{"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/sum-of-squares-decomposition-of-positive","title":"Sum of squares decomposition of positive polynomials with rational coefficients","arxiv_id":"2312.16801","date":"2023-12-28","proceeding":null,"authors":["Santiago Laplagne"],"abstract":"We present an example of a strictly positive polynomial with rational coefficients that can be decomposed as a sum of squares of polynomials over $\\R$ but not over $\\Q$. This answers an open question by C. Scheiderer posed as the second question in Section 5.1 of the paper Sums of squares of polynomials with rational coefficients (2012). We verify that the example we construct defines a nonsingular projective hypersurface, giving also a positive answer to the third question posed in that section.","url_abs":"https://arxiv.org/abs/2312.16801v1","url_pdf":"https://arxiv.org/pdf/2312.16801v1.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":"sum-of-squares-decomposition-of-positive","repo_url":"https://github.com/slap/sums-of-squares","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}