def test_moeb_to(self):
U = ComplexNumber.rnd(.0, +50, NUMBER_TESTS)
V = ComplexNumber.rnd(.0, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
u, v = U[i], V[i]
self.assertEqual(moeb_to(u, v)(u) - v, ZERO)
def test_real_im_conj2(self):
A = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
B = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual((A[i] + B[i]).conj(), A[i].conj() + B[i].conj())
self.assertEqual((A[i] * B[i]).conj(), A[i].conj() * B[i].conj())
self.assertEqual((A[i] / B[i]).conj(), A[i].conj() / B[i].conj())
def test_real_im_conj1(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual(Z[i], ComplexNumber(Z[i].re, Z[i].im))
self.assertEqual((Z[i] + Z[i].conj()) * .5, Z[i].re)
self.assertEqual((Z[i] - Z[i].conj()) / (_i * 2.0), Z[i].im)
self.assertEqual(Z[i], Z[i].conj().conj())
self.assertEqual(Z[i].conj().re, Z[i].re)
self.assertEqual(Z[i].conj().im, - Z[i].im)
def test_field_laws(self):
A = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
B = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
C = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
a, b, c = A[i], B[i], C[i]
self.assertEqual(associative_property_add(a, b, c), ZERO)
self.assertEqual(commutative_portperty_add(a, b, c), ZERO)
self.assertEqual(associative_property_mul(a, b, c), ZERO)
self.assertEqual(commutative_portperty_mul(a, b, c), ZERO)
self.assertEqual(right_distributive(a, b, c), ZERO)
self.assertEqual(left_distributive(a, b, c), ZERO)
def circ_to_circ(c_0, c_1):
"""Returns the Moebius transformation mapping the geodesic circle c_0 to the circle c_1.
Parameters
----------
c_0 : Line of LineType CIRCLE
Geodesic circle to be mapped to
c_1 : Line of LineType CIRCLE
Target circle
Returns
-------
Moeb
Moebius transformation mapping the geodesic circle c_0 to the circle c_1
"""
c0 = c_0.Center
r0 = c_0.Radius
c1 = c_1.Center
r1 = c_1.Radius
return moeb_to(ComplexNumber(c0, r0), ComplexNumber(c1, r1))
import unittest
import numpy as np
from hypgeo.complex_plane import _i, ComplexNumber, RootOfUnity
from hypgeo.transformations import *
from hypgeo.moebius import moeb_id
from hypgeo.geometry import *
NUMBER_TESTS = 1000
ZERO = ComplexNumber(.0, .0)
class TestTransfomations(unittest.TestCase):
def test_moeb_to(self):
U = ComplexNumber.rnd(.0, +50, NUMBER_TESTS)
V = ComplexNumber.rnd(.0, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
u, v = U[i], V[i]
self.assertEqual(moeb_to(u, v)(u) - v, ZERO)
def test_refl_0(self):
R = np.random.uniform(.0, 20.0, NUMBER_TESTS)
for r in R:
self.assertEqual(refl_0(r) * refl_0(r), moeb_id)
self.assertEqual(refl_0(r) * refl_0(r), moeb_id)
def test_circ_to_circ(self):
C0 = HalfCircle.rnd(10.0, -10.0, +10.0, NUMBER_TESTS)
C1 = HalfCircle.rnd(10.0, -10.0, +10.0, NUMBER_TESTS)
def test_neutral_mul(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual(neutral_element_mul(Z[i], ONE), ZERO)
def test_inverse_add(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual(inv_element_add(Z[i], - Z[i], ZERO), ZERO)
def test_inverse_mul(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual(inv_element_mul(Z[i], Z[i].inv(), ONE), ZERO)
def test_inverse(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
self.assertEqual(Z[i].inv(), Z[i].conj() / (Z[i].norm_sq()))
import unittest
import sys
import numpy as np
from hypgeo.complex_plane import _i, ComplexNumber, RootOfUnity
from hypgeo.helpers.field import *
NUMBER_TESTS = 1000
ZERO = ComplexNumber(.0, .0)
ONE = ComplexNumber(1.0, .0)
class TestComplexNumber(unittest.TestCase):
def test_field_laws(self):
A = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
B = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
C = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)
for i in range(0, NUMBER_TESTS):
a, b, c = A[i], B[i], C[i]
self.assertEqual(associative_property_add(a, b, c), ZERO)
self.assertEqual(commutative_portperty_add(a, b, c), ZERO)
self.assertEqual(associative_property_mul(a, b, c), ZERO)
self.assertEqual(commutative_portperty_mul(a, b, c), ZERO)
self.assertEqual(right_distributive(a, b, c), ZERO)
self.assertEqual(left_distributive(a, b, c), ZERO)
def test_identity(self):
self.assertEqual(_i * _i, - ONE)
def test_inverse(self):
Z = ComplexNumber.rnd(-50, +50, NUMBER_TESTS)