Computing the Algebraic Relations of C-finite Sequences and Multisequences

Burkhard Zimmermann; Manuel Kauers

Computing the Algebraic Relations of C-finite Sequences and Multisequences

Burkhard Zimmermann
, Manuel Kauers

Research Institute for Symbolic Computation

Research output: Working paper and reports › Research report

Abstract

We present an algorithm for computing generators for the ideal of algebraic relations among sequences which are given by homogeneous linear recurrence equations with constant coefficients. Knowing these generators makes it possible to use Gr\"obner basis methods for carrying out certain basic operations in the ring of such sequences effectively. In particular, one can answer the question whether a given sequence can be represented in terms of other given sequences. A collection of examples, which were done with an implementation of our algorithm, is included.

Original language	English
Place of Publication	Altenbergerstrasse 69, 4040 Linz, Austria
Publisher	Johannes Kepler Universität
Number of pages	23
Publication status	Published - 2006

Publication series

Name	SFB F013 Reports
No.	2006-24

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

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AB - We present an algorithm for computing generators for the ideal of algebraic relations among sequences which are given by homogeneous linear recurrence equations with constant coefficients. Knowing these generators makes it possible to use Gr\"obner basis methods for carrying out certain basic operations in the ring of such sequences effectively. In particular, one can answer the question whether a given sequence can be represented in terms of other given sequences. A collection of examples, which were done with an implementation of our algorithm, is included.

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BT - Computing the Algebraic Relations of C-finite Sequences and Multisequences

PB - Johannes Kepler Universität

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