I wrote some programs for Macsyma that did bfloat symmetric elliptic
integrals. I also wrote some for MuPAD.
The latest versions of these elliptic integrals are for DERIVE.
There are tables of elliptic integrals on my web page.
http://www.getnet.net/~cherry/derive/index.html
These tables are complete, containing many integrals not in
Gradshteyn and Ryzhik. The DERIVE integrals are better than
the elliptic integrals in Maple. I had lots of help from the
developers of Macsyma to write my Macsyma symmetric elliptic integrals.
I would like to add some more elliptic integral support to Maxima.
The methods used belong to Bill Carlson.
Regards, Jim FitzSimons