# Monodromy Solver: Sequential and Parallel

arXiv: https://arxiv.org/abs/1805.12212 · HTML: https://mlsanity.com/paper/1805.12212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2018.

## Built on by (most cited first, 1 of 1)

- [Numerically Computing Galois Groups of Minimal Problems](https://mlsanity.com/paper/2507.10407/) (2025)

## Abstract (arXiv)

We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in the presence of a large number of failures of the homotopy continuation subroutine. We give special attention to parallelization and probabilistic analysis of a model adapted to parallelization and failures. Apart from theoretical results, we developed a simulator that allows us to run a large number of experiments without recomputing the outcomes of the continuation subroutine.