def test_bound_degree():
# Base
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
assert bound_degree(Poly(1, x), Poly(-2*x, x), Poly(1, x), DE) == 0
# Primitive (see above test_bound_degree_fail)
# TODO: Add test for when the degree bound becomes larger after limited_integrate
# TODO: Add test for db == da - 1 case
# Exp
# TODO: Add tests
# TODO: Add test for when the degree becomes larger after parametric_log_deriv()
# Nonlinear
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert bound_degree(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), DE) == 0
def test_bound_degree_fail():
# Primitive
DE = DifferentialExtension(extension={'D': [Poly(1, x),
Poly(t0/x**2, t0), Poly(1/x, t)]})
assert bound_degree(Poly(t**2, t), Poly(-(1/x**2*t**2 + 1/x), t),
Poly((2*x - 1)*t**4 + (t0 + x)/x*t**3 - (t0 + 4*x**2)/2*x*t**2 + x*t,
t), DE) == 3
def param_rischDE(fa, fd, G, DE):
"""
Solve a Parametric Risch Differential Equation: Dy + f*y == Sum(ci*Gi, (i, 1, m)).
"""
_, (fa, fd) = weak_normalizer(fa, fd, DE)
a, (ba, bd), G, hn = prde_normal_denom(ga, gd, G, DE)
A, B, G, hs = prde_special_denom(a, ba, bd, G, DE)
g = gcd(A, B)
A, B, G = A.quo(g), B.quo(g), [gia.cancel(gid*g, include=True) for
gia, gid in G]
Q, M = prde_linear_constraints(A, B, G, DE)
M, _ = constant_system(M, zeros(M.rows, 1), DE)
# Reduce number of constants at this point
try:
# Similar to rischDE(), we try oo, even though it might lead to
# non-termination when there is no solution. At least for prde_spde,
# it will always terminate no matter what n is.
n = bound_degree(A, B, G, DE, parametric=True)
except NotImplementedError:
debug("param_rischDE: Proceeding with n = oo; may cause "
"non-termination.")
n = oo
A, B, Q, R, n1 = prde_spde(A, B, Q, n, DE)