def test_cp_key():
# from cyclic4 with grlex
p1 = (((0, 0, 0, 0), 4), [((0, 1, 1, 2), QQ(1, 1)),
((0, 0, 2, 2), QQ(1, 1)),
((0, 0, 0, 4), QQ(-1, 1)),
((0, 0, 0, 0), QQ(-1, 1))], 4)
q1 = (((0, 0, 0, 0), 2), [((0, 2, 0, 0), QQ(-1, 1)),
((0, 1, 0, 1), QQ(-1, 1)),
((0, 0, 1, 1), QQ(-1, 1)),
((0, 0, 0, 2), QQ(-1, 1))], 2)
p2 = (((0, 0, 0, 2), 3), [((0, 0, 3, 2), QQ(1, 1)),
((0, 0, 2, 3), QQ(1, 1)),
((0, 0, 1, 0), QQ(-1, 1)),
((0, 0, 0, 1), QQ(-1, 1))], 5)
q2 = (((0, 0, 2, 2), 2), [((0, 0, 1, 5), QQ(1,
1)), ((0, 0, 0, 6), QQ(1, 1)),
((0, 1, 1, 0), QQ(1, 1)),
((0, 0, 1, 1), QQ(1, 1))], 13)
cp1 = critical_pair(p1, q1, 3, grlex, QQ)
cp2 = critical_pair(p2, q2, 3, grlex, QQ)
assert cp_key(cp1, grlex) < cp_key(cp2, grlex)
cp1 = critical_pair(p1, p2, 3, grlex, QQ)
cp2 = critical_pair(q1, q2, 3, grlex, QQ)
assert cp_key(cp1, grlex) < cp_key(cp2, grlex)
def test_cp_key():
# from cyclic4 with grlex
p1 = (((0, 0, 0, 0), 4), [((0, 1, 1, 2), QQ(1,1)), ((0, 0, 2, 2), QQ(1,1)), ((0, 0, 0, 4), QQ(-1,1)), ((0, 0, 0, 0), QQ(-1,1))], 4)
q1 = (((0, 0, 0, 0), 2), [((0, 2, 0, 0), QQ(-1,1)), ((0, 1, 0, 1), QQ(-1,1)), ((0, 0, 1, 1), QQ(-1,1)), ((0, 0, 0, 2), QQ(-1,1))], 2)
p2 = (((0, 0, 0, 2), 3), [((0, 0, 3, 2), QQ(1,1)), ((0, 0, 2, 3), QQ(1,1)), ((0, 0, 1, 0), QQ(-1,1)), ((0, 0, 0, 1), QQ(-1,1))], 5)
q2 = (((0, 0, 2, 2), 2), [((0, 0, 1, 5), QQ(1,1)), ((0, 0, 0, 6), QQ(1,1)), ((0, 1, 1, 0), QQ(1,1)), ((0, 0, 1, 1), QQ(1,1))], 13)
cp1 = critical_pair(p1, q1, 3, grlex, QQ)
cp2 = critical_pair(p2, q2, 3, grlex, QQ)
assert cp_key(cp1, grlex) < cp_key(cp2, grlex)
cp1 = critical_pair(p1, p2, 3, grlex, QQ)
cp2 = critical_pair(q1, q2, 3, grlex, QQ)
assert cp_key(cp1, grlex) < cp_key(cp2, grlex)
def test_cp_key():
# from cyclic4 with grlex
R, x,y,z,t = ring("x,y,z,t", QQ, grlex)
p1 = (((0, 0, 0, 0), 4), y*z*t**2 + z**2*t**2 - t**4 - 1, 4)
q1 = (((0, 0, 0, 0), 2), -y**2 - y*t - z*t - t**2, 2)
p2 = (((0, 0, 0, 2), 3), z**3*t**2 + z**2*t**3 - z - t, 5)
q2 = (((0, 0, 2, 2), 2), y*z + z*t**5 + z*t + t**6, 13)
cp1 = critical_pair(p1, q1, R)
cp2 = critical_pair(p2, q2, R)
assert cp_key(cp1, R) < cp_key(cp2, R)
cp1 = critical_pair(p1, p2, R)
cp2 = critical_pair(q1, q2, R)
assert cp_key(cp1, R) < cp_key(cp2, R)
def test_cp_key():
# from cyclic4 with grlex
R, x, y, z, t = ring("x,y,z,t", QQ, grlex)
p1 = (((0, 0, 0, 0), 4), y * z * t**2 + z**2 * t**2 - t**4 - 1, 4)
q1 = (((0, 0, 0, 0), 2), -y**2 - y * t - z * t - t**2, 2)
p2 = (((0, 0, 0, 2), 3), z**3 * t**2 + z**2 * t**3 - z - t, 5)
q2 = (((0, 0, 2, 2), 2), y * z + z * t**5 + z * t + t**6, 13)
cp1 = critical_pair(p1, q1, R)
cp2 = critical_pair(p2, q2, R)
assert cp_key(cp1, R) < cp_key(cp2, R)
cp1 = critical_pair(p1, p2, R)
cp2 = critical_pair(q1, q2, R)
assert cp_key(cp1, R) < cp_key(cp2, R)