English

A short proof for the parameter continuation theorem

Algebraic Geometry 2024-07-18 v5 Numerical Analysis Numerical Analysis

Abstract

The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gr\"obner bases. Our approach gives a method for computing discriminants.

Keywords

Cite

@article{arxiv.2302.14697,
  title  = {A short proof for the parameter continuation theorem},
  author = {Viktoriia Borovik and Paul Breiding},
  journal= {arXiv preprint arXiv:2302.14697},
  year   = {2024}
}
R2 v1 2026-06-28T08:52:01.625Z