How might this elliptic_e issue on SPARC hardware with ECL be debugged?
Subject: How might this elliptic_e issue on SPARC hardware with ECL be debugged?
From: Raymond Toy
Date: Mon, 10 Aug 2009 12:15:57 -0400
Dr. David Kirkby wrote:
> You probably see my previous posts on the fact that elliptic_e is giving
> incorrect results on SPARC hardware using ECL. If not,
>
> http://sagetrac.org/sage_trac/ticket/6716
>
> has the details.
>
> Can anyone who knows the internals of Maxima tell me what standard
> libraries supplied with Solaris the functions 'elliptic_e' might be
> expected to call?
>
>
>From looking at the code in src/ellipt.lisp, I see that elliptic_e is
computed using Carlson's Rf and Rd formulas. Rf and Rd does not require
trig functions, but computing elliptic-e from Rf and Rd does.
I'm too lazy to type in the formulas here, but a google search will show
how to compute Rf and Rd and elliptic-e is
elliptic_e(phi,k) = sin(phi)*Rf(cos(phi)^2,1-k^2*sin(phi)^2,1) -
k^2/3*sin(phi)^3*Rd(cos(phi)^2,1-k^2*sin(phi)^2),1)
(Note that maxima uses m = k^2, not k in the definition of ellipitic_e).
Ray
(I dropped the other lists since I'm not subscribed to them.)