{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tropical-homotopy-continuation","title":"Tropical Homotopy Continuation","arxiv_id":"1601.02818","date":"2016-01-12","proceeding":null,"authors":["Anders Nedergaard Jensen"],"abstract":"Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the numerical \"regeneration\" technique leads to a new method for enumerating the mixed cells of a mixed subdivision. This tropical approach shares some ideas with the recent algorithm by Malajovich. However, our algorithm has several advantages. It is memoryless, parallelisable as a tree traversal, exact and relies on symbolic perturbations. Our computational experiments show that the method is competitive and especially fast on the Katsura class of examples.","url_abs":"http://arxiv.org/abs/1601.02818v1","url_pdf":"http://arxiv.org/pdf/1601.02818v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"tropical-homotopy-continuation","repo_url":"https://github.com/JuliaHomotopyContinuation/TropicalHomotopyContinuation.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"tropical-homotopy-continuation","repo_url":"https://github.com/UnofficialJuliaMirror/MixedSubdivisions.jl-291d046c-3347-11e9-1e74-c3d251d406c6","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"tropical-homotopy-continuation","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/MixedSubdivisions.jl-291d046c-3347-11e9-1e74-c3d251d406c6","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"tropical-homotopy-continuation","repo_url":"https://github.com/saschatimme/MixedSubdivisions.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}