Changing order of factors affects sympy expansion
there is a strange behaviour when using sympy inside sage:
from sympy import Symbol, exp, I import sympy x = Symbol("x", real=True)
then, asking for
exp(I*8*x).expand(complex=True) I get
I*sin(8*x) + cos(8*x)
that's ok. however, asking for
exp(8*I*x).expand(complex=True), I get
I*exp(-8*im(x))*sin(8*re(x)) + exp(-8*im(x))*cos(8*re(x))
Why in the second case it forgets that $x$ is real? Is this behaviour expected?
this was causing me real trouble in another context, since I was calling functions from a package that itself uses sympy, and they didn't work unless some special ordering of the arguments was given.
I'm on SMC with sagemath kernel 6.10. I've checked in Live SymPy, the 1st result is obtained in both cases.