Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 1242 by [email protected]: Simplifying of complex exponentials
http://code.google.com/p/sympy/issues/detail?id=1242
I was toying around with the idea of converting trig functions to
exponentials for the purposes of
simplification, however the results of simplify appear to be non-optimal:
>>> x = Symbol('x')
>>> c = cos(x)._eval_rewrite_as_exp(x)
>>> t = tan(x)._eval_rewrite_as_exp(x)
>>> c * t
I*(1/2*exp(I*x) + 1/2*exp(-I*x))*(-exp(I*x) + exp(-I*x))/(exp(I*x) +
exp(-I*x))
>>> simplify(_)
>>> (2*I*exp(I*x) - 2*I*exp(5*I*x))/(4*exp(2*I*x) + 4*exp(4*I*x))
Although the simplification is valid, it is not the expected result. t * c
can be reduced quite
simply by hand if you first combine 1/2*exp(I*x) + 1/2*exp(-I*x) to give:
1/2*(exp(I*x) + exp(-I*x));
take the 1/2 'down' to give
I*(exp(I*x) + exp(-I*x))*(-exp(I*x) + exp(-I*x))/(2*(exp(I*x) + exp(-I*x)));
cancel exp(I*x) + exp(-I*x)
(I*(-exp(I*x) + exp(-I*x))) / 2;
which is our good old friend sin(x).
I am not sure exactly how the current simplify function works, but it would
be good if it could
'pick-up' on this case (and others similar).
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