script for linear recurrences with polynomial coefficients

Bill Allombert <[email protected]>
Newsgroups gmane.comp.mathematics.pari.user
Message-ID <Z4gsBK_4cdAJJqrT@seventeen>
Dear PARI users,

I have written a simple GP script to deal with linear recurrences with polynomial coefficients.
It is available here https://pari.math.u-bordeaux.fr/Scripts/rec.gp
This is preliminary work.

For example
R = [-2,(n-1)^3;-1,-(34*n^3-51*n^2+27*n-5);0,n^3]
is the relation
(n-1)^3*u_{n-2} -(34*n^3-51*n^2+27*n-5) * u_{n-1} + n^3*u_n
(-2 means u_{n-2}, etc.)

V=reccoefs(R,[0,6],30)
give 30 terms starting by 0,6

recfind allow to find the relations from the sequence:
? recfind(V,[-2,-1,0],3)
%7 = [[-2,x^3-3*x^2+3*x-1;-1,-34*x^3+51*x^2-27*x+5;0,x^3]]

reccheck allow to check if a sequence satisfies a given relation.

Cheers,
Bill
lmpx.com only provides a reader for public news (NNTP) servers. It is not affiliated with the servers or forums shown here and is not responsible for the content of articles, which is written by their respective authors.