Jérémy Berthomieu Computer Algebra · Polynomial Systems

Research

Software

Computer algebra and polynomial system solving.

Quasi-Linear Guessing of Minimal Lexicographic Gröbner Bases of Ideals of C-Relations of Random Bi-Indexed Sequences

Jérémy Berthomieu, Romain Lebreton and Kevin Tran
Maple

Implementation of quasi-linear guessing algorithms for linear recurrence relations with constant coefficients of bi-indexed sequences.

MultiLinG

Daniela Kaufmann and Jérémy Berthomieu
C++

A formal verification tool for verifying And-Inverter Graphs using Gröbner bases computations through msolve.

Guessing Linear Recurrence Relations

Jérémy Berthomieu
Maple

Implementation of guessing algorithms for linear recurrence relations with constant coefficients of a multidimensional table with the Berlekamp–Massey–Sakata, Artinian Gorenstein border basis and Scalar-FGLM algorithms.

Isomorphism of Polynomials with One Secret

Jérémy Berthomieu, Jean-Charles Faugère and Ludovic Perret
Maple

Implementation of the algorithms given in Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials: The Regular Case to determine matrix A such that $A^T\cdot H_i\cdot A=H_i$.

Convex-dense Bivariate Factorization

Jérémy Berthomieu and Grégoire Lecerf
Maple

Implementation of the algorithm given in Reduction of bivariate polynomials from convex-dense to dense, with application to factorization to speed up the factorization of bivariate polynomials.

Homogeneous Polynomial Ideal Ridge Computation

Jérémy Berthomieu, Pascal Hivert and Hussein Mourtada
Maple

Implementation of the algorithms given in Computing Hironaka's invariants: Ridge and Directrix to determine the least number of additive polynomials needed to write a homogeneous algebraic system.

Multihomogeneous Polynomial Ideal Ridge Computation

Jérémy Berthomieu
Maple

Extension of the algorithm for computing the ridge to muli-homogeneous polynomials.