While learning and playing around with elliptic functions and
integrals, I'm getting tired of manually looking up the rules for
differentiation and integration of elliptic functions.
Can someone tell me how to get maxima to understand this?
For example
diff(sn(u),u) = cn(u)*dn(u),
diff(cn(u),u) = -sn(u)*dn(u),
etc.
Also, how can I get maxima to recognize the 12 basic elliptic
integrals. That is, can I get maxima to see
integrate(1/sqrt((a^2-t^2)*(b^2-t^2)),t,0,x)
is an elliptic integral whose value is
1/s*asn(x/b|b^2/a^2)?
where asn is the inverse sn function?
If things go well, I'd like to add some support for elliptic functions
to maxima.
Thanks,
Ray
P.S. maxima understands sn and friends but only accepts numeric
arguments. If you give it symbolic args, it produces some random
floating-point answer. I'll need to change this.