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.Zero
elif arg.is_negative:
return -self(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return S.ImaginaryUnit * Basic.tanh(i_coeff)
else:
pi_coeff = arg.as_coefficient(S.Pi)
if pi_coeff is not None:
if pi_coeff.is_integer:
return S.Zero
elif isinstance(pi_coeff, Basic.Rational):
cst_table = {
#2 : S.ComplexInfinity,
3 : Basic.sqrt(3),
4 : S.One,
6 : 1 / Basic.sqrt(3),
}
try:
result = cst_table[pi_coeff.q]
if (2*pi_coeff.p // pi_coeff.q) % 4 in (1, 3):
return -result
else:
return result
except KeyError:
pass
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -self(-arg)
