research-article

Computing the N-th term of a q-holonomic sequence

Author:

Alin BostanAuthors Info & Claims

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

Pages 46 - 53

https://doi.org/10.1145/3373207.3404060

Published: 27 July 2020 Publication History

Abstract

In 1977, Strassen invented a famous baby-step / giant-step algorithm that computes the factorial N! in arithmetic complexity quasi-linear in [EQUATION]. In 1988, the Chudnovsky brothers generalized Strassen's algorithm to the computation of the N-th term of any holonomic sequence in the same arithmetic complexity. We design q-analogues of these algorithms. We first extend Strassen's algorithm to the computation of the q-factorial of N, then Chudnovskys' algorithm to the computation of the N-th term of any q-holonomic sequence. Both algorithms work in arithmetic complexity quasi-linear in [EQUATION]. We describe various algorithmic consequences, including the acceleration of polynomial and rational solving of linear q-differential equations, and the fast evaluation of large classes of polynomials, including a family recently considered by Nogneng and Schost.

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Cited By

Bostan AYurkevich S(2022)Fast Computation of the N-th Term of a q-Holonomic Sequence and ApplicationsJournal of Symbolic Computation10.1016/j.jsc.2022.07.008Online publication date: Aug-2022
https://doi.org/10.1016/j.jsc.2022.07.008
Sugizaki YTakahashi D(2022)A Fast Algorithm for Computing the Number of Magic SeriesAnnals of Combinatorics10.1007/s00026-022-00584-526:2(511-532)Online publication date: 28-Apr-2022
https://doi.org/10.1007/s00026-022-00584-5
Giesbrecht MHuang HLabahn GZima E(2021)Efficient q-Integer Linear Decomposition of Multivariate PolynomialsJournal of Symbolic Computation10.1016/j.jsc.2021.02.001Online publication date: Feb-2021
https://doi.org/10.1016/j.jsc.2021.02.001

Index Terms

Computing the N-th term of a q-holonomic sequence
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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

July 2020

480 pages

ISBN:9781450371001

DOI:10.1145/3373207

General Chairs:
Ioannis Z. Emiris
National and Kapodistrian University of Athens, ATHENA Research and Innovation Center, Greece
,
Lihong Zhi
Academia Sinica, China
,
Publications Chair:
Angelos Mantzaflaris
Inria, France

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Published: 27 July 2020

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ISSAC '20: International Symposium on Symbolic and Algebraic Computation

July 20 - 23, 2020

Kalamata, Greece

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Cited By

Bostan AYurkevich S(2022)Fast Computation of the N-th Term of a q-Holonomic Sequence and ApplicationsJournal of Symbolic Computation10.1016/j.jsc.2022.07.008Online publication date: Aug-2022
https://doi.org/10.1016/j.jsc.2022.07.008
Sugizaki YTakahashi D(2022)A Fast Algorithm for Computing the Number of Magic SeriesAnnals of Combinatorics10.1007/s00026-022-00584-526:2(511-532)Online publication date: 28-Apr-2022
https://doi.org/10.1007/s00026-022-00584-5
Giesbrecht MHuang HLabahn GZima E(2021)Efficient q-Integer Linear Decomposition of Multivariate PolynomialsJournal of Symbolic Computation10.1016/j.jsc.2021.02.001Online publication date: Feb-2021
https://doi.org/10.1016/j.jsc.2021.02.001

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