def test_splitfactor():
p = Poly(4 * x**4 * t**5 + (-4 * x**3 - 4 * x**4) * t**4 +
(-3 * x**2 + 2 * x**3) * t**3 +
(2 * x + 7 * x**2 + 2 * x**3) * t**2 +
(1 - 4 * x - 4 * x**2) * t - 1 + 2 * x,
t,
field=True)
DE = DifferentialExtension(extension={
'D': [Poly(1, x),
Poly(-t**2 - 3 / (2 * x) * t + 1 / (2 * x), t)]
})
assert splitfactor(p, DE) == (Poly(
4 * x**4 * t**3 + (-8 * x**3 - 4 * x**4) * t**2 +
(4 * x**2 + 8 * x**3) * t - 4 * x**2,
t), Poly(t**2 + 1 / x * t + (1 - 2 * x) / (4 * x**2),
t,
domain='ZZ(x)'))
assert splitfactor(Poly(x, t), DE) == (Poly(x, t), Poly(1, t))
r = Poly(
-4 * x**4 * z**2 + 4 * x**6 * z**2 - z * x**3 - 4 * x**5 * z**3 +
4 * x**3 * z**3 + x**4 + z * x**5 - x**6, t)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 / x, t)]})
assert splitfactor(r, DE, coefficientD=True) == \
(Poly(x*z - x**2 - z*x**3 + x**4, t), Poly(-x**2 + 4*x**2*z**2, t))
assert splitfactor_sqf(r, DE, coefficientD=True) == \
(((Poly(x*z - x**2 - z*x**3 + x**4, t), 1),), ((Poly(-x**2 + 4*x**2*z**2, t), 1),))
assert splitfactor(Poly(0, t), DE) == (Poly(0, t), Poly(1, t))
assert splitfactor_sqf(Poly(0, t), DE) == (((Poly(0, t), 1), ), ())
def test_splitfactor():
p = Poly(4*x**4*t**5 + (-4*x**3 - 4*x**4)*t**4 + (-3*x**2 + 2*x**3)*t**3 +
(2*x + 7*x**2 + 2*x**3)*t**2 + (1 - 4*x - 4*x**2)*t - 1 + 2*x, t, field=True)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - 3/(2*x)*t + 1/(2*x), t)]})
assert splitfactor(p, DE) == (Poly(4*x**4*t**3 + (-8*x**3 - 4*x**4)*t**2 +
(4*x**2 + 8*x**3)*t - 4*x**2, t), Poly(t**2 + 1/x*t + (1 - 2*x)/(4*x**2), t, domain='ZZ(x)'))
assert splitfactor(Poly(x, t), DE) == (Poly(x, t), Poly(1, t))
r = Poly(-4*x**4*z**2 + 4*x**6*z**2 - z*x**3 - 4*x**5*z**3 + 4*x**3*z**3 + x**4 + z*x**5 - x**6, t)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
assert splitfactor(r, DE, coefficientD=True) == \
(Poly(x*z - x**2 - z*x**3 + x**4, t), Poly(-x**2 + 4*x**2*z**2, t))
assert splitfactor_sqf(r, DE, coefficientD=True) == \
(((Poly(x*z - x**2 - z*x**3 + x**4, t), 1),), ((Poly(-x**2 + 4*x**2*z**2, t), 1),))
assert splitfactor(Poly(0, t), DE) == (Poly(0, t), Poly(1, t))
assert splitfactor_sqf(Poly(0, t), DE) == (((Poly(0, t), 1),), ())
