{"paper":{"title":"Computing explicit isomorphisms with full matrix algebras over $\\mathbb{F}_q(x)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"math.RA","authors_text":"G\\'abor Ivanyos, