Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

Johannes Middeke

Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

Johannes Middeke

Research Institute for Symbolic Computation

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

Abstract

We consider systems A_ell(t )y(q^ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.

Original language	English
Title of host publication	Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation
Editors	Michael Burr
Pages	325-332
Number of pages	7
Publication status	Published - 2017

Fields of science

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

JKU Focus areas

Computation in Informatics and Mathematics

Cite this

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title = "Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K",

abstract = "We consider systems A\_ell(t )y(q\textasciicircum{}ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.",

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AB - We consider systems A_ell(t )y(q^ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.

M3 - Conference proceedings

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EP - 332

BT - Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation

A2 - Michael Burr, null

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