Homotopy Iterators
Algebraic Geometry
2025-09-11 v1
Abstract
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which tracks them along the homotopy. Doing so produces a representation of the target solutions, bypassing the need to hold all solutions in memory. We discuss several applications of this datatype ranging from solution counting to data compression.
Keywords
Cite
@article{arxiv.2509.08084,
title = {Homotopy Iterators},
author = {Paul Breiding and Taylor Brysiewicz and Hannah Friedman},
journal= {arXiv preprint arXiv:2509.08084},
year = {2025}
}
Comments
20 pages, 6 figures