Substitution and quotient of the isotropy group action

[2607.15069] Substitution and quotient of the isotropy group action Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2607.15069 (math) [Submitted on 16 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Substitution and quotient of the isotropy group action Authors: Xin Li , Yu Wang , Shenglong Hu View a PDF of the paper titled Substitution and quotient of the isotropy group action, by Xin Li and 1 other authors View PDF HTML (experimental) Abstract: Given a solution of the Brent equations, a partial solution can be substituted into the Brent equations which makes it a reduced polynomial system. Then the reduced polynomial system can be solved by symbolic software, and a parameterized solution set can often be found. However, the solution set admits a positive-dimensional isotropy group action. The parameterized solution set may lie entirely in a single isotropy group orbit. In this paper, we give a geometric explanation of making the substitution. Considering the foliation structure of the solution set, a method on choosing the partial solution is proposed. By the proposed method, parameterized solution sets that intersect distinct isotropy group orbits can be efficiently determined. In particular, the rational solution found by Dumas, Pernet and Sedoglavic is parameterized. In the parameterized solution set, we can find infinitely many inequivalent 48-multiplication algorithms with only rational coefficients. Comments: The second version, many typos have been changed Subjects: Algebraic Geometry (math.AG) MSC classes: Primary 14L30, Secondary 68W30 Cite as: arXiv:2607.15069 [math.AG] (or arXiv:2607.15069v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2607.15069 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xin Li [ view email ] [v1] Thu, 16 Jul 2026 14:43:28 UTC (26 KB) [v2] Sat, 15 Aug 2026 04:30:46 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Substitution and quotient of the isotropy group action, by Xin Li and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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