Comment #5 on issue 1242 by [email protected]: Simplifying of complex
exponentials
http://code.google.com/p/sympy/issues/detail?id=1242
In current master:
In [1]: c = cos(x)._eval_rewrite_as_exp(x)
In [2]: t = tan(x)._eval_rewrite_as_exp(x)
In [3]: simplify(c*t)
In [1]: c = cos(x)._eval_rewrite_as_exp(x)
In [2]: t = tan(x)._eval_rewrite_as_exp(x)
In [3]: simplify(c*t)
Out[3]: (I - I*exp(2*I*x))*exp(-I*x)/2
In [5]: simplify(c*t).expand()
Out[5]: -I*exp(I*x)/2 + I*exp(-I*x)/2
It is correct, but .expand() usage is needed.
But (3 hours ago and now) I have tested in my fork, where
`simplify(c*t)` yield `-I*exp(I*x)/2 + I*exp(-I*x)/2` straightly, without
expand()
Also, I do not the precise politics of `simplify` what to do simpler
(Out[3] or Out[5]).
In any case, the tests have to be presented in sympy about it.
So, formally, issue is not fixed now (no test).
Additionally:
(it is out of this issue, but may be another new),
to avoid many similar problems with comlexes - it is a question,
I will cite myself:
"Complex numbers:
I observe that there are two ways to operate with them.
Pure symbolical way (with assumption option): I can operate symbolical with
complex variable with the help of standard operations (multiplicity, abs,
conjugate and so on):
Another way with the aim of I symbol: I can observe real and imaginary
parts, and with the aim of I behaviour operations are maintaining:
E.g. for
1 + cos(x) + I + sin(x)*I
if I multiply this by I, than sympy scan every sub-expression in Add class
and every sub-expression is multiplied by I.
I wonder that there is no class of complex number as like as Rational(p/q),
which tracking real and imaginary part. In this way, this operation would
be separated:
1 + cos(x) moved to imaginary field of class and 1 + sin(x) to real field
of class.
The reason is not only for complex number, but for one way to operate with
para complex numbers (where I**2 = 1) or dual numbers (I**2==0 ), and for
extension for other dimensions (quaternions, Clifford algebra and so on)."
But I am not sure is it a poper time for rising it right now.
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