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

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

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]