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Re: Simplifying Jacobian elliptic functions

  • To: mathgroup at
  • Subject: [mg56372] Re: Simplifying Jacobian elliptic functions
  • From: Peter Pein <petsie at>
  • Date: Sat, 23 Apr 2005 01:16:05 -0400 (EDT)
  • References: <d2j8j8$k2$> <d4ak9q$iof$>
  • Sender: owner-wri-mathgroup at

John Billingham wrote:
>>JacobiDN[p_, k_]^2 + k_ JacobiSN[p_, k_]^2 := 1
> 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??
> John
There are (at least) two reasons:
 1.) 1 -  JacobiSN[p_, m_]^2 has no call of the Function Minus[] in it:
FullForm[1 - JacobiSN[p_, m_]^2]
Plus[1, Times[-1, Power[JacobiSN[
    Pattern[p, Blank[]], Pattern[m, Blank[]]], 2]]]

2.) Minus is not the operator for subtraction:
?? Minus
"-x is the arithmetic negation of x."*
  Button[More\[Ellipsis], ButtonData :> "Minus", Active -> True,
   ButtonStyle -> "RefGuideLink"]
Attributes[Minus] = {Listable, NumericFunction, Protected}

As you can see from the FullForm of the difference, even Subtract[] does
not appear in your expression.
Peter Pein

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