Sriram Gopalakrishnan

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cs.SC2024

On the arithmetic complexity of computing GrÃ¶bner bases of comaximal determinantal ideals

Sriram Gopalakrishnan

Let $M$ be an $n \times n$ matrix of homogeneous linear forms over a field $k$ . If the ideal $I_{n - 2} (M)$ generated by minors of size $n - 1$ is Cohen-Macaulay, then the…

cs.SC2024

Optimized GrÃ¶bner 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 $g$ …