Vincent Neiger

activity

20162024

collaborators

Showing cs.SCShow all

4 papers · 1 filter

cs.SC2024

Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations

Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din

Given polynomials $g$ and $f_{1}, \dots, f_{p}$ , all in $k [x_{1}, \dots, x_{n}]$ for some field $k$ , we consider the problem of computing the critical points of the restriction of $g$ …

cs.SC2023

Refined $F_{5}$ Algorithms for Ideals of Minors of Square Matrices

Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din

We consider the problem of computing a grevlex Gröbner basis for the set $F_{r} (M)$ of minors of size $r$ of an $n \times n$ matrix $M$ of generic linear forms over a field of charact…

cs.SC2023

Beating binary powering for polynomial matrices

Alin Bostan, Vincent Neiger, Sergey Yurkevich

The $N$ th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~ $N$ . When Fast Fourier…

cs.SC2016

Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix

George Labahn, Vincent Neiger, Wei Zhou

Given a nonsingular $n \times n$ matrix of univariate polynomials over a field $K$ , we give fast and deterministic algorithms to compute its determinant and its Hermite no…

Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations

Refined F5​ Algorithms for Ideals of Minors of Square Matrices

Beating binary powering for polynomial matrices

Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix

Refined $F_{5}$ Algorithms for Ideals of Minors of Square Matrices