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1 rue Honoré d'Estienne d'Orves
Campus de l'École polytechnique
91120 Palaiseau
France
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Recent and forthcoming activities
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19 jul 2018conference
Generalized Hermite reduction, creative telescoping and definite integration of differentially finite functions, presented at ISSAC 2018, New York City.
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28 may 2018conference
Conférence Algèbre, arithmétique et combinatoire des équations différentielles et aux différences, CIRM, Marseille.
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7 may 2018new preprint
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22 feb 2018conference
Numerical computation of the homology of basic semialgebraic sets, TAGS (linking topology to algebraic geometry and statistics), MPI Leipzig.
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1 feb 2018seminar
Rigid continuation paths, Kolloquium Algorithmische Algebra, TU Berlin.
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14 dec 2017seminar
Periods in action, PhD seminar of Ghent University.
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7 dec 2017seminar
Calculs symboliques et numériques avec les équations de Picard-Fuchs, Institut Fourier, Grenoble.
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10 nov 2017conference
Periods in action, Combinatorics and Arithmetic for Physics at IHES.
Latest work
Generalized Hermite reduction, creative telescoping and definite integration
2018
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.
A classical identity relating Chebyshev polynomials with Bessel functions