def test_contains_gen(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Assert we contain our generators
self.assertTrue(sm.contains([x, y + z, z**3 - 2 * y]))
self.assertTrue(sm.contains([x, y, z]))
def test_contains_fail(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Detect that certain vectors are not contained
self.assertFalse(sm.contains([one, x, z]))
self.assertFalse(sm.contains([y, y, y]))
self.assertFalse(sm.contains([z, y, x]))
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_contains_fail_multiple(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x**2, x * y, x * z]])
#Detect that this is not contianed even though a multiple is
self.assertFalse(sm.contains([x, y, z]))
def test_contains_combination(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Assert we contain a combination of the generorators
self.assertTrue(sm.contains([2 * x, 2 * y + z, z**3 - 2 * y + z]))
def test_contains_zero(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
zero = self.poly_ring.zero()
#Assert we always contain zero
self.assertTrue(sm.contains([zero, zero, zero]))
def test_contains_module(self):
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
smA = SingularModule([[x**2, x * y, y * z], [x, y, z]])
smB = SingularModule([[x**2 + x, x * y + y, y * z + z],
[zero, zero, y * z - x * z]])
self.assertTrue(smA.contains(smB))
