{"paper":{"title":"Algorithm for computing $\\mu$-bases of univariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.AC"],"primary_cat":"math.AG","authors_text":"Hoon Hong, Irina A. Kogan, Zachary Hough","submitted_at":"2016-03-15T18:46:15Z","abstract_excerpt":"We present a new algorithm for computing a $\\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\\mathbb{K}$. The algorithm is conceptually different from the previously-developed algorithms by Cox, Sederberg, Chen, Zheng, and Wang for $n=3$, and by Song and Goldman for an arbitrary $n$. It involves computing a \"partial\" reduced row-echelon form of a $ (2d+1)\\times n(d+1)$ matrix over $\\mathbb{K}$, where $d$ is the maximum degree of the input polynomials. The proof of the algorithm is based on standard linear algebra and is completely self-contained. It i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04813","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}