Integral bases for P-recursive sequences

Shaoshi Chen; Lixin Du; Manuel Kauers; Thibaut Verron

doi:10.1145/3373207.3404004

Integral bases for P-recursive sequences

Shaoshi Chen
, Lixin Du
, Manuel Kauers
, Thibaut Verron

Institute for Algebra

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

In an earlier paper, the notion of integrality known for algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In order to do so, we formulate a general algorithm for finding all integral elements for valued vector spaces and then show that this algorithm includes not only the algebraic and the D-finite cases but also covers the case of P-recursive sequences.

Original language	English
Title of host publication	ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
Editors	Angelos Mantzaflaris
Pages	91-98
Number of pages	8
ISBN (Electronic)	9781450371001
DOIs	https://doi.org/10.1145/3373207.3404004
Publication status	Published - 20 Jul 2020

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Digital Transformation

Access to Document

10.1145/3373207.3404004

Cite this

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title = "Integral bases for P-recursive sequences",

abstract = "In an earlier paper, the notion of integrality known for algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In order to do so, we formulate a general algorithm for finding all integral elements for valued vector spaces and then show that this algorithm includes not only the algebraic and the D-finite cases but also covers the case of P-recursive sequences.",

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N2 - In an earlier paper, the notion of integrality known for algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In order to do so, we formulate a general algorithm for finding all integral elements for valued vector spaces and then show that this algorithm includes not only the algebraic and the D-finite cases but also covers the case of P-recursive sequences.

AB - In an earlier paper, the notion of integrality known for algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In order to do so, we formulate a general algorithm for finding all integral elements for valued vector spaces and then show that this algorithm includes not only the algebraic and the D-finite cases but also covers the case of P-recursive sequences.

UR - https://www.scopus.com/pages/publications/85090353216

U2 - 10.1145/3373207.3404004

DO - 10.1145/3373207.3404004

M3 - Conference proceedings

SP - 91

EP - 98

BT - ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation

A2 - Mantzaflaris, Angelos

ER -

Integral bases for P-recursive sequences

Abstract

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