Polynomial Equations: Theory and Practice
Algebraic Geometry
2023-04-24 v2 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts. The theory is illustrated by many examples using different software packages.
Cite
@article{arxiv.2210.04939,
title = {Polynomial Equations: Theory and Practice},
author = {Simon Telen},
journal= {arXiv preprint arXiv:2210.04939},
year = {2023}
}
Comments
This article will appear as a chapter of a forthcoming book presenting research acitivies conducted in the European Network POEMA. It discusses polynomial equations, with optimization as point of entry. 24 pages, 7 figures