable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B) is True
p = lbp(sig((0, 1, 1, 0), 2), R.zero, 7)
B = [lbp(sig((0, 0, 0, 0), 3), QQ(10,3)*y*z + QQ(4,3)*y*t - QQ(1,3)*y + 4*z**2 + QQ(22,3)*z*t - QQ(4,3)*z + 4*t**2 - QQ(4,3)*t, 3)]
# comparable:
assert is_rewritable_or_comparable(Sign(p), Num(p), B) is True
