{"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/a-signature-based-algorithm-for-computing-the","title":"A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System","arxiv_id":"2202.13784","date":"2022-02-28","proceeding":null,"authors":["Christian Eder","Pierre Lairez","Rafael Mohr","Mohab Safey El Din"],"abstract":"Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The nondegenerate locus of a polynomial system is the set of points where the codimension of the solution set matches the number of equations. Computing the nondegenerate locus is classically done through ideal-theoretic operations in commutative algebra such as saturation ideals or equidimensional decompositions to extract the component of maximal codimension. By exploiting the algebraic features of signature-based Gr\\\"obner basis algorithms we design an algorithm which computes a Gr\\\"obner basis of the equations describing the closure of the nondegenerate locus of a polynomial system, without computing first a Gr\\\"obner basis for the whole polynomial system.","url_abs":"https://arxiv.org/abs/2202.13784v2","url_pdf":"https://arxiv.org/pdf/2202.13784v2.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":"a-signature-based-algorithm-for-computing-the","repo_url":"https://github.com/rafaeldavidmohr/signaturegb.jl","is_official":1,"mentioned_in_paper":1,"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}