Decoupling multivariate fractions

Autor: François Lemaire, Adrien Poteaux

Publikováno v: Computer Algebra in Scientific Computing
Computer Algebra in Scientific Computing, Sep 2021, Sochi, Russia. pp.209--231
casc-conference.org/2021/
Computer Algebra in Scientific Computing ISBN: 9783030851644
CASC

International audience; We present a new algorithm for computing compact forms of multivariate fractions. Given a fraction presented as a quotient of two polynomials, our algorithm builds a tree where internal nodes are operators, and leaves are frac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea2a7dde909b0a4bd3a37ddd142910cf
https://hal.science/hal-03285870

Computing Puiseux series: a fast divide and conquer algorithm

Autor: Adrien Poteaux, Martin Weimann

Publikováno v: Annales Henri Lebesgue
Annales Henri Lebesgue, 2021, 4, pp.1061--1102. ⟨10.5802/ahl.97⟩
Annales Henri Lebesgue, UFR de Mathématiques-IRMAR, 2021, 4, pp.1061--1102. ⟨10.5802/ahl.97⟩

Let $F\in \mathbb{K}[X, Y ]$ be a polynomial of total degree $D$ defined over a perfect field $\mathbb{K}$ of characteristic zero or greater than $D$. Assuming $F$ separable with respect to $Y$ , we provide an algorithm that computes the singular par

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a58af97bd5d232de3a0b7886af9860c5
https://inria.hal.science/hal-01578214v3/document

Computing the equisingularity type of a pseudo-irreducible polynomial

Autor: Adrien Poteaux, Martin Weimann

Publikováno v: Applicable Algebra in Engineering, Communication and Computing
Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 2020, 31, pp.435-460. ⟨10.1007/s00200-020-00451-x⟩
Applicable Algebra in Engineering, Communication and Computing, 2020, 31, pp.435-460. ⟨10.1007/s00200-020-00451-x⟩

Germs of plane curve singularities can be classified accordingly to their equisingularity type. For singularities over C, this important data coincides with the topological class. In this paper, we characterise a family of singularities, containing i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f39689224ee43d5c8793222aaceb61c9
http://arxiv.org/abs/1911.05596

A Symbolic Computation Approach Towards the Asymptotic Stability Analysis of Differential Systems with Commensurate Delays

Autor: Alban Quadrat, Yacine Bouzidi, Adrien Poteaux

Publikováno v: Delays and Interconnections: Methodology, Algorithms and Applications ISBN: 9783030115531

This paper aims at studying the asymptotic stability of retarded type linear differential systems with commensurate delays. Within the frequency-domain approach, it is well-known that the asymptotic stability of such a system is ensured by the condit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a0e0b1a843e1262f33e0a58cb3e39d58
https://doi.org/10.1007/978-3-030-11554-8_11

Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling

Autor: Nathalie Corson, Nathalie Verdière, Hélène Castel, Adrien Poteaux, Alban Quadrat, François Boulier, Valentina Lanza, François Lemaire

Publikováno v: Developments in Language Theory ISBN: 9783319986531
CASC
CASC 2018-The 20th International Workshop on Computer Algebra in Scientific Computing
CASC 2018-The 20th International Workshop on Computer Algebra in Scientific Computing, Sep 2018, Lille, France. ⟨10.1007/978-3-319-99639-4_6⟩
HAL

International audience; This paper presents a proof of concept for symbolic and numeric methods dedicated to the parameter estimation problem for models formulated by means of nonlinear integro-differential equations (IDE). In particular, we address:

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d999f453b5e4ffb25d8f7f6c8c4dce1
https://doi.org/10.1007/978-3-319-99639-4_6