Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

Alin Bostan 1 Frédéric Chyzak 1 Pierre Lairez 1 Bruno Salvy 2
1 SPECFUN - Symbolic Special Functions : Fast and Certified
Inria Saclay - Ile de France
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite reduction to arbitrary linear differential operators instead of the pure derivative, and develop efficient algorithms for this reduction. We then apply the generalized Hermite reduction to the computation of linear operators satisfied by single definite integrals of D-finite functions of several continuous or discrete parameters. The resulting algorithm is a generalization of reduction-based methods for creative telescoping.
Document type :
Conference papers
Complete list of metadatas

Cited literature [45 references]  Display  Hide  Download
https://hal.inria.fr/hal-01788619
Contributor : Frédéric Chyzak <>
Submitted on : Wednesday, May 9, 2018 - 11:39:00 AM
Last modification on : Tuesday, May 22, 2018 - 10:10:54 AM
Long-term archiving on : Tuesday, September 25, 2018 - 7:03:15 PM

File

redct-final.pdf
Files produced by the author(s)

Identifiers

Collections

ENS-LYON | UNIV-LYON1 | INRIA | LIP | UNIV-PARIS-SACLAY

Citation

Alin Bostan, Frédéric Chyzak, Pierre Lairez, Bruno Salvy. Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions. ISSAC 2018 - International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.1-8, ⟨10.1145/3208976.3208992⟩. ⟨hal-01788619⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

306

Files downloads

108

Contact


archive-ouverte@inria.fr