Exemplo n.º 1
0
def test_hyper_as_trig():
    from sympy.simplify.fu import _osborne, _osbornei

    eq = sinh(x)**2 + cosh(x)**2
    t, f = hyper_as_trig(eq)
    assert f(fu(t)) == cosh(2 * x)
    e, f = hyper_as_trig(tanh(x + y))
    assert f(TR12(e)) == (tanh(x) + tanh(y)) / (tanh(x) * tanh(y) + 1)

    d = Dummy()
    assert _osborne(sinh(x), d) == I * sin(x * d)
    assert _osborne(tanh(x), d) == I * tan(x * d)
    assert _osborne(coth(x), d) == cot(x * d) / I
    assert _osborne(cosh(x), d) == cos(x * d)
    assert _osborne(sech(x), d) == sec(x * d)
    assert _osborne(csch(x), d) == csc(x * d) / I
    for func in (sinh, cosh, tanh, coth, sech, csch):
        h = func(pi)
        assert _osbornei(_osborne(h, d), d) == h
    # /!\ the _osborne functions are not meant to work
    # in the o(i(trig, d), d) direction so we just check
    # that they work as they are supposed to work
    assert _osbornei(cos(x * y + z), y) == cosh(x + z * I)
    assert _osbornei(sin(x * y + z), y) == sinh(x + z * I) / I
    assert _osbornei(tan(x * y + z), y) == tanh(x + z * I) / I
    assert _osbornei(cot(x * y + z), y) == coth(x + z * I) * I
    assert _osbornei(sec(x * y + z), y) == sech(x + z * I)
    assert _osbornei(csc(x * y + z), y) == csch(x + z * I) * I
Exemplo n.º 2
0
def _futrig(e, **kwargs):
    """Helper for futrig."""
    from sympy.simplify.fu import (
        TR1, TR2, TR3, TR2i, TR10, L, TR10i,
        TR8, TR6, TR15, TR16, TR111, TR5, TRmorrie, TR11, TR14, TR22,
        TR12)
    from sympy.core.compatibility import _nodes

    if not e.has(TrigonometricFunction):
        return e

    if e.is_Mul:
        coeff, e = e.as_independent(TrigonometricFunction)
    else:
        coeff = S.One

    Lops = lambda x: (L(x), x.count_ops(), _nodes(x), len(x.args), x.is_Add)
    trigs = lambda x: x.has(TrigonometricFunction)

    tree = [identity,
        (
        TR3,  # canonical angles
        TR1,  # sec-csc -> cos-sin
        TR12,  # expand tan of sum
        lambda x: _eapply(factor, x, trigs),
        TR2,  # tan-cot -> sin-cos
        [identity, lambda x: _eapply(_mexpand, x, trigs)],
        TR2i,  # sin-cos ratio -> tan
        lambda x: _eapply(lambda i: factor(i.normal()), x, trigs),
        TR14,  # factored identities
        TR5,  # sin-pow -> cos_pow
        TR10,  # sin-cos of sums -> sin-cos prod
        TR11, TR6, # reduce double angles and rewrite cos pows
        lambda x: _eapply(factor, x, trigs),
        TR14,  # factored powers of identities
        [identity, lambda x: _eapply(_mexpand, x, trigs)],
        TRmorrie,
        TR10i,  # sin-cos products > sin-cos of sums
        [identity, TR8],  # sin-cos products -> sin-cos of sums
        [identity, lambda x: TR2i(TR2(x))],  # tan -> sin-cos -> tan
        [
            lambda x: _eapply(expand_mul, TR5(x), trigs),
            lambda x: _eapply(
                expand_mul, TR15(x), trigs)], # pos/neg powers of sin
        [
            lambda x:  _eapply(expand_mul, TR6(x), trigs),
            lambda x:  _eapply(
                expand_mul, TR16(x), trigs)], # pos/neg powers of cos
        TR111,  # tan, sin, cos to neg power -> cot, csc, sec
        [identity, TR2i],  # sin-cos ratio to tan
        [identity, lambda x: _eapply(
            expand_mul, TR22(x), trigs)],  # tan-cot to sec-csc
        TR1, TR2, TR2i,
        [identity, lambda x: _eapply(
            factor_terms, TR12(x), trigs)],  # expand tan of sum
        )]
    e = greedy(tree, objective=Lops)(e)

    return coeff*e
Exemplo n.º 3
0
def test_TR12():
    assert TR12(tan(x + y)) == (tan(x) + tan(y)) / (-tan(x) * tan(y) + 1)
    assert TR12(tan(x + y + z)) ==\
        (tan(z) + (tan(x) + tan(y))/(-tan(x)*tan(y) + 1))/(
        1 - (tan(x) + tan(y))*tan(z)/(-tan(x)*tan(y) + 1))
    assert TR12(tan(x * y)) == tan(x * y)