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# Convert exponential form to hyperbolic functions

Is there a method to convert expression containing exponentials like (e^a + e^-a) / 2 to hyperbolic functions? I tried to even call maxima functions directly, but thinks like  cosh(a)._maxima_().exponentialize().demoivre()  still don't give me cosh(a) back but instead return the form in exponentials.

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That's a {{{Maxima}}} bug :

sage: [(t,t(x)._maxima_().exponentialize().demoivre().sage()) for t in [sin,cos,
....: tan,sinh,cosh,tanh]]

[(sin, sin(x)),
(cos, cos(x)),
(tan, sin(x)/cos(x)),
(sinh, -1/2*e^(-x) + 1/2*e^x),
(cosh, 1/2*e^(-x) + 1/2*e^x),
(tanh, -(e^(-x) - e^x)/(e^(-x) + e^x))]


The same is still present in 5.40.0 (as packaged by Debian).

This is now Trac#24231, also reported as Maxima's bug #3358

Thanks for reporting !

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Asked: 2017-11-16 13:49:23 +0200

Seen: 1,170 times

Last updated: Nov 17 '17