def _eval_apply(cls, arg):
arg = Basic.sympify(arg)
if isinstance(arg, Basic.Number):
if isinstance(arg, Basic.NaN):
return S.NaN
elif isinstance(arg, Basic.Infinity):
return S.Zero
elif isinstance(arg, Basic.NegativeInfinity):
return S.Zero
elif isinstance(arg, Basic.Zero):
return S.Pi/ 2
elif isinstance(arg, Basic.One):
return S.Pi / 4
elif isinstance(arg, Basic.NegativeOne):
return -S.Pi / 4
else:
cst_table = {
Basic.sqrt(3)/3 : 3,
-Basic.sqrt(3)/3 : -3,
1/Basic.sqrt(3) : 3,
-1/Basic.sqrt(3) : -3,
Basic.sqrt(3) : 6,
-Basic.sqrt(3) : -6,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * Basic.acoth(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -cls(-arg)
