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src/s/y/sympy-0.7.5/sympy/integrals/prde.py   sympy(Download)
    NonElementaryIntegralException, residue_reduce, splitfactor,
    residue_reduce_derivation, DecrementLevel, recognize_log_derivative)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
    bound_degree, spde, solve_poly_rde)
from sympy.core.compatibility import reduce, xrange
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)

src/s/y/sympy-HEAD/sympy/integrals/prde.py   sympy(Download)
    NonElementaryIntegralException, residue_reduce, splitfactor,
    residue_reduce_derivation, DecrementLevel, recognize_log_derivative)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
    bound_degree, spde, solve_poly_rde)
from sympy.core.compatibility import reduce, xrange
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)

src/s/y/sympy-0.7.5/sympy/integrals/tests/test_rde.py   sympy(Download)
"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, S, symbols, oo, I
from sympy.integrals.risch import (DifferentialExtension,
    NonElementaryIntegralException)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
def test_weak_normalizer():
    a = Poly((1 + x)*t**5 + 4*t**4 + (-1 - 3*x)*t**3 - 4*t**2 + (-2 + 2*x)*t, t)
    d = Poly(t**4 - 3*t**2 + 2, t)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
    r = weak_normalizer(a, d, DE, z)
    assert r == (Poly(t**5 - t**4 - 4*t**3 + 4*t**2 + 4*t - 4, t),
        (Poly((1 + x)*t**2 + x*t, t), Poly(t + 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE) == (Poly(1, t), r[1])
    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
    assert r == (Poly(t**4 - 2*t**2 + 1, t), (Poly(-3*t**2 + 1, t), Poly(t**2 - 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2)]})
    r = weak_normalizer(Poly(1 + t**2), Poly(t, t), DE, z)

src/s/y/sympy-HEAD/sympy/integrals/tests/test_rde.py   sympy(Download)
"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, S, symbols, oo, I
from sympy.integrals.risch import (DifferentialExtension,
    NonElementaryIntegralException)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
def test_weak_normalizer():
    a = Poly((1 + x)*t**5 + 4*t**4 + (-1 - 3*x)*t**3 - 4*t**2 + (-2 + 2*x)*t, t)
    d = Poly(t**4 - 3*t**2 + 2, t)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
    r = weak_normalizer(a, d, DE, z)
    assert r == (Poly(t**5 - t**4 - 4*t**3 + 4*t**2 + 4*t - 4, t),
        (Poly((1 + x)*t**2 + x*t, t), Poly(t + 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE) == (Poly(1, t), r[1])
    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
    assert r == (Poly(t**4 - 2*t**2 + 1, t), (Poly(-3*t**2 + 1, t), Poly(t**2 - 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2)]})
    r = weak_normalizer(Poly(1 + t**2), Poly(t, t), DE, z)