Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

Autor: Frédéric Chyzak, Bruno Salvy, Pierre Lairez, Alin Bostan

Publikováno v: ISSAC 2018-International Symposium on Symbolic and Algebraic Computation
ISSAC 2018-International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.1-8, ⟨10.1145/3208976.3208992⟩

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 arbi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d40f4457ff9084907d259043f8d73b33
https://inria.hal.science/hal-01788619/file/redct-final.pdf

Computation of the Similarity Class of the p-Curvature

Autor: Xavier Caruso, Alin Bostan, Éric Schost

Publikováno v: ISSAC 2016
ISSAC 2016, Jul 2016, Waterloo, ON, Canada. ACM Press, pp.111-118, 〈http://www.issac-conference.org/2016/〉. 〈10.1145/2930889.2930897〉
ISSAC 2016, Jul 2016, Waterloo, ON, Canada. pp.111-118, ⟨10.1145/2930889.2930897⟩

The $p$-curvature of a system of linear differential equations in positive characteristic $p$ is a matrix that measures how far the system is from having a basis of polynomial solutions. We show that the similarity class of the $p$-curvature can be d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::35de1f3277cfe119b296fdb2012c45b6

A survey on signature-based algorithms for computing Gröbner basis computations

Autor: Eder, Christian, Faugère, Jean-Charles

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, Elsevier, 2016, pp.1-75. ⟨10.1016/j.jsc.2016.07.031⟩
Journal of Symbolic Computation, 2016, pp.1-75. ⟨10.1016/j.jsc.2016.07.031⟩

International audience; This paper is a survey on the area of signature-based Gröbner basis algorithms that was initiated by Faugère's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the va

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::5f2549541716024a4355d6b1669613c3
https://hal.inria.fr/hal-00974810v2/document

Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets

Autor: Ivan Bannwarth, Mohab Safey El Din

Publikováno v: ISSAC'15-40th International Symposium on Symbolic and Algebraic Computation
ISSAC'15-40th International Symposium on Symbolic and Algebraic Computation, Jul 2015, Bath, United Kingdom. pp.37-44, ⟨10.1145/2755996.2756670⟩
ISSAC

International audience; Let f ∈ Q[X1,. .. , Xn] be a polynomial of degree D. We consider the problem of computing the real dimension of the real algebraic set defined by f = 0. Such a problem can be reduced to quanti-fier elimination. Hence it can

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9dd093aea110abaebe09215b7df48074
https://hal.archives-ouvertes.fr/hal-01152751/file/HAL_issac_2015.pdf

Sub-cubic Change of Ordering for Gröner Basis: A Probabilistic Approach

Autor: Guénaël Renault, Pierrick Gaudry, Jean-Charles Faugère, Louise Huot

Publikováno v: ISSAC '14-Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation
ISSAC '14-39th International Symposium on Symbolic and Algebraic Computation
ISSAC '14-39th International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. pp.170--177, ⟨10.1145/2608628.2608669⟩
ISSAC

International audience; The usual algorithm to solve polynomial systems using Gröbner bases consists of two steps: first computing the DRL Gröbner basis using the F5 algorithm then computing the LEX Gröbner basis using a change of ordering algorit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21169da4391d9be78ec26a55ff2b2120
https://inria.hal.science/hal-01064551