1)thanks, and 2)automatic proves of identities with elliptic functions?

David,

an equality with Jacobi elliptic functions that I would like to prove automatically is:

l = r,

where l - the left-hand side - is as follows:

v[i,j] := jacobi_sn(x[i]-x[j], k);

l: (v[1,4]*v[2,3]*v[2,4]?v[1,3]*v[2,3]*v[2,4]+v[1,3]*v[1,4]*v[2,4]
      ?v[1,2]*v[1,4]*v[2,4]?v[1,3]*v[1,4]*v[2,3]+v[1,2]*v[1,3]*v[2,3]) /
      (v[1,4]*v[2,3]*v[2,4]?v[1,3]*v[2,3]*v[2,4]+v[1,3]*v[1,4]*v[2,4]
      +v[1,2]*v[1,4]*v[2,4]?v[1,3]*v[1,4]*v[2,3]?v[1,2]*v[1,3]*v[2,3]);

and r - the right-hand side - is as follows:

w[i,j] := jacobi_sc((x[i]?x[j])/2,k)*jacobi_nd((x[i]?x[j])/2,k);

r: w[2,3]/w[1,3] * w[2,4]/w[1,4];

Of course, in this specific example classical methods (checking zeros and poles, or searching in fat books) must also work...


04.11.2013, 12:52, "David Billinghurst" <dbmaxima at gmail.com>:
> On 3/11/2013 6:52 PM, Igor Korepanov wrote:
>
>> ?Now one more question. My current aim is actually to (guess correctly - this is done already - and then) prove a certain identity between Jacobi elliptic functions. That my identity does hold, there is no doubt - because numeric calculations with any precision (and randomly chosen parameters) show this. And I know from a book entitled "A=B" by Petkov?ek, Wilf and Zeilberger that identities with elliptic functions are proved, in our enlightened age, automatically - but using, alas, Maple or Mathematica. So, my obvious question is - what about Maxima?
>
> Igor,
>
> There are some functions for simplifying equations containing Bessel
> functions and exponential integrals in
> share/contrib/diffequations/contrib_ode.mac,
> see
> http://sourceforge.net/p/maxima/code/ci/master/tree/share/contrib/diffequations/contrib_ode.mac.
> Recurrence relations are applied systematically to reduce the order of
> the functions, and if all goes well the expression simplifies to 0.
>
> A similar approach may work with Jacobi elliptic functions. ?Can you
> provide an example.