def test_hermite_reduce():
DE = DifferentialExtension(
extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t), Poly(t, t)), (Poly(0, t), Poly(1, t)), (Poly(-x, t), Poly(1, t)))
DE = DifferentialExtension(extension={
'D': [Poly(1, x),
Poly(-t**2 - t / x - (1 - nu**2 / x**2), t)]
})
# TODO: Fix this domain='EX' bug
assert hermite_reduce(Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 -
(x**2 - nu**2)*t - x**5/4, t), Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 +
x**4 + x**6/4, t), DE) == \
((Poly(-1 - x**2/4, t, domain='EX'), Poly(t**2 + 1 + x**2/2, t, domain='EX')),
(Poly((2*nu**2 + x**4)/-(2*x**2)*t - (1 + x**2)/x, t, domain='EX', expand=False),
Poly(t**2 + 1 + x**2/2, t, domain='EX')), (Poly(t + 1/x, t, domain='EX'),
Poly(1, t, domain='EX')))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 / x, t)]})
assert hermite_reduce(Poly(-t**2 + 2*t + 2, t),
Poly(-x*t**2 + 2*x*t - x, t), DE) == \
((Poly(3, t), Poly(t - 1, t)), (Poly(0, t), Poly(1, t)), (Poly(1, t), Poly(x, t)))
assert hermite_reduce(Poly(-x**2*t**6 + (-1 - 2*x**3 + x**4)*t**3 +
(-3 - 3*x**4)*t**2 - 2*x*t - x - 3*x**2, t),
Poly(x**4*t**6 - 2*x**2*t**3 + 1, t), DE) == \
((Poly(x**5*t + x**2 + x**6, t), Poly(x**5*t**3 - x**3, t)), (Poly(0, t),
Poly(1, t)), (Poly(-1, t), Poly(x**2, t)))
assert hermite_reduce(Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 +
(-4*x + 2*x**2)*t + x**2, t), Poly(x*t**6 - 4*x**2*t**5 +
6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t), DE) == \
((Poly(t**2 + t/3 + x, t), Poly(t**4 - 3*x*t**3 + 3*x**2*t**2 -
x**3*t, t)), (Poly(0, t), Poly(1, t)), (Poly(0, t), Poly(1, t)))
def test_hermite_reduce():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t), Poly(t, t)), (Poly(0, t), Poly(1, t)), (Poly(-x, t), Poly(1, t)))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
# TODO: Fix this domain='EX' bug
assert hermite_reduce(Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 -
(x**2 - nu**2)*t - x**5/4, t), Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 +
x**4 + x**6/4, t), DE) == \
((Poly(-1 - x**2/4, t, domain='EX'), Poly(t**2 + 1 + x**2/2, t, domain='EX')),
(Poly((2*nu**2 + x**4)/-(2*x**2)*t - (1 + x**2)/x, t, domain='EX', expand=False),
Poly(t**2 + 1 + x**2/2, t, domain='EX')), (Poly(t + 1/x, t, domain='EX'),
Poly(1, t, domain='EX')))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
assert hermite_reduce(Poly(-t**2 + 2*t + 2, t),
Poly(-x*t**2 + 2*x*t - x, t), DE) == \
((Poly(3, t), Poly(t - 1, t)), (Poly(0, t), Poly(1, t)), (Poly(1, t), Poly(x, t)))
assert hermite_reduce(Poly(-x**2*t**6 + (-1 - 2*x**3 + x**4)*t**3 +
(-3 - 3*x**4)*t**2 - 2*x*t - x - 3*x**2, t),
Poly(x**4*t**6 - 2*x**2*t**3 + 1, t), DE) == \
((Poly(x**3*t + 1 + x**4, t), Poly(x**3*t**3 - x, t)), (Poly(0, t),
Poly(1, t)), (Poly(-1, t), Poly(x**2, t)))
assert hermite_reduce(Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 +
(-4*x + 2*x**2)*t + x**2, t), Poly(x*t**6 - 4*x**2*t**5 +
6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t), DE) == \
((Poly(3*t**2 + t + 3*x, t), Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 -
3*x**3*t, t)), (Poly(0, t), Poly(1, t)), (Poly(0, t), Poly(1, t)))
def test_hermite_reduce():
DE = DifferentialExtension(
extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t, domain='QQ[x]'), Poly(t, t, domain='QQ[x]')),
(Poly(0, t, domain='QQ[x]'), Poly(1, t, domain='QQ[x]')),
(Poly(-x, t, domain='QQ[x]'), Poly(1, t, domain='QQ[x]')))
DE = DifferentialExtension(extension={
'D': [Poly(1, x),
Poly(-t**2 - t / x - (1 - nu**2 / x**2), t)]
