def test_apart_list():
assert apart_list(1) == 1
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),
[(Poly(w0 - 2, w0), Lambda(_a, 2), Lambda(_a, -_a + x), 1)]))
assert (apart_list(2/(x**2-2), x, dummies=numbered_symbols('w')) ==
(1, Poly(0, x),
[(Poly(w0**2 - 2, w0), 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),
[(Poly(w0 - 2, w0), Lambda(_a, 4), Lambda(_a, -_a + x), 1),
(Poly(w1**2 - 1, w1), Lambda(_a, -3*_a - 6), Lambda(_a, -_a + x), 2),
(Poly(w2 + 1, w2), Lambda(_a, -4), Lambda(_a, -_a + x), 1)]))
f = 1/(2*(x - 1)**2)
assert (apart_list(f, x, dummies=numbered_symbols('w')) ==
(1, Poly(0, x),
[(Poly(2, w0), Lambda(_a, 0), Lambda(_a, x - _a), 1),
(Poly(w1 - 1, w1), Lambda(_a, Rational(1, 2)), Lambda(_a, x - _a), 2),
(Poly(1, w2), Lambda(_a, 0), Lambda(_a, x - _a), 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)))