Comment #2 on issue 2296 by [email protected]: x*x.conjugate() should be
recognized as real
http://code.google.com/p/sympy/issues/detail?id=2296
I'm not sure if that's a good idea. Right now we can simplify things with
expand(complex=True):
In [9]: expand(x*x.conjugate(),complex=True)
Out[9]:
2 2
re (x) + im (x)
In [10]: expand(im(x*x.conjugate()),complex=True)
Out[10]: 0
This could be too costly, if you'll do this automatically. E.g. while
doing Mul() or even in as_real_imag(). May be we should add to simplify()
some option, like expand's "complex"? Or just close this bug.
Mathematica does like suggested above:
In[1]:= x Conjugate[x]
Out[1]=
x Conjugate[x]
In[2]:= Simplify[%]
Out[2]=
x Conjugate[x]
In[3]:= FullSimplify[%]
Out[3]=
2
Abs[x]
In[4]:= Element[x Conjugate[x], Reals]
Out[4]=
x Conjugate[x] \[Element] Reals
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