Python exponential.exp_polar函数代码示例

    def eval(cls, arg):
        from sympy.functions.elementary.complexes import arg as argument
        if arg.is_number:
            ar = argument(arg)
            # In general we want to affirm that something is known,
            # e.g. `not ar.has(argument) and not ar.has(atan)`
            # but for now we will just be more restrictive and
            # see that it has evaluated to one of the known values.
            if ar in (0, pi/2, -pi/2, pi):
                return exp_polar(I*ar)*abs(arg)

        if arg.is_Mul:
            args = arg.args
        else:
            args = [arg]
        included = []
        excluded = []
        positive = []
        for arg in args:
            if arg.is_polar:
                included += [arg]
            elif arg.is_positive:
                positive += [arg]
            else:
                excluded += [arg]
        if len(excluded) < len(args):
            if excluded:
                return Mul(*(included + positive))*polar_lift(Mul(*excluded))
            elif included:
                return Mul(*(included + positive))
            else:
                return Mul(*positive)*exp_polar(0)

    def _eval_expand_func(self, **hints):
        from sympy import exp, I, floor, Add, Poly, Dummy, exp_polar, unpolarify
        z, s, a = self.args
        if z == 1:
            return zeta(s, a)
        if s.is_Integer and s <= 0:
            t = Dummy('t')
            p = Poly((t + a)**(-s), t)
            start = 1/(1 - t)
            res = S(0)
            for c in reversed(p.all_coeffs()):
                res += c*start
                start = t*start.diff(t)
            return res.subs(t, z)

        if a.is_Rational:
            # See section 18 of
            #   Kelly B. Roach.  Hypergeometric Function Representations.
            #   In: Proceedings of the 1997 International Symposium on Symbolic and
            #   Algebraic Computation, pages 205-211, New York, 1997. ACM.
            # TODO should something be polarified here?
            add = S(0)
            mul = S(1)
            # First reduce a to the interaval (0, 1]
            if a > 1:
                n = floor(a)
                if n == a:
                    n -= 1
                a -= n
                mul = z**(-n)
                add = Add(*[-z**(k - n)/(a + k)**s for k in range(n)])
            elif a <= 0:
                n = floor(-a) + 1
                a += n
                mul = z**n
                add = Add(*[z**(n - 1 - k)/(a - k - 1)**s for k in range(n)])

            m, n = S([a.p, a.q])
            zet = exp_polar(2*pi*I/n)
            root = z**(1/n)
            return add + mul*n**(s - 1)*Add(
                *[polylog(s, zet**k*root)._eval_expand_func(**hints)
                  / (unpolarify(zet)**k*root)**m for k in range(n)])

        # TODO use minpoly instead of ad-hoc methods when issue 5888 is fixed
        if isinstance(z, exp) and (z.args[0]/(pi*I)).is_Rational or z in [-1, I, -I]:
            # TODO reference?
            if z == -1:
                p, q = S([1, 2])
            elif z == I:
                p, q = S([1, 4])
            elif z == -I:
                p, q = S([-1, 4])
            else:
                arg = z.args[0]/(2*pi*I)
                p, q = S([arg.p, arg.q])
            return Add(*[exp(2*pi*I*k*p/q)/q**s*zeta(s, (k + a)/q)
                         for k in range(q)])

        return lerchphi(z, s, a)

def unpolarify(eq, subs={}, exponents_only=False):
    """
    If p denotes the projection from the Riemann surface of the logarithm to
    the complex line, return a simplified version eq' of `eq` such that
    p(eq') == p(eq).
    Also apply the substitution subs in the end. (This is a convenience, since
    ``unpolarify``, in a certain sense, undoes polarify.)

    >>> from sympy import unpolarify, polar_lift, sin, I
    >>> unpolarify(polar_lift(I + 2))
    2 + I
    >>> unpolarify(sin(polar_lift(I + 7)))
    sin(7 + I)
    """
    if isinstance(eq, bool):
        return eq

    eq = sympify(eq)
    if subs != {}:
        return unpolarify(eq.subs(subs))
    changed = True
    pause = False
    if exponents_only:
        pause = True
    while changed:
        changed = False
        res = _unpolarify(eq, exponents_only, pause)
        if res != eq:
            changed = True
            eq = res
        if isinstance(res, bool):
            return res
    # Finally, replacing Exp(0) by 1 is always correct.
    # So is polar_lift(0) -> 0.
    return res.subs({exp_polar(0): 1, polar_lift(0): 0})

def test_sympy__functions__elementary__exponential__exp_polar():
    from sympy.functions.elementary.exponential import exp_polar
    assert _test_args(exp_polar(2))