def test_apart_list():
from sympy.utilities.iterables import numbered_symbols
def dummy_eq(i, j):
if type(i) in (list, tuple):
return all(dummy_eq(i, j) for i, j in zip(i, j))
return i == j or i.dummy_eq(j)
w0, w1, w2 = Symbol("w0"), Symbol("w1"), Symbol("w2")
_a = Dummy("a")
f = (-2 * x - 2 * x**2) / (3 * x**2 - 6 * x)
got = apart_list(f, x, dummies=numbered_symbols("w"))
ans = (-1, Poly(Rational(2, 3),
x, domain='QQ'), [(Poly(w0 - 2, w0, domain='ZZ'),
Lambda(_a, 2), Lambda(_a, -_a + x), 1)])
assert dummy_eq(got, ans)
got = apart_list(2 / (x**2 - 2), x, dummies=numbered_symbols("w"))
ans = (1, Poly(0, x, domain='ZZ'), [(Poly(w0**2 - 2, w0,
domain='ZZ'), Lambda(_a, _a / 2),
Lambda(_a, -_a + x), 1)])
assert dummy_eq(got, ans)
f = 36 / (x**5 - 2 * x**4 - 2 * x**3 + 4 * x**2 + x - 2)
got = apart_list(f, x, dummies=numbered_symbols("w"))
ans = (1, Poly(0, x, domain='ZZ'), [
(Poly(w0 - 2, w0, domain='ZZ'), Lambda(_a, 4), Lambda(_a, -_a + x), 1),
(Poly(w1**2 - 1, w1,
domain='ZZ'), Lambda(_a, -3 * _a - 6), Lambda(_a, -_a + x), 2),
(Poly(w2 + 1, w2, domain='ZZ'), Lambda(_a, -4), Lambda(_a, -_a + x), 1)
])
assert dummy_eq(got, ans)
def test_apart_list():
from sympy.utilities.iterables import numbered_symbols
w0, w1, w2 = Symbol("w0"), Symbol("w1"), Symbol("w2")
_a = Dummy("a")
f = (-2 * x - 2 * x ** 2) / (3 * x ** 2 - 6 * x)
assert apart_list(f, x, dummies=numbered_symbols("w")) == (
-1,
Poly(S(2) / 3, x, domain="QQ"),
[(Poly(w0 - 2, w0, domain="ZZ"), Lambda(_a, 2), Lambda(_a, -_a + x), 1)],
)
assert apart_list(2 / (x ** 2 - 2), x, dummies=numbered_symbols("w")) == (
1,
Poly(0, x, domain="ZZ"),
[(Poly(w0 ** 2 - 2, w0, domain="ZZ"), Lambda(_a, _a / 2), Lambda(_a, -_a + x), 1)],
)
f = 36 / (x ** 5 - 2 * x ** 4 - 2 * x ** 3 + 4 * x ** 2 + x - 2)
assert apart_list(f, x, dummies=numbered_symbols("w")) == (
1,
Poly(0, x, domain="ZZ"),
[
(Poly(w0 - 2, w0, domain="ZZ"), Lambda(_a, 4), Lambda(_a, -_a + x), 1),
(Poly(w1 ** 2 - 1, w1, domain="ZZ"), Lambda(_a, -3 * _a - 6), Lambda(_a, -_a + x), 2),
(Poly(w2 + 1, w2, domain="ZZ"), Lambda(_a, -4), Lambda(_a, -_a + x), 1),
],
)
def test_assemble_partfrac_list():
f = 36 / (x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2)
pfd = apart_list(f)
assert assemble_partfrac_list(pfd) == -4/(x + 1) - 3/(x + 1)**2 - 9/(x - 1)**2 + 4/(x - 2)
a = Dummy("a")
pfd = (1, Poly(0, x, domain='ZZ'), [([sqrt(2),-sqrt(2)], Lambda(a, a/2), Lambda(a, -a + x), 1)])
assert assemble_partfrac_list(pfd) == -1/(sqrt(2)*(x + sqrt(2))) + 1/(sqrt(2)*(x - sqrt(2)))
def test_assemble_partfrac_list():
f = 36 / (x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2)
pfd = apart_list(f)
assert assemble_partfrac_list(pfd) == -4/(x + 1) - 3/(x + 1)**2 - 9/(x - 1)**2 + 4/(x - 2)
a = Dummy("a")
pfd = (1, Poly(0, x, domain='ZZ'), [([sqrt(2),-sqrt(2)], Lambda(a, a/2), Lambda(a, -a + x), 1)])
assert assemble_partfrac_list(pfd) == -1/(sqrt(2)*(x + sqrt(2))) + 1/(sqrt(2)*(x - sqrt(2)))
def test_apart_list():
from sympy.utilities.iterables import numbered_symbols
w0, w1, w2 = Symbol("w0"), Symbol("w1"), Symbol("w2")
_a = Dummy("a")
f = (-2 * x - 2 * x**2) / (3 * x**2 - 6 * x)
assert apart_list(f, x, dummies=numbered_symbols("w")) == (
-1,
Poly(Rational(2, 3), x, domain="QQ"),
[(Poly(w0 - 2, w0, domain="ZZ"), Lambda(_a, 2), Lambda(_a,
-_a + x), 1)],
)
assert apart_list(2 / (x**2 - 2), x, dummies=numbered_symbols("w")) == (
1,
Poly(0, x, domain="ZZ"),
[(
Poly(w0**2 - 2, w0, domain="ZZ"),
Lambda(_a, _a / 2),
Lambda(_a, -_a + x),
1,
)],
)
f = 36 / (x**5 - 2 * x**4 - 2 * x**3 + 4 * x**2 + x - 2)
assert apart_list(f, x, dummies=numbered_symbols("w")) == (
1,
Poly(0, x, domain="ZZ"),
[
(Poly(w0 - 2, w0, domain="ZZ"), Lambda(_a, 4), Lambda(_a,
-_a + x), 1),
(
Poly(w1**2 - 1, w1, domain="ZZ"),
Lambda(_a, -3 * _a - 6),
Lambda(_a, -_a + x),
2,
),
(Poly(w2 + 1, w2,
domain="ZZ"), Lambda(_a, -4), Lambda(_a, -_a + x), 1),
],
)
