Python residue_reduce_to_basic 예제들

예제 #1

파일: test_risch.py 프로젝트: Blendify/diofant

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 + Rational(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 + 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)

예제 #2

파일: test_risch.py 프로젝트: skirpichev/diofant

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 + Rational(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 + 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)