Solving Equations Using Khovanskii Bases
Algebraic Geometry
2023-08-23 v2
Abstract
We develop a new eigenvalue method for solving structured polynomial equations over any field. The equations are defined on a projective algebraic variety which admits a rational parameterization by a Khovanskii basis, e.g., a Grassmannian in its Pl\"ucker embedding. This generalizes established algorithms for toric varieties, and introduces the effective use of Khovanskii bases in computer algebra. We investigate regularity questions and discuss several applications.
Cite
@article{arxiv.2306.14871,
title = {Solving Equations Using Khovanskii Bases},
author = {Barbara Betti and Marta Panizzut and Simon Telen},
journal= {arXiv preprint arXiv:2306.14871},
year = {2023}
}
Comments
25 pages, 1 figure, 2 tables