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arXiv · 2509.08084

Homotopy Iterators

Paul Breiding·Taylor Brysiewicz·Hannah Friedman
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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.

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Paul Breiding, Taylor Brysiewicz, Hannah Friedman. 2025-09-09. Homotopy Iterators. https://arxiv.org/abs/2509.08084

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