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

This paper gives a new algorithm to compute Gröbner bases of maximal minors of matrices of polynomials, and applies this algorithm to compute the critical points of a polynomial restricted to an algebraic variety. A complexity analysis of this new algorithm is also given.

February 2024 · Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din

Refined $F_5$ algorithms for ideals of minors of square matrices

This paper gives new criteria for the detection and avoidance of reductions to zero when computing Gröbner bases of determinantal ideals of square matrices of polynomials. In the comaximal case and under certain genericity assumptions, all reductions to zero are avoided and a complexity analysis of the resulting algorithm is provided.

February 2023 · Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din

A survey of mathematical structures for lunar networks

This paper surveys various possible mathematical foundations for delay tolerant networking on temporal networks with the goal of applicability to pathfinding and related problems in a solar system internet.

May 2022 · Alan Hylton, Robert Short, Jacob Cleveland, Olivia Freides, Zander Memon, Robert Cardona, Robert Green, Justin Curry, Sriram Gopalakrishnan, Devavrat Vivek Dabke, Brittany Story, Michael Moy, Brendan Mallery