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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))

this was causing me trouble in a real 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.

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 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))

this was causing me trouble in a real 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.

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 a real 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.