})
assert hermite_reduce(
Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 - nu**2)*t - x**5/4, t),
Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 + x**4 + x**6/4, t), DE) == \
((Poly(-x**2 - 4, t, domain='ZZ(x,nu)'), Poly(4*t**2 + 2*x**2 + 4, t, domain='ZZ(x,nu)')),
(Poly((-2*nu**2 - x**4)*t - (2*x**3 + 2*x), t, domain='ZZ(x,nu)'),
Poly(2*x**2*t**2 + x**4 + 2*x**2, t, domain='ZZ(x,nu)')),
(Poly(x*t + 1, t, domain='ZZ(x,nu)'), Poly(x, t, domain='ZZ(x,nu)')))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 / x, t)]})
a = Poly(
(-2 + 3 * x) * t**3 + (-1 + x) * t**2 + (-4 * x + 2 * x**2) * t + x**2,
t)
d = Poly(
x * t**6 - 4 * x**2 * t**5 + 6 * x**3 * t**4 - 4 * x**4 * t**3 +
x**5 * t**2, t)
assert hermite_reduce(a, d, DE) == \
((Poly(3*t**2 + t + 3*x, t, domain='ZZ(x)'),
Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')))
assert hermite_reduce(
Poly(-t**2 + 2*t + 2, t, domain='ZZ(x)'),
Poly(-x*t**2 + 2*x*t - x, t, domain='ZZ(x)'), DE) == \
((Poly(3, t, domain='ZZ(x)'), Poly(t - 1, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
(Poly(1, t, domain='ZZ(x)'), Poly(x, t, domain='ZZ(x)')))
assert hermite_reduce(
Poly(-x**2*t**6 + (-1 - 2*x**3 + x**4)*t**3 + (-3 - 3*x**4)*t**2 -
2*x*t - x - 3*x**2, t, domain='ZZ(x)'),
Poly(x**4*t**6 - 2*x**2*t**3 + 1, t, domain='ZZ(x)'), DE) == \
((Poly(x**3*t + x**4 + 1, t, domain='ZZ(x)'), Poly(x**3*t**3 - x, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
(Poly(-1, t, domain='ZZ(x)'), Poly(x**2, t, domain='ZZ(x)')))
assert hermite_reduce(
Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 + (-4*x + 2*x**2)*t + x**2, t),
Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t), DE) == \
((Poly(3*t**2 + t + 3*x, t, domain='ZZ(x)'),
Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')),
(Poly(0, t, domain='ZZ(x)'), Poly(1, t, domain='ZZ(x)')))
def test_hermite_reduce():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t), Poly(t, t)), (Poly(0, t), Poly(1, t)), (Poly(-x, t), Poly(1, t)))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})
assert hermite_reduce(
Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 - nu**2)*t - x**5/4, t),
Poly(x**2*t**4 + x**2*(x**2 + 2)*t**2 + x**2 + x**4 + x**6/4, t), DE) == \
((Poly(-x**2 - 4, t), Poly(4*t**2 + 2*x**2 + 4, t)),
(Poly((-2*nu**2 - x**4)*t - (2*x**3 + 2*x), t), Poly(2*x**2*t**2 + x**4 + 2*x**2, t)),
(Poly(x*t + 1, t), Poly(x, t)))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
a = Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 + (-4*x + 2*x**2)*t + x**2, t)
d = Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t)
assert hermite_reduce(a, d, DE) == \
((Poly(3*t**2 + t + 3*x, t), Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t)),
(Poly(0, t), Poly(1, t)),
(Poly(0, t), Poly(1, t)))
assert hermite_reduce(
Poly(-t**2 + 2*t + 2, t),
Poly(-x*t**2 + 2*x*t - x, t), DE) == \
((Poly(3, t), Poly(t - 1, t)),
(Poly(0, t), Poly(1, t)),
(Poly(1, t), Poly(x, t)))
assert hermite_reduce(
Poly(-x**2*t**6 + (-1 - 2*x**3 + x**4)*t**3 + (-3 - 3*x**4)*t**2 - 2*x*t - x - 3*x**2, t),
Poly(x**4*t**6 - 2*x**2*t**3 + 1, t), DE) == \
((Poly(x**3*t + x**4 + 1, t), Poly(x**3*t**3 - x, t)),
(Poly(0, t), Poly(1, t)),
(Poly(-1, t), Poly(x**2, t)))
assert hermite_reduce(
Poly((-2 + 3*x)*t**3 + (-1 + x)*t**2 + (-4*x + 2*x**2)*t + x**2, t),
Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t), DE) == \
((Poly(3*t**2 + t + 3*x, t), Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t)),
(Poly(0, t), Poly(1, t)),
(Poly(0, t), Poly(1, t)))
