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Around the Numerical Evaluation of D-Finite Functions
D-Finite functions of one variable (also known as holonomic functions) are the solutions of linear ordinary differential equations with polynomial coefficients.... -
Topologically certified approximation of umbilics and ridges on polynomial pa...
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves... -
Bernstein's basis and real root isolation
The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method... -
An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases
This paper presents an algebraic cryptanalysis of nonlinear filter generator. A linear shift register of length L filtered by a non linear boolear function f of degree... -
Algebraic cryptanalysis of HFE using Gröbner bases
HFE (Hidden Fields Equations) is a public key cryptosystem using (multivariat- e) polynomial operations over finite fields. It has been proposed by Jacques Patarin... -
Using computer algebra tools to classify serial cuspidal manipulators
In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work that this ability to... -
Linear algebra for skew-polynomial matrices
We describe an algorithm for transforming skew-polynomial matrices over an Ore domain in row-reduced form, and show that this algorithm can be used to perform the... -
Overview of the Mathemagix type system
The goal of the Mathemagix project is to develop a new and free software for computer algebra and computer analysis, based on a strongly typed and compiled language.... -
An Integrated Development of Buchberger's Algorithm in Coq
We present an integrated formal development of Buchberger's algorithm in Coq, that is we prove constructively the existence of Gröbner bases without explicitly writing... -
Resolvent Representation for Regular Differential Ideals
We show that the generic zeros of a differential ideal $\dreg[A]$ defined by a differential chain $A$ are birationally equivalent to the general zeros of a single... -
Multi-Valued Computer Algebra
One of the main strengths of computer algebra is being able to solve a family of problems with one computation. In order to express not only one problem but a family... -
Motif Statistics
We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers «motifs» widely used in... -
Proving and Computing: a Certified Version of the Buchberger's Algorithm
This paper shows on a non-trivial example that it is possible to mix proving and computing using current technologies. We present a proof of the Buchberger's algorithm... -
On the Algorithms of Guruswami-Sudan List Decoding over Finite Rings
This thesis studies the algorithmic techniques of list decoding, first proposed by Guruswami and Sudan in 1998, in the context of Reed-Solomon codes over finite rings.... -
Automatic computation of Stokes matrices
International audience -
Stokes phenomenon for the prolate spheroidal wave equation
Special Issue: Approximation and extrapolation of convergent and divergent sequences and series (CIRM, Luminy - France, 2009) -
Computing Closed-Form Solutions of Integrable Connections
International audience -
Proving formally the implementation of an efficient gcd algorithm for polynom...
Last version published in the proceedings of IJCAR 06, part of FLOC 06. -
A Reduced Form for Linear Differential Systems and its Application to Integra...
International audience -
Solving Parametric Polynomial Systems
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0,...
