Summation theory of difference rings and applications - lecture 3 | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Summation theory of difference rings and applications - lecture 3

De Carsten Schneider

Apparaît dans la collection : Enumerative combinatorics and effective aspects of differential equations Thematic Month Week 5 / Combinatoire énumérative et aspects effectifs des équations différentielles Mois thématique semaine 5

The mini-course is structured into three parts. In the first part, we provide a general overview of the tools available in the summation package Sigma, with a particular focus on parameterized telescoping (which includes Zeilberger's creative telescoping as a special case) and recurrence solving for the class of indefinite nested sums defined over nested products. The second part delves into the core concepts of the underlying difference ring theory, offering detailed insights into the algorithmic framework. Special attention is given to the representation of indefinite nested sums and products within the difference ring setting. As a bonus, we obtain a toolbox that facilitates the construction of summation objects whose sequences are algebraically independent of one another. In the third part, we demonstrate how this summation toolbox can be applied to tackle complex problems arising in enumerative combinatorics, number theory, and elementary particle physics.

Informations sur la vidéo

Date de captation 27/02/2025
Date de publication 13/03/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20316003
Citer cette vidéo Schneider, Carsten (27/02/2025). Summation theory of difference rings and applications - lecture 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20316003
URL https://dx.doi.org/10.24350/CIRM.V.20316003

Domaine(s)

Symbolic Computation

Bibliographie

SCHNEIDER, Carsten. Symbolic summation assists combinatorics. Sém. Lothar. Combin, 2007, vol. 56, no 1-36, p. B56b. - http://eudml.org/doc/224549
SCHNEIDER, Carsten. Simplifying multiple sums in difference fields. Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, 2013, p. 325-360. - https://doi.org/10.1007/978-3-7091-1616-6_14
SCHNEIDER, Carsten. Term algebras, canonical representations and difference ring theory for symbolic summation. Anti-Differentiation and the Calculation of Feynman Amplitudes, 2021, p. 423-485. - https://doi.org/10.1007/978-3-030-80219-6_17

Codes MSC

Document(s)

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2025

Donner son avis