2017/04/30 by Johannes Middeke, Carsten Schneider, Middeke, Johannes +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebra over a field #Applied mathematics #Computer science #FOS: Computer and information sciences #Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Pure mathematics #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1705.00280
arxiv created 2017/04/30 · openalex publication_date 2017/04/30 · arxiv updated 2017/05/02 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28
We consider linear systems of recurrence equations whose coefficients are given in terms of indefinite nested sums and products covering, e.g., the harmonic numbers, hypergeometric products, q-hypergeometric products or their mixed versions. These linear systems are formulated in the setting of ΠΣ-extensions and our goal is to find a denominator bound (also known as universal denominator) for the solutions; i.e., a non-zero polynomial d such that the denominator of every solution of the system divides d. This is the first step in computing all rational solutions of such a rather general recurrence system. Once the denominator bound is known, the problem of solving for rational solutions is reduced to the problem of solving for polynomial solutions.