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MathGroup Archive 2011

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Evaluating WeierstrassP at large arguments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120568] Evaluating WeierstrassP at large arguments
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 29 Jul 2011 04:43:36 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

The WeierstrassP function is doubly periodic. Do the numerical evaluation
routines for this function take this into account when evaluating for large
arguments, using a Mod function on the argument?  If not, would there be
something to be gained by the user writing a "front end" for
WeierstrassP[z,{g2,g3}] moving z to the principal period parallelogram?
Especially if g2 and g3 were fixed and z was scanned only along the
direction of one half-period.

 

I'm thinking of something like a high precision mod function followed by a
MachinePrecision evaluation of WeierstrassP.

 

My experience has been that calculating the half-periods from g2-g3 has a
fair loss of significance but if we only had to calculate them once we could
afford extra high precision.

 

David Park

djmpark at comcast.net

 <http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark/  



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