def eval(cls, z):
if z == 0:
return cls._atzero
elif z is S.Infinity:
return cls._atinf
elif z is S.NegativeInfinity:
return cls._atneginf
nz = z.extract_multiplicatively(polar_lift(I))
if nz is None and cls._trigfunc(0) == 0:
nz = z.extract_multiplicatively(I)
if nz is not None:
return cls._Ifactor(nz, 1)
nz = z.extract_multiplicatively(polar_lift(-I))
if nz is not None:
return cls._Ifactor(nz, -1)
nz = z.extract_multiplicatively(polar_lift(-1))
if nz is None and cls._trigfunc(0) == 0:
nz = z.extract_multiplicatively(-1)
if nz is not None:
return cls._minusfactor(nz)
nz, n = z.extract_branch_factor()
if n == 0 and nz == z:
return
return 2*pi*I*n*cls._trigfunc(0) + cls(nz)
def eval(cls, z):
if not z.is_polar and z.is_negative:
# Note: is this a good idea?
return Ei(polar_lift(z)) - pi*I
nz, n = z.extract_branch_factor()
if n:
return Ei(nz) + 2*I*pi*n
def _eval_rewrite_as_expint(self, z):
return -(E1(polar_lift(I)*z) + E1(polar_lift(-I)*z))/2
def _eval_rewrite_as_expint(self, z):
# XXX should we polarify z?
return pi/2 + (E1(polar_lift(I)*z) - E1(polar_lift(-I)*z))/2/I
def _eval_rewrite_as_expint(self, z):
return -expint(1, polar_lift(-1)*z) - I*pi
def _eval_rewrite_as_uppergamma(self, z):
from sympy import uppergamma
# XXX this does not currently work usefully because uppergamma
# immediately turns into expint
return -uppergamma(0, polar_lift(-1)*z) - I*pi
def _eval_evalf(self, prec):
if (self.args[0]/polar_lift(-1)).is_positive:
return Function._eval_evalf(self, prec) + (I*pi)._eval_evalf(prec)
return Function._eval_evalf(self, prec)
def _eval_rewrite_as_expint(self, z):
# XXX should we polarify z?
return pi/2 + (E1(polar_lift(I)*z) - E1(polar_lift(-I)*z))/2/I
def _eval_rewrite_as_expint(self, z):
return -(E1(polar_lift(I)*z) + E1(polar_lift(-I)*z))/2
def _eval_rewrite_as_expint(self, z):
return -expint(1, polar_lift(-1)*z) - I*pi
def _eval_rewrite_as_uppergamma(self, z):
from sympy import uppergamma
# XXX this does not currently work usefully because uppergamma
# immediately turns into expint
return -uppergamma(0, polar_lift(-1)*z) - I*pi
def _eval_evalf(self, prec):
if (self.args[0]/polar_lift(-1)).is_positive:
return Function._eval_evalf(self, prec) + (I*pi)._eval_evalf(prec)
return Function._eval_evalf(self, prec)
def test_sympy__functions__elementary__complexes__polar_lift():
from sympy.functions.elementary.complexes import polar_lift
assert _test_args(polar_lift(x))
def test_sympy__functions__elementary__complexes__polar_lift():
from sympy.functions.elementary.complexes import polar_lift
assert _test_args(polar_lift(x))