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sympy.integrals.rde.solve_poly_rde

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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

            # denominator and degree bound from above.
            B, C, m, alpha, beta = spde(A, B, C, N, DE)
            y = solve_poly_rde(B, C, m, DE)
 
            return ((alpha*y + beta, h), list(l[0][1:]))


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

            # denominator and degree bound from above.
            B, C, m, alpha, beta = spde(A, B, C, N, DE)
            y = solve_poly_rde(B, C, m, DE)
 
            return ((alpha*y + beta, h), list(l[0][1:]))


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_solve_poly_rde_no_cancel():
    # deg(b) large
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
    assert solve_poly_rde(Poly(t**2 + 1, t), Poly(t**3 + (x + 1)*t**2 + t + x + 2, t),
    oo, DE) == Poly(t + x, t)
    # deg(b) small
    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
    assert solve_poly_rde(Poly(0, x), Poly(x/2 - S(1)/4, x), oo, DE) == \

        Poly(x**2/4 - x/4, x)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
    assert solve_poly_rde(Poly(2, t), Poly(t**2 + 2*t + 3, t), 1, DE) == \
        Poly(t + 1, t, x)
    # deg(b) == deg(D) - 1


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_solve_poly_rde_no_cancel():
    # deg(b) large
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
    assert solve_poly_rde(Poly(t**2 + 1, t), Poly(t**3 + (x + 1)*t**2 + t + x + 2, t),
    oo, DE) == Poly(t + x, t)
    # deg(b) small
    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
    assert solve_poly_rde(Poly(0, x), Poly(x/2 - S(1)/4, x), oo, DE) == \

        Poly(x**2/4 - x/4, x)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
    assert solve_poly_rde(Poly(2, t), Poly(t**2 + 2*t + 3, t), 1, DE) == \
        Poly(t + 1, t, x)
    # deg(b) == deg(D) - 1