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.