{"paper":{"title":"Computing Canonical Bases of Modules of Univariate Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Thi Xuan Vu, Vincent Neiger","submitted_at":"2017-05-30T13:56:27Z","abstract_excerpt":"We study the computation of canonical bases of sets of univariate relations $(p_1,\\ldots,p_m) \\in \\mathbb{K}[x]^{m}$ such that $p_1 f_1 + \\cdots + p_m f_m = 0$; here, the input elements $f_1,\\ldots,f_m$ are from a quotient $\\mathbb{K}[x]^n/\\mathcal{M}$, where $\\mathcal{M}$ is a $\\mathbb{K}[x]$-module of rank $n$ given by a basis $\\mathbf{M}\\in\\mathbb{K}[x]^{n\\times n}$ in Hermite form. We exploit the triangular shape of $\\mathbf{M}$ to generalize a divide-and-conquer approach which originates from fast minimal approximant basis algorithms. Besides recent techniques for this approach, we rely o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10649","kind":"arxiv","version":1},"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"}