EllipticTheta and "rules"
- To: mathgroup at yoda.physics.unc.edu
- Subject: EllipticTheta and "rules"
- From: Richard Muirhead <muirhead at u.washington.edu>
- Date: Mon, 20 Sep 1993 11:33:26 -0700 (PDT)
I'm working with a small group studying aspects of "quantum chaos", and our meanderings have brought us to the use of the elliptic theta functions. These functions are, fortunately, defined within Mma, but none of the crucial properties (various recursion relationships) seem to be known to Mma!! For example, define: theta3[z_,s_]:=EllipticTheta[3,z,E^(I*Pi*s)] theta4[z_,s_]:=EllipticTheta[4,z,E^(I*Pi*s)] I would like ... theta3[z,s]-theta4[z+Pi/2,s]... to test True. But, alas, Mma seems not to know these various relationships, and must be trained with, I presume, "rules". And this is where we're getting into trouble. In particular, those more complicated relationships involving connections between the various derivatives of the elliptic functions have us stumped. How do we construct the appropriate rules so that the EllipticTheta is not just a more-or-less useless symbol?? We've read Maeder's relevant chapters, and have some luck with rules that don't involving relating the derivatives (... and I do mean just **some** luck...), but we're unable to generalize. I come from the "procedural programming" paradigm and just haven't seen the light yet on this "functional" approach (...is that the right vocabulary??...). The closer I look at Mma and the more complicated the problem, the more confused I become. For me, Mma has that in common with quantum mechanics and members of the opposite sex. And my frustration is not unique based on the comments from fellow Mma novices on this quantum chaos project. So I guess yet another question I have, more vague and I suspect more difficult to field, is "how does one get the 'functional' message." Is there a "right" book? (...a right prayer, a right genuflection, etc). I thank the members of the group for any insights/directions they might offer on our elliptic function problem. I have been amazed at the insightful responses I have received from previous posts. And I again extend my sincere thanks. Maybe if I keep hammering away at this complex beast, I too will "see the pattern" and then be able to return the many favors I have received from this community. Thanks Rick Muirhead Physics UW muirhead at phys.washington.edu