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Elliptic functions.

• To: mathgroup at yoda.physics.unc.edu
• Subject: Elliptic functions.
• From: belopols at marie.mit.edu (Alexander Belopolsky)
• Date: Mon, 3 Jan 1994 21:00:22 -0500

	Dear Mathgroup!
I need to perform some calculations involving elliptic functions.
after the first attempt to use Mathematica's WeierstrassP function I
found that it is defined in terms of the invariants g2 and g3, not
the torus periods omega and omega prime:

In[1]:= ?WeierstrassP

WeierstrassP[u, g2, g3] gives the Weierstrass elliptic function P.


Moreover it is not defined for all complex values of g2 and g3:

Mathematica 2.0 for DEC RISC
Copyright 1988-91 Wolfram Research, Inc.
 -- X11 windows graphics initialized -- 

In[1]:=WeierstrassP[1,I,I] 

Out[1]= WeierstrassP[1, I, I]

In[2]:= %//N

Out[2]= WeierstrassP[1., 1. I, 1. I]

At the same time

In[3]:= WeierstrassP[1,1,I]//N 

Out[3]= 1.20281

but

In[4]:= WeierstrassP[1,1,I+1]//N 

Out[4]= WeierstrassP[1., 1., 1. + 1. I]

Can anyone explain this strange behavior? 

Please let me know if anyone has a package for calculation of elliptic
functions in terms of torus periods rather then the coefficients of
the cubic.

Any help would be deeply appreciated.

Alexander Belopolsky.