RandomPoints package for Macaulay2
Sankhaneel Bisui, Zhan Jiang, Sarasij Maitra, Th\'ai Th\`anh Nguy\^en,, Karl Schwede
TL;DR
The paper introduces the RandomPoints package for Macaulay2, which helps identify rational points, estimate variety dimensions, and find non-vanishing minors by evaluating matrices at points.
Contribution
It provides new tools within Macaulay2 for analyzing varieties over finite fields, focusing on point identification and matrix evaluations.
Findings
Efficient methods to find rational points on varieties.
Tools to estimate the dimension of a variety.
Algorithms to obtain non-vanishing minors in matrices.
Abstract
We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to obtain non-vanishing minors of a given size in a given matrix, by evaluating the matrix at a point.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Tensor decomposition and applications