Maxima's demoivre() doesn't work with hyperbolic functions. #24231
Description
A nice one :
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))]
This is a Maxima problem :
(%i5) map(lambda([t],[t,demoivre(exponentialize(t(x)))]),[sin,cos,tan,sinh,cosh,tanh]);
(%o5) [[sin,sin(x)],[cos,cos(x)],[tan,sin(x)/cos(x)],[sinh,(%e^x-%e^-x)/2],
[cosh,(%e^x+%e^-x)/2],[tanh,(%e^x-%e^-x)/(%e^x+%e^-x)]]
One also notes that sin(x)/cos(x) is not simplified in tan(x).
Reported on this ask question.
Related Maxima discussions:
Upstream: Reported upstream. Developers deny it's a bug.
CC: @slel
Component: symbolics
Keywords: maxima, demoivre, cosh, sinh
Reviewer: Emmanuel Charpentier, Samuel Lelièvre
Issue created by migration from https://trac.sagemath.org/ticket/24231