Towards signature-based gröbner basis algorithms for computing the nondegenerate locus of a polynomial system

Autor: Christian Eder, Pierre Lairez, Rafael Mohr, Mohab Safey El Din

Publikováno v: ACM Communications in Computer Algebra. 56:41-45

Problem statement. Let K be a field and K be an algebraic closure of K. Consider the polynomial ring R = K[ x 1 ,..., x n ] over K and a finite sequence of polynomials f 1 ,..., f c in R with c ≤ n. Let V ⊂ K n be the algebraic set defined by the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3a3db8e1224cf87b5942cfbaf9febb2e
https://doi.org/10.1145/3572867.3572872

The Sage Package comb_walks for Walks in the Quarter Plane

Autor: Antonio Jiménez-Pastor, Pierre Lairez, Alin Bostan, Frédéric Chyzak

Publikováno v: ACM Communications in Computer Algebra
ACM Communications in Computer Algebra, Association for Computing Machinery (ACM), 2020, 54 (212), pp.9. ⟨10.1145/3427218.3427220⟩
ACM Communications in Computer Algebra, 2020, 54 (212), pp.9. ⟨10.1145/3427218.3427220⟩

Software Presentation accepted at ISSAC '20 (Kalamata, Greece, July 20-22, 2020); International audience; We present in this extended abstract a new software designed to work with generating functions that count walks in the quarter plane. With this

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be36f8f651c8bdfd71fc605d89525604
https://hal.inria.fr/hal-02902709/document

A numerical transcendental method in algebraic geometry: Computation of Picard groups and related invarian

Autor: Pierre Lairez, Emre Can Sertöz

Publikováno v: SIAM Journal on Applied Algebra and Geometry
SIAM Journal on Applied Algebra and Geometry, Society for Industrial and Applied Mathematics 2019, 3 (4), pp.559-584. ⟨10.1137/18M122861X⟩
SIAM Journal on Applied Algebra and Geometry, 2019, 3 (4), pp.559-584. ⟨10.1137/18M122861X⟩

International audience; Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces in P3. As an application, we count the number of rational curves of a given degree lying on each s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a681a119250866d4bf3bce3becee8021
https://hal.archives-ouvertes.fr/hal-01932147v2/document

Computing periods of rational integrals

Autor: Pierre Lairez

Publikováno v: Foundations of computational mathematics 2014, workshop “symbolic analysis”
Foundations of computational mathematics 2014, workshop “symbolic analysis”, Dec 2014, Montevideo, Uruguay
Mathematics of Computation
Mathematics of Computation, American Mathematical Society, 2016, 85, pp.1719-1752. ⟨10.1090/mcom/3054⟩
Mathematics of Computation, 2016, 85, pp.1719-1752. ⟨10.1090/mcom/3054⟩

A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period under consider

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fe90fd3dc0f4e6bda8a6776ec1e3995
https://doi.org/10.1090/mcom/3054

Computing the homology of basic semialgebraic sets in weak exponential time

Autor: Pierre Lairez, Peter Bürgisser, Felipe Cucker

Publikováno v: Journal of the ACM (JACM)
Journal of the ACM (JACM), 2018, 66 (1), pp.1-30. ⟨10.1145/3275242⟩
Journal of the ACM
Journal of the ACM (JACM), Association for Computing Machinery, 2018, 66 (1), pp.1-30. ⟨10.1145/3275242⟩

International audience; We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is, out of a set of exponentially small measure in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::36a0d76380ea2eadaed0dff201e1fca7