Solving Equations Using Khovanskii Bases
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 Plücker 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.
The picture below represents the initial algebra of the Del Pezzo surface in Example 2.6 in the paper.
Our Julia code can be downloaded here
All the examples computed and discussed in the paper can be reproduced using this code, and they can be downloaded here
The following tables report the computations performed over the Grassmannians Gr(3,6) and Gr(2,4).
Project page created: 23/06/2023
Project contributors: Barbara Betti, Marta Panizzut, Simon Telen
Corresponding author of this page: Barbara Betti, email firstname.lastname@example.org
Software used: Julia (Version 1.9).
License for code of this project page: MIT License https://spdx.org/licenses/MIT.html.