def test_intersection_symetry(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y**2, z**3]])
sm_1_2 = sm1.intersection(sm2)
sm_2_1 = sm2.intersection(sm1)
#Assert that equals is symetric
self.assertTrue(sm_1_2.equals(sm_2_1))
def test_intersect_contains(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y**2, z**3]])
#Assert the intersection is contained in both modules
gens = (sm1.intersection(sm2)).gens
for gen in gens:
self.assertTrue(sm1.contains(gen))
for gen in gens:
self.assertTrue(sm2.contains(gen))
def test_intersect(self):
x = self.x
y = self.y
z = self.z
smA = SingularModule([[x, y**3, z + x], [z, x, x**2]])
smB = SingularModule([[z, y, x], [-z, x**2, 4 * y + z]])
smI = smA.intersection(smB)
gen_1_1 = x**5 * z + x * y**3 * z**2 + 4 * y**4 * z**2 + y**3 * z**3 + x**3 * y * z - x**3 * z**2 - x**2 * z**3 - x**3 * z - 4 * x**2 * y * z - x**2 * z**2 - x * y * z**2 - y * z**3
gen_2_1 = x**4 * y**3 * z - x**3 * y**3 * z + x**2 * y**4 * z + 4 * y**5 * z + y**4 * z**2 + x**5 - x**4 * z - x**3 * z**2 - 4 * x**2 * y**2 - 2 * x**2 * y * z - x * y * z**2
gen_3_1 = x**3 * y**3 * z - x**3 * y * z + 4 * x**2 * y**4 * z + x**2 * y**3 * z**2 + x**6 - 4 * x**3 * y**2 - x**4 * z - x**3 * z**2 - x**3 * z - 4 * x**2 * y * z + 4 * x * y**2 * z - 2 * x**2 * z**2 - 3 * x * y * z**2 + 4 * y**2 * z**2 - x * z**3 + y * z**3
gens = [[gen_1_1, gen_2_1, gen_3_1]]
#Test this example
self.assertEqual(gens, smI.gens)