def test_get_max_degrees():
"""Tests max degrees function."""
p = x + y
q = x ** 2 + y **3
h = x ** 2 + y
dixon = DixonResultant(polynomials=[p, q, h], variables=[x, y])
dixon_polynomial = dixon.get_dixon_polynomial()
assert dixon.get_max_degrees(dixon_polynomial) == [1, 2]
def test_get_dixon_matrix():
"""Test Dixon's resultant for a numerical example."""
x, y = symbols('x, y')
p = x + y
q = x ** 2 + y ** 3
h = x ** 2 + y
dixon = DixonResultant([p, q, h], [x, y])
polynomial = dixon.get_dixon_polynomial()
assert dixon.get_dixon_matrix(polynomial).det() == 0
def test_get_KSY_Dixon_resultant_example_one():
"""Tests the KSY Dixon resultant for example one"""
x, y, z = symbols('x, y, z')
p = x * y * z
q = x**2 - z**2
h = x + y + z
dixon = DixonResultant([p, q, h], [x, y])
dixon_poly = dixon.get_dixon_polynomial()
dixon_matrix = dixon.get_dixon_matrix(dixon_poly)
D = dixon.get_KSY_Dixon_resultant(dixon_matrix)
assert D == -z**3
def test_get_dixon_matrix():
"""Test Dixon's resultant for a numerical example."""
x, y = symbols('x, y')
p = x + y
q = x ** 2 + y ** 3
h = x ** 2 + y
dixon = DixonResultant([p, q, h], [x, y])
polynomial = dixon.get_dixon_polynomial()
assert dixon.get_dixon_matrix(polynomial).det() == 0
def test_get_dixon_matrix_example_two():
"""Test Dixon's matrix for example from [Palancz08]_."""
x, y, z = symbols('x, y, z')
f = x ** 2 + y ** 2 - 1 + z * 0
g = x ** 2 + z ** 2 - 1 + y * 0
h = y ** 2 + z ** 2 - 1
example_two = DixonResultant([f, g, h], [y, z])
poly = example_two.get_dixon_polynomial()
matrix = example_two.get_dixon_matrix(poly)
expr = 1 - 8 * x ** 2 + 24 * x ** 4 - 32 * x ** 6 + 16 * x ** 8
assert (matrix.det() - expr).expand() == 0
def test_get_KSY_Dixon_resultant_example_two():
"""Tests the KSY Dixon resultant for example two"""
x, y, A = symbols('x, y, A')
p = x * y + x * A + x - A**2 - A + y**2 + y
q = x**2 + x * A - x + x * y + y * A - y
h = x**2 + x * y + 2 * x - x * A - y * A - 2 * A
dixon = DixonResultant([p, q, h], [x, y])
dixon_poly = dixon.get_dixon_polynomial()
dixon_matrix = dixon.get_dixon_matrix(dixon_poly)
D = factor(dixon.get_KSY_Dixon_resultant(dixon_matrix))
assert D == -8 * A * (A - 1) * (A + 2) * (2 * A - 1)**2
def test_get_dixon_matrix_example_two():
"""Test Dixon's matrix for example from [Palancz08]_."""
x, y, z = symbols('x, y, z')
f = x ** 2 + y ** 2 - 1 + z * 0
g = x ** 2 + z ** 2 - 1 + y * 0
h = y ** 2 + z ** 2 - 1
example_two = DixonResultant([f, g, h], [y, z])
poly = example_two.get_dixon_polynomial()
matrix = example_two.get_dixon_matrix(poly)
expr = 1 - 8 * x ** 2 + 24 * x ** 4 - 32 * x ** 6 + 16 * x ** 8
assert (matrix.det() - expr).expand() == 0
def test_get_dixon_polynomial_numerical():
"""Test Dixon's polynomial for a numerical example."""
a = IndexedBase("alpha")
p = x + y
q = x ** 2 + y **3
h = x ** 2 + y
dixon = DixonResultant([p, q, h], [x, y])
polynomial = -x * y ** 2 * a[0] - x * y ** 2 * a[1] - x * y * a[0] \
* a[1] - x * y * a[1] ** 2 - x * a[0] * a[1] ** 2 + x * a[0] - \
y ** 2 * a[0] * a[1] + y ** 2 * a[1] - y * a[0] * a[1] ** 2 + y * \
a[1] ** 2
assert dixon.get_dixon_polynomial().factor() == polynomial
def test_get_dixon_polynomial_numerical():
"""Test Dixon's polynomial for a numerical example."""
a = IndexedBase("alpha")
p = x + y
q = x ** 2 + y **3
h = x ** 2 + y
dixon = DixonResultant([p, q, h], [x, y])
polynomial = -x * y ** 2 * a[0] - x * y ** 2 * a[1] - x * y * a[0] \
* a[1] - x * y * a[1] ** 2 - x * a[0] * a[1] ** 2 + x * a[0] - \
y ** 2 * a[0] * a[1] + y ** 2 * a[1] - y * a[0] * a[1] ** 2 + y * \
a[1] ** 2
assert dixon.get_dixon_polynomial().factor() == polynomial
"""Tests for Dixon's and Macaulay's classes. """
from sympy import Matrix
from sympy.core import symbols
from sympy.tensor.indexed import IndexedBase
from sympy.polys.multivariate_resultants import (DixonResultant,
MacaulayResultant)
c, d = symbols("a, b")
x, y = symbols("x, y")
p = c * x + y
q = x + d * y
dixon = DixonResultant(polynomials=[p, q], variables=[x, y])
macaulay = MacaulayResultant(polynomials=[p, q], variables=[x, y])
def test_dixon_resultant_init():
"""Test init method of DixonResultant."""
a = IndexedBase("alpha")
assert dixon.polynomials == [p, q]
assert dixon.variables == [x, y]
assert dixon.n == 2
assert dixon.m == 2
assert dixon.dummy_variables == [a[0], a[1]]
def test_get_dixon_polynomial_numerical():
"""Test Dixon's polynomial for a numerical example."""
a = IndexedBase("alpha")
def test_get_upper_degree():
"""Tests upper degree function."""
h = c * x**2 + y
dixon = DixonResultant(polynomials=[h, q], variables=[x, y])
assert dixon.get_upper_degree() == 3
def test_get_upper_degree():
"""Tests upper degree function."""
h = c * x ** 2 + y
dixon = DixonResultant(polynomials=[h, q], variables=[x, y])
assert dixon.get_upper_degree() == 3
