Computing the Algebraic Relations of C-finite Sequences and Multisequences

Manuel Kauers; Burkhard Zimmermann

doi:10.1016/j.jsc.2008.03.002

Computing the Algebraic Relations of C-finite Sequences and Multisequences

Manuel Kauers, Burkhard Zimmermann

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

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 Groebner bases 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.

Original language	English
Pages (from-to)	787-803
Number of pages	17
Journal	Journal of Symbolic Computation
Volume	43
Issue number	11
DOIs	https://doi.org/10.1016/j.jsc.2008.03.002
Publication status	Published - Nov 2008

Fields of science

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

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10.1016/j.jsc.2008.03.002

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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 Groebner bases 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.",

author = "Manuel Kauers and Burkhard Zimmermann",

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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 Groebner bases 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.

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M3 - Article

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JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 11

ER -

Computing the Algebraic Relations of C-finite Sequences and Multisequences

Abstract

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