4–6 sept. 2019
Strasbourg
Fuseau horaire Europe/Paris

Integration on Darbouxian foliations

5 sept. 2019, 16:20
1h
Salle séminaire (Strasbourg)

Salle séminaire

Strasbourg

IRMA, université de Strasbourg

Orateur

M. Thierry Combot

Description

Consider a Darbouxian function $f=F_0+\sum \lambda_i \ln F_i$ with $F_i$ rational functions in two variables, and the foliation of curves $\mathcal{C}_h=\{f(x,y)=h\}$. We consider the problem of symbolic integration of a rational function $G$ along $\mathcal{C}_h$. If the monodromy of the integral satisfies a differential equation in $h$, then it is linear with constant coefficients, and the integral can be expressed in terms of Liouvillian functions restricted to $\mathcal{C}_h$. Such situation is exceptional, but is however more general than elementary integration. We present an algorithm to test the existence of such differential equation and return the Liouvillian expression of the integral if it exists.

Documents de présentation

Aucun document.