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04/14/2023
Faster List Decoding of AG Codes
In this article, we present a fast algorithm performing an instance of t...
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02/10/2023
Refined F_5 Algorithms for Ideals of Minors of Square Matrices
We consider the problem of computing a grevlex Gröbner basis for the set...
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02/08/2023
Beating binary powering for polynomial matrices
The Nth power of a polynomial matrix of fixed size and degree can be com...
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02/18/2022
Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix
Consider a matrix 𝐅∈𝕂[x]^m × n of univariate polynomials over a field 𝕂....
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02/18/2022
Faster change of order algorithm for Gröbner bases under shape and stability assumptions
Solving zero-dimensional polynomial systems using Gröbner bases is usual...
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10/15/2021
Faster Modular Composition
A new Las Vegas algorithm is presented for the composition of two polyno...
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02/06/2021
Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
Linear recurrent sequences are those whose elements are defined as linea...
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10/09/2020
Deterministic computation of the characteristic polynomial in the time of matrix multiplication
This paper describes an algorithm which computes the characteristic poly...
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03/27/2020
Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation
Suppose 𝕂 is a large enough field and 𝒫⊂𝕂^2 is a fixed, generic set of p...
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02/15/2020
A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension
Let f_1,…,f_m be elements in a quotient R^n / N which has finite dimensi...
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12/04/2019
Computing syzygies in finite dimension using fast linear algebra
We consider the computation of syzygies of multivariate polynomials in a...
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10/02/2019
An Algebraic Attack on Rank Metric Code-Based Cryptosystems
The Rank metric decoding problem is the main problem considered in crypt...
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05/10/2019
Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants
Complexity bounds for many problems on matrices with univariate polynomi...
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07/03/2018
Verification Protocols with Sub-Linear Communication for Polynomial Matrix Operations
We design and analyze new protocols to verify the correctness of various...
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07/03/2018
Interactive Certificates for Polynomial Matrices with Sub-Linear Communication
We develop and analyze new protocols to verify the correctness of variou...
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02/06/2018
Computing Popov and Hermite forms of rectangular polynomial matrices
We consider the computation of two normal forms for matrices over the un...
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02/06/2018
Certification of minimal approximant bases
Considering a given computational problem, a certificate is a piece of a...
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01/14/2018
Fast computation of approximant bases in canonical form
In this article, we design fast algorithms for the computation of approx...
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12/12/2017
Block-Krylov techniques in the context of sparse-FGLM algorithms
Consider a zero-dimensional ideal I in K[X_1,...,X_n]. Inspired by Faugè...
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07/06/2017
Algorithms for zero-dimensional ideals using linear recurrent sequences
Inspired by Faugère and Mou's sparse FGLM algorithm, we show how using l...
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05/30/2017
Fast Computation of the Roots of Polynomials Over the Ring of Power Series
We give an algorithm for computing all roots of polynomials over a univa...
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05/30/2017
Computing Canonical Bases of Modules of Univariate Relations
We study the computation of canonical bases of sets of univariate relati...
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07/14/2016
Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix
Given a nonsingular n × n matrix of univariate polynomials over a field ...
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02/01/2016
Fast Computation of Shifted Popov Forms of Polynomial Matrices via Systems of Modular Polynomial Equations
We give a Las Vegas algorithm which computes the shifted Popov form of a...
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02/01/2016
Fast Computation of Minimal Interpolation Bases in Popov Form for Arbitrary Shifts
We compute minimal bases of solutions for a general interpolation proble...
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12/11/2015