{"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/balancing-chemical-equations-form-the","title":"Balancing chemical equations: form the perspective of Hilbert basis","arxiv_id":"2410.06023","date":"2024-10-08","proceeding":null,"authors":["Zeying Zhang","Xueqin Zhang","Y. X. Zhao","Shengyuan A. Yang"],"abstract":"The balancing of chemical equations is a basic problem in chemistry. A commonly employed method is to convert the task to a linear algebra problem, and then solve the null space of the constructed formula matrix. However, in this method, the directly obtained solution may be invalid, and there is no canonical choice of independent basis reactions. Here, we show that these drawbacks originate from the fact that the fundamental structure of solutions here is not a linear space but a positive affine monoid. This new understanding enables a systematic approach and a complete description of all possible reactions by a unique set of independent elementary reactions, called Hilbert-basis reactions. By clarifying its underlying mathematical structure, our work offers a new perspective on this old problem of balancing chemical equations.","url_abs":"https://arxiv.org/abs/2410.06023v1","url_pdf":"https://arxiv.org/pdf/2410.06023v1.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":"balancing-chemical-equations-form-the","repo_url":"https://github.com/zhangzeyingvv/HilbertBalance","is_official":1,"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}