{"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/square-root-of-a-multivector-of-clifford","title":"Square root of a multivector of Clifford algebras in 3D: A game with signs","arxiv_id":"2003.06873","date":"2020-03-15","proceeding":null,"authors":["A. Acus","A. Dargys"],"abstract":"An algorithm to extract the square root in radicals from a multivector (MV) in real Clifford algebras Cl(p,q) for n=p+q <=3 is presented. We show that in the algebras Cl(3,0), Cl(1,2) and Cl(0,3) there are up to four isolated roots in a case of the most general (generic) MV. The algebra Cl(2,1) makes up an exception and the MV here can have up to 16 isolated roots. In addition to isolated roots, a continuum of roots can appear in all algebras except p+q=1. A number of examples are provided to illustrate properties of various roots that may appear in n=3 Clifford algebras.","url_abs":"https://arxiv.org/abs/2003.06873v2","url_pdf":"https://arxiv.org/pdf/2003.06873v2.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":"square-root-of-a-multivector-of-clifford","repo_url":"https://github.com/polychromatist/three","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}