{"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/matrix-method-for-persistence-modules-on","title":"Matrix Method for Persistence Modules on Commutative Ladders of Finite Type","arxiv_id":"1706.10027","date":"2017-06-30","proceeding":null,"authors":["Hideto Asashiba","Emerson G. Escolar","Yasuaki Hiraoka","Hiroshi Takeuchi"],"abstract":"The theory of persistence modules on the commutative ladders $CL_n(\\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persistence module $M$ on $CL_n(\\tau)$ as a morphism between zigzag modules, which can be expressed in a block matrix form. For the representation finite case ($n\\leq 4)$, we provide an algorithm that uses certain permissible row and column operations to compute a normal form of the block matrix. In this form an indecomposable decomposition of $M$, and thus its persistence diagram, is obtained.","url_abs":"http://arxiv.org/abs/1706.10027v1","url_pdf":"http://arxiv.org/pdf/1706.10027v1.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":"matrix-method-for-persistence-modules-on","repo_url":"https://github.com/emerson-escolar/intervals","is_official":0,"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}