Adding differentiation/integration rules.. and simplification too

>>>>> "Richard" == Richard Fateman <fateman@cs.berkeley.edu> writes:

    Richard> You haven't said what you want done.  identities
    Richard> go both ways.  if you want to substitute
    Richard> (1-cn(u)/(1+dn(u)) for sn(u/2)^2 then try

    Richard> ratsubst(..., sn(u/2)^2,  expression).


    Richard> Also, for specific u or "any" u?

"Any" u.  I was just wondering if such a thing could be done without
going into Lisp and the guts of maxima.  But perhaps the best thing
would be some functions analogous to trigexpand and trigreduce to
handle these.

    Richard> Also, for sin/cos/tan etc  there are complex exponentials
    Richard> which provide a clue to canonical forms. Exponentialize
    Richard> does this..

    Richard>   Maybe there
    Richard> is something similar for sn cn etc.

I guess that would be the Jacobi theta functions, but I'm just
learning about these and playing around for fun.  There's no
application or anything "real" behind my questions.  

Elliptic functions have a very pretty theory and I always wanted to
know what the actual period of a simple pendulum is without using the
small angle approximation.

Ray