def test_lift_linear(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
vec = sm1.lift([3 * x, 3 * y + z, z**3 - 2 * y + 2 * z], True)
self.assertEqual(vec, [1, 2])
def test_lift_zero(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
zero = self.poly_ring.zero()
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2], [one, x, y]])
vec = sm1.lift([zero, zero, zero])
self.assertEqual(vec, [zero for _ in range(4)])
def test_lift_satisfy(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
vec = sm1.lift([
x**2 + x * z + x, x * y + x * z + y * z + y,
z**3 * x - 2 * y * x + z**2 + z
])
self.assertEqual(vec[0] * x + vec[1] * x, x**2 + x * z + x)
self.assertEqual(vec[0] * (y + z) + vec[1] * y,
x * y + x * z + y * z + y)
self.assertEqual(vec[0] * (z**3 - 2 * y) + vec[1] * z,
z**3 * x - 2 * y * x + z**2 + z)
def lift_to_basis(form,basis,make_linear=False):
graded_basis = {}
poly_ring = basis[0].diff_forms.poly_ring
lift = [poly_ring.zero() for _ in basis]
for i,b in enumerate(basis):
if b.degree in graded_basis.keys():
graded_basis[b.degree].append((i,b))
else:
graded_basis[b.degree] = [(i,b)]
for f in form:
if f.degree in graded_basis.keys():
g_part = graded_basis[f.degree]
b_mod = SingularModule([b.vec for _,b in g_part])
res = b_mod.lift(f.vec,make_linear)
for i,c in enumerate(res):
lift[g_part[i][0]] = c
return lift