Homotopy Iterators
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915487424708608 |
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| author | Breiding, Paul Brysiewicz, Taylor Friedman, Hannah |
| author_facet | Breiding, Paul Brysiewicz, Taylor Friedman, Hannah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy Iterators Breiding, Paul Brysiewicz, Taylor Friedman, Hannah Algebraic Geometry 65H14 (Primary) 68N19, 14Q20 (Secondary) 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. |
| title | Homotopy Iterators |
| topic | Algebraic Geometry 65H14 (Primary) 68N19, 14Q20 (Secondary) |
| url | https://arxiv.org/abs/2509.08084 |