Adding new rules to Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg56311] Adding new rules to Simplify*From*: John Billingham <John.Billingham at Nottingham.ac.uk>*Date*: Fri, 22 Apr 2005 06:22:35 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I'm trying to teach Mathematica the obvious simplification rules for Jacobi elliptic functions, which i had hoped would be built in! Grumble Having defined sn[x_ /; !FreeQ[x, JacobiSN] := x /. JacobiSN[u_, m_]-> Sqrt[(1 - JacobiDN[u, m]^2)/m]; sn[x_] := x; mySimplify = Simplify[#, TransformationFunctions -> {sn, Automatic}] &; I find that mySimplify[1 - (1 - k^2) JacobiSN[p, 1 - k^2]] gives me JacobiDN[p, 1 - k^2]^2 as I had hoped, but that the equivalent expression mySimplify[1 + (-1 + k^2) JacobiSN[p, 1 - k^2] leaves the formula unsimplified. What Mathematica subtlety am I missing here?? Thanks, John

**Follow-Ups**:**Re: Adding new rules to Simplify***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>