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Convert exponential form to hyperbolic functions

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

TobiasD gravatar image

updated 2024-07-09 08:30:40 +0200

FrédéricC gravatar image

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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answered 2017-11-17 11:38:13 +0200

Emmanuel Charpentier gravatar image

updated 2017-11-17 13:43:53 +0200

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: 1,595 times

Last updated: Nov 17 '17