def test_sub(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
logdfA = LogarithmicDifferentialForm(2, [self.x, self.y, self.z],
self.normal_logdf)
logdfB = LogarithmicDifferentialForm(2, [self.z, self.y, self.x],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = 1 / (y * z) - 1 / (x * y)
form[0, 2] = 0
form[1, 2] = 1 / (x * y) - 1 / (y * z)
logdf_diff = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(logdf_diff.equals(logdfA - logdfB))
def test_wedge(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
norm = self.x * self.y * self.z
logdfA = LogarithmicDifferentialForm(
1, [self.x * norm, self.y * norm, self.z * norm],
self.normal_logdf)
logdfB = LogarithmicDifferentialForm(1, [self.z, self.y, self.x],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = 1 / z - 1 / x
form[0, 2] = (x / (y * z)) - (z / (x * y))
form[1, 2] = 1 / z - 1 / x
logdf_wedge = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(logdf_wedge.equals(logdfA.wedge(logdfB)))
def test_interior_0_form(self):
x = self.x
y = self.y
z = self.z
logdf = LogarithmicDifferentialForm(
0, [x * y - y * z + x**2 - z**2 + x * x - y * z],
self.normal_logdf)
int_product = logdf.interior_product()
zero = LogarithmicDifferentialForm.make_zero(0, self.normal_logdf)
self.assertTrue(int_product.equals(zero))
def test_derivative(self):
x = self.x
y = self.y
z = self.z
logdf = LogarithmicDifferentialForm(1, [y * z, x * z, x * y],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
logdf_der = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(logdf_der.equals(logdf.derivative()))
def test_creationA(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
logdf = LogarithmicDifferentialForm(2, [self.x, self.y, self.z],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = 1 / (y * z)
form[0, 2] = 1 / (x * z)
form[1, 2] = 1 / (x * y)
self.assertEqual(form, logdf.form)
def test_creation_B(self):
x = self.whitney_logdf.form_vars[0]
y = self.whitney_logdf.form_vars[1]
z = self.whitney_logdf.form_vars[2]
whitney = x**2 * y - z**2
logdf = LogarithmicDifferentialForm(2, [self.x, self.y, self.z],
self.whitney_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = x / whitney
form[0, 2] = y / whitney
form[1, 2] = z / whitney
self.assertEqual(form, logdf.form)
def test_interior_1_form(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
form = DifferentialForm(self.normal_logdf.form_space, 0,
(x + y + z) / (x * y * z))
one = self.poly_ring.one()
logdf = LogarithmicDifferentialForm(1, [one, one, one],
self.normal_logdf)
int_product = logdf.interior_product()
logdf_form = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(int_product.equals(logdf_form))
def test_create_from_0_form(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
xp = self.x
yp = self.y
zp = self.z
logdf = LogarithmicDifferentialForm(0, [xp + yp + zp],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 0,
(x + y + z) / (x * y * z))
logdf_form = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(logdf.equals(logdf_form))
def test_mul(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
logdf = LogarithmicDifferentialForm(2, [self.x, self.y, self.z],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = -5 / (y * z)
form[0, 2] = -5 / (x * z)
form[1, 2] = -5 / (x * y)
self.assertTrue((logdf * (-5)).equals((-5) * logdf))
logdf_mul = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue((-5 * logdf).equals(logdf_mul))
def test_create_from_form(self):
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
xp = self.x
yp = self.y
zp = self.z
logdf = LogarithmicDifferentialForm(
2, [xp * yp - yp * zp, xp**2 - zp**2, xp * yp - yp * zp],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 2)
form[0, 1] = 1 / z - 1 / x
form[0, 2] = (x / (y * z)) - (z / (x * y))
form[1, 2] = 1 / z - 1 / x
logdf_form = LogarithmicDifferentialForm.create_from_form(
form, self.normal_logdf)
self.assertTrue(logdf.equals(logdf_form))
def test_interior(self):
xp = self.x
yp = self.y
zp = self.z
logdf = LogarithmicDifferentialForm(
2, [xp**2, xp + 4 * yp + zp, xp**3 * zp**3], self.whitney_logdf)
int_product = logdf.interior_product()
x = self.normal_logdf.form_vars[0]
y = self.normal_logdf.form_vars[1]
z = self.normal_logdf.form_vars[2]
whitney = x**2 * y - z**2
form = DifferentialForm(self.normal_logdf.form_space, 1)
form[0] = (-2 * x**2 * y - 2 * x * z - 8 * y * z - 2 * z**2) / whitney
form[1] = (x**3 - 2 * x**3 * z**4) / whitney
form[2] = (x**2 + 4 * x * y + x * z + 2 * x**3 * y * z**3) / whitney
logdf_form = LogarithmicDifferentialForm.create_from_form(
form, self.whitney_logdf)
self.assertTrue(int_product.equals(logdf_form))
def test_creation_0_form(self):
z = self.normal_logdf.form_vars[2]
logdf = LogarithmicDifferentialForm(0, [self.x * self.y],
self.normal_logdf)
form = DifferentialForm(self.normal_logdf.form_space, 0, 1 / z)
self.assertEqual(form, logdf.form)
