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Re: Simplifying Jacobian elliptic functions

• To: mathgroup at smc.vnet.net
• Subject: [mg56325] Re: Simplifying Jacobian elliptic functions
• From: John Billingham <John.Billingham at Nottingham.ac.uk>
• Date: Fri, 22 Apr 2005 06:22:51 -0400 (EDT)
• References: <16439696.1114083913364.JavaMail.jakarta@nitrogen.mathforum.org>
• Sender: owner-wri-mathgroup at wolfram.com

> > Unprotect[Plus]
> > JacobiDN[p_, k_]^2 + k_ JacobiSN[p_, k_]^2 := 1
> > Protect[Plus]
> > 
> 
> Thanks for the tip. Why does your suggestion work,
> but
> 
> Unprotect[Minus];
> 1 -  JacobiSN[p_, m_]^2 := JacobiCN[p, m]^2;
> Protect[Minus];
> 
> doesn't??

OK. Sorry. Having read some help files, I can see that

Unprotect[Plus];
JacobiDN[p_, k_]^2 + k_ JacobiSN[p_, k_]^2 := 1
1 + Minus[ JacobiSN[p_, m_]^2] := JacobiCN[p, m]^2;
Protect[Plus];

Does the trick.

John