Dependencies

A Mathematica Package for Computing Algebraic Relations of C-finite Sequences and Multi-Sequences

Authors

Software URL

This package is part of the RISCErgoSum bundle. See Download and Installation.

Short Description

For any tuple $f_1, f_2,\ldots f_r$ of sequences, the set of multivariate polynomials $p$ such that $p(f1(n),f2(n),\ldots,fr(n))=0$ for all points $n$ forms an ideal of the polynomial ring. The package provides a function for computing a basis for that ideal in the case where $f_1,f_2,\ldots,f_r$ are C-finite sequences (or multi-sequences), i.e., they satisfy homogeneous linear recurrence equations with constant coefficients.

Accompanying files

demo.nb

Literature

To use the implementation it is sufficient to study the notebook demo.nb. It contains a few examples to start with.

M. Kauers and B. Zimmermann Computing the Algebraic Relations of C-Finite Sequences and Multisequences, Journal of Symbolic Computation, Volume 43 Issue 11, November, 2008. [pdf from JSC] [techreport]