27 novembre 2023 à 11 décembre 2023
Institut Henri Poincaré
Fuseau horaire Europe/Paris

Submodule approach to creative telescoping by Mark van Hoeij

5 déc. 2023, 16:30
1h
Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Amphithéâtre Hermite / Darboux

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris

Description

Abstract.This talk proposes ideas to speed up the process of creative telescoping, particularly when the telescoper is reducible. One can interpret telescoping as computing an annihilator L in D for an element H in a D-module M. The main idea is to look for submodules of M. For a non-trivial submodule N, constructing the minimal operator R of the image of H in M/N gives a right-factor of L in D. Then L=LR where L is the telescoper of R(H). To expedite computing L, compute the action of D on a natural basis of N, then obtain the telescoper L for R(H) with a cyclic vector computation. The next main idea is that when N has automorphisms, use them to construct submodules. An automorphism with distinct eigenvalues can be used to decompose N as a direct sum of submodules N1,,Nk. Then L=LCLM(L1,,Lk) where Li is the telescoper of the projection of R(H) on Ni. An LCLM can greatly increase the degrees of the coefficients, so L and hence L can be much larger than the factors L1,,Lk and R. Examples show that computing each factor Li and R separately can save a lot of CPU time compared to computing the full telescoper L all at once with standard creative telescoping.

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