def as_real_imag(self, deep=True, **hints):
"""
Returns this function as a complex coordinate.
Examples
========
>>> from sympy import I
>>> from sympy.abc import x
>>> from sympy.functions import log
>>> log(x).as_real_imag()
(log(Abs(x)), arg(x))
>>> log(I).as_real_imag()
(0, pi/2)
>>> log(1+I).as_real_imag()
(log(sqrt(2)), pi/4)
>>> log(I*x).as_real_imag()
(log(Abs(x)), arg(I*x))
"""
if deep:
abs = C.Abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.Abs(self.args[0])
arg = C.arg(self.args[0])
if hints.get('log', False): # Expand the log
hints['complex'] = False
return (log(abs).expand(deep, **hints), arg)
else:
return (log(abs), arg)
def as_real_imag(self, deep=True, **hints):
if deep:
abs = C.Abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.Abs(self.args[0])
arg = C.arg(self.args[0])
if hints.get("log", False): # Expand the log
hints["complex"] = False
return (log(abs).expand(deep, **hints), arg)
else:
return (log(abs), arg)
def _eval_expand_complex(self, deep=True, **hints):
if deep:
abs = C.abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.abs(self.args[0])
arg = C.arg(self.args[0])
if hints['log']: # Expand the log
hints['complex'] = False
return log(abs).expand(deep, **hints) + S.ImaginaryUnit * arg
else:
return log(abs) + S.ImaginaryUnit * arg
def as_real_imag(self, deep=True, **hints):
if deep:
abs = C.abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.abs(self.args[0])
arg = C.arg(self.args[0])
if hints['log']: # Expand the log
hints['complex'] = False
return (log(abs).expand(deep, **hints), arg)
else:
return (log(abs), arg)
def as_real_imag(self, deep=True, **hints):
if deep:
abs = C.Abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.Abs(self.args[0])
arg = C.arg(self.args[0])
if hints['log']: # Expand the log
hints['complex'] = False
return (log(abs).expand(deep, **hints), arg)
else:
return (log(abs), arg)
def _eval_expand_complex(self, deep=True, **hints):
if deep:
abs = C.abs(self.args[0].expand(deep, **hints))
arg = C.arg(self.args[0].expand(deep, **hints))
else:
abs = C.abs(self.args[0])
arg = C.arg(self.args[0])
if hints['log']: # Expand the log
hints['complex'] = False
return log(abs).expand(deep, **hints) + S.ImaginaryUnit * arg
else:
return log(abs) + S.ImaginaryUnit * arg
