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Adding new rules to Simplify

  • To: mathgroup at
  • Subject: [mg56311] Adding new rules to Simplify
  • From: John Billingham <John.Billingham at>
  • Date: Fri, 22 Apr 2005 06:22:35 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

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??



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