special values of lesser hyperbolic functions

[kcrisman]

Even though Maxima can evaluate sech(0), Sage does this:

sage: cosh(0)
1
sage: sech(0)
sech(0)

It seems reasonable to fix this. Part of this is probably that sech is not a GiNaC function.

Component: symbolics

Keywords: sech, coth, csch

Author: Ralf Stephan

Branch/Commit: e064ff3

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/10074

[benjaminfjones]

comment:1

Is there a way of initializing a Ginac / Pynac function using a symbolic expression? It would be nice to be able to initialize sech by calling simply:

GinacExpression.__init__(self, '1/cosh', ... 

And the result would behave just like defining sech(z) = 1/cosh(z) in Sage. Then we'd get (as in sage-5.0.beta9):

sage: sech(z) = 1/cosh(z)
sage: sech(0)
1

Maybe this is naive...