def _eval_expand_complex(self, *args):
if self[0].is_real:
return self
re, im = self[0].as_real_imag()
denom = sin(re)**2 + Basic.sinh(im)**2
return (sin(re)*cos(re) - \
S.ImaginaryUnit*Basic.sinh(im)*Basic.cosh(im))/denom
def _eval_apply(self, arg):
arg = Basic.sympify(arg)
if isinstance(arg, Basic.Number):
if isinstance(arg, Basic.NaN):
return S.NaN
elif isinstance(arg, Basic.Zero):
return S.One
elif arg.is_negative:
return self(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return Basic.cosh(i_coeff)
else:
pi_coeff = arg.as_coefficient(S.Pi)
if pi_coeff is not None:
if isinstance(pi_coeff, Basic.Rational):
cst_table = {
1 : S.One,
2 : S.Zero,
3 : S.Half,
4 : S.Half*Basic.sqrt(2),
6 : S.Half*Basic.sqrt(3),
}
try:
result = cst_table[pi_coeff.q]
if (2*pi_coeff.p // pi_coeff.q) % 4 in (1, 2):
return -result
else:
return result
except KeyError:
pass
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return self(-arg)
def _eval_expand_complex(self, *args):
if self[0].is_real:
return self
re, im = self[0].as_real_imag()
return cos(re)*Basic.cosh(im) - \
S.ImaginaryUnit*sin(re)*Basic.sinh(im)
