research-article

A Fast Algorithm for Computing the P-curvature

Authors:

Éric SchostAuthors Info & Claims

ISSAC '15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

Pages 69 - 76

https://doi.org/10.1145/2755996.2756674

Published: 24 June 2015 Publication History

Abstract

We design an algorithm for computing the p-curvature of a differential system in positive characteristic p. For a system of dimension r with coefficients of degree at most d, its complexity is O~ (p d r^ω) operations in the ground field (where ω denotes the exponent of matrix multiplication), whereas the size of the output is about p d r². Our algorithm is then quasi-optimal assuming that matrix multiplication is (i.e. ω = 2). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.

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Cited By

Kauers MKoutschan CVerron T(2023)Transcendence Certificates for D-finite FunctionsProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597091(372-380)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597091
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Kauers MKauers M(2023)OperatorsD-Finite Functions10.1007/978-3-031-34652-1_4(287-391)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_4
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Index Terms

A Fast Algorithm for Computing the P-curvature
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
      2. Computations on polynomials

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cover image ACM Conferences

ISSAC '15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

June 2015

374 pages

ISBN:9781450334358

DOI:10.1145/2755996

Conference Chair:
Daniel Robertz
Plymouth University, United Kingdom
,
General Chair:
Steve Linton
University of St Andrews, United Kingdom
,
Program Chair:
Kazuhiro Yokoyama
Rikkyo University, Japan

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Published: 24 June 2015

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ISSAC'15: International Symposium on Symbolic and Algebraic Computation

July 6 - 9, 2015

Bath, United Kingdom

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ISSAC '15 Paper Acceptance Rate 43 of 71 submissions, 61%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Kauers MKoutschan CVerron T(2023)Transcendence Certificates for D-finite FunctionsProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597091(372-380)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597091
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Kauers MKauers M(2023)OperatorsD-Finite Functions10.1007/978-3-031-34652-1_4(287-391)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_4
Kauers MKauers M(2023)The Differential Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_3(185-286)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_3
Kauers MKauers M(2023)The Recurrence Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_2(81-183)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_2
Kauers MKauers M(2023)Background and Fundamental ConceptsD-Finite Functions10.1007/978-3-031-34652-1_1(1-80)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_1
Bostan AEmiris IZhi LMantzaflaris A(2020)Computing the N-th term of a q-holonomic sequenceProceedings of the 45th International Symposium on Symbolic and Algebraic Computation10.1145/3373207.3404060(46-53)Online publication date: 20-Jul-2020
https://dl.acm.org/doi/10.1145/3373207.3404060
Barkatou MCluzeau TWeil JDi Vizio LAbramov SZima EGao X(2016)Computing the Lie Algebra of the Differential Galois Group of a Linear Differential SystemProceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930932(63-70)Online publication date: 20-Jul-2016
https://dl.acm.org/doi/10.1145/2930889.2930932
Bostan ACaruso XSchost ÉAbramov SZima EGao X(2016)Computation of the Similarity Class of the p-CurvatureProceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930897(111-118)Online publication date: 20-Jul-2016
https://dl.acm.org/doi/10.1145/2930889.2930897

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