On Fri, May 28, 2010 at 1:31 AM, Je Suis <testelor at yahoo.com> wrote:
> First, I tried the direct approach, with solve(k=elliptic_kc(t2_)/elliptic_kc(t2),ws),
> but I got this in return: elliptic_kc((ws^2-1)/ws^2)=elliptic_kc(1/ws^2)*k
>? -- not helpful.
Maxima's solve function is pretty weak. In particular it can't solve
equations with elliptic functions.
My advice on this point is to approximate the function to be solved
and then solve k = (approximate function).
Or perhaps approximate the inverse of the function and evaluate it
at k.
elliptic_kc(t2_)/elliptic_kc(t2) seems to be pretty well-behaved.
Maybe you can approximate it with a rational function.
I don't know much about that. You could probably try a Taylor
series if you can stay away from the edges.
> The results were the expected ones _except_ one: K1_=157.445 (result
> of integration) instead of 5.99391 (value given by elliptic_kc(t1_)).
> I then thought to install Scilab and make a comparison. I use Ubuntu
> 10.04 x86_64, installed, ran this:
>
> K1_=integrate('1/sqrt(1-t1_^2*sin(phi)^2)','phi',0,%pi/2)
> ?K1_=5.9939133
>
> Then I thought I would verify the error and did this:
>
> K1_=integrate('1/sqrt(1-t1_^2)','phi',0,%pi/2)
> ?K1_=157.44518
>
> which is a confirmation to me.
I;m kind of confused about this. If you can clarify and simplify the
erroneous output and post a bug report about, that would be helpful.
See: http://sourceforge.net/projects/maxima/bugs
Sorry I can't be more helpful.
Robert Dodier