Numerically Computing Galois Groups of Minimal Problems

2025/07/14 by Timothy Duff, Duff, Timothy · 1 citation
Computer Science · Engineering · #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2507.10407

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions.

Cited by

• A priori bounds for certified Krawczyk homotopy tracking

Related

• A Galois-Theoretic Complexity Measure for Solving Systems of Algebraic Equations
• Solving Parameterized Polynomial Systems with Decomposable Projections
• Numerical computation of Galois groups
• The complexity and geometry of numerically solving polynomial systems
• A note on Solving Parametric Polynomial Systems