def test_residue_reduce():
a = Poly(2*t**2 - t - x**2, t)
d = Poly(t**3 - x**2*t, t)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)], 'Tfuncs': [log]})
assert residue_reduce(a, d, DE, z, invert=False) == \
([(Poly(z**2 - S(1)/4, z), Poly((1 + 3*x*z - 6*z**2 -
2*x**2 + 4*x**2*z**2)*t - x*z + x**2 + 2*x**2*z**2 - 2*z*x**3, t))], False)
assert residue_reduce(a, d, DE, z, invert=True) == \
([(Poly(z**2 - S(1)/4, z), Poly(t + 2*x*z, t))], False)
assert residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t,), DE, z, invert=False) == \
([(Poly(z**2 - 1, z), Poly(-2*z*t/x - 2/x, t))], True)
ans = residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t), DE, z, invert=True)
assert ans == ([(Poly(z**2 - 1, z), Poly(t + z, t))], True)
assert residue_reduce_to_basic(ans[0], DE, z) == -log(-1 + log(x)) + log(1 + log(x))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
# TODO: Skip or make faster
assert residue_reduce(Poly((-2*nu**2 - x**4)/(2*x**2)*t - (1 + x**2)/x, t),
Poly(t**2 + 1 + x**2/2, t), DE, z) == \
([(Poly(z + S(1)/2, z, domain='QQ'), Poly(t**2 + 1 + x**2/2, t, domain='EX'))], True)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
assert residue_reduce(Poly(-2*x*t + 1 - x**2, t),
Poly(t**2 + 2*x*t + 1 + x**2, t), DE, z) == \
([(Poly(z**2 + S(1)/4, z), Poly(t + x + 2*z, t))], True)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert residue_reduce(Poly(t, t), Poly(t + sqrt(2), t), DE, z) == \
([(Poly(z - 1, z), Poly(t + sqrt(2), t))], True)
def test_residue_reduce():
a = Poly(2*t**2 - t - x**2, t)
d = Poly(t**3 - x**2*t, t)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)], 'Tfuncs': [log]})
assert residue_reduce(a, d, DE, z, invert=False) == \
([(Poly(z**2 - S(1)/4, z), Poly((1 + 3*x*z - 6*z**2 -
2*x**2 + 4*x**2*z**2)*t - x*z + x**2 + 2*x**2*z**2 - 2*z*x**3, t))], False)
assert residue_reduce(a, d, DE, z, invert=True) == \
([(Poly(z**2 - S(1)/4, z), Poly(t + 2*x*z, t))], False)
assert residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t,), DE, z, invert=False) == \
([(Poly(z**2 - 1, z), Poly(-z*t - 1, t))], True)
ans = residue_reduce(Poly(-2/x, t), Poly(t**2 - 1, t), DE, z, invert=True)
assert ans == ([(Poly(z**2 - 1, z), Poly(t + z, t))], True)
assert residue_reduce_to_basic(ans[0], DE, z) == -log(-1 + log(x)) + log(1 + log(x))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
# TODO: Skip or make faster
assert residue_reduce(Poly((-2*nu**2 - x**4)/(2*x**2)*t - (1 + x**2)/x, t),
Poly(t**2 + 1 + x**2/2, t), DE, z) == \
([(Poly(z + S(1)/2, z, domain='QQ'), Poly(t**2 + 1 + x**2/2, t, domain='EX'))], True)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
assert residue_reduce(Poly(-2*x*t + 1 - x**2, t),
Poly(t**2 + 2*x*t + 1 + x**2, t), DE, z) == \
([(Poly(z**2 + S(1)/4, z), Poly(t + x + 2*z, t))], True)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert residue_reduce(Poly(t, t), Poly(t + sqrt(2), t), DE, z) == \
([(Poly(z - 1, z), Poly(t + sqrt(2), t))], True)
def test_residue_reduce():
a = Poly(2 * t ** 2 - t - x ** 2, t)
d = Poly(t ** 3 - x ** 2 * t, t)
DE = DifferentialExtension(
extension={"D": [Poly(1, x), Poly(1 / x, t)], "Tfuncs": [log]}
)
assert residue_reduce(a, d, DE, z, invert=False) == (
[
(
Poly(z ** 2 - Rational(1, 4), z),
Poly(
(1 + 3 * x * z - 6 * z ** 2 - 2 * x ** 2 + 4 * x ** 2 * z ** 2) * t
- x * z
+ x ** 2
+ 2 * x ** 2 * z ** 2
- 2 * z * x ** 3,
t,
),
)
],
False,
)
assert residue_reduce(a, d, DE, z, invert=True) == (
[(Poly(z ** 2 - Rational(1, 4), z), Poly(t + 2 * x * z, t))],
False,
)
assert residue_reduce(
Poly(-2 / x, t), Poly(t ** 2 - 1, t,), DE, z, invert=False
) == ([(Poly(z ** 2 - 1, z), Poly(-2 * z * t / x - 2 / x, t))], True)
ans = residue_reduce(Poly(-2 / x, t), Poly(t ** 2 - 1, t), DE, z, invert=True)
assert ans == ([(Poly(z ** 2 - 1, z), Poly(t + z, t))], True)
assert residue_reduce_to_basic(ans[0], DE, z) == -log(-1 + log(x)) + log(1 + log(x))
DE = DifferentialExtension(
extension={
"D": [Poly(1, x), Poly(-(t ** 2) - t / x - (1 - nu ** 2 / x ** 2), t)]
}
)
# TODO: Skip or make faster
assert residue_reduce(
Poly((-2 * nu ** 2 - x ** 4) / (2 * x ** 2) * t - (1 + x ** 2) / x, t),
Poly(t ** 2 + 1 + x ** 2 / 2, t),
DE,
z,
) == (
[
(
Poly(z + S.Half, z, domain="QQ"),
Poly(t ** 2 + 1 + x ** 2 / 2, t, domain="EX"),
)
],
True,
)
DE = DifferentialExtension(extension={"D": [Poly(1, x), Poly(1 + t ** 2, t)]})
assert residue_reduce(
Poly(-2 * x * t + 1 - x ** 2, t),
Poly(t ** 2 + 2 * x * t + 1 + x ** 2, t),
DE,
z,
) == ([(Poly(z ** 2 + Rational(1, 4), z), Poly(t + x + 2 * z, t))], True)
DE = DifferentialExtension(extension={"D": [Poly(1, x), Poly(t, t)]})
assert residue_reduce(Poly(t, t), Poly(t + sqrt(2), t), DE, z) == (
[(Poly(z - 1, z), Poly(t + sqrt(2), t))],
True,
)
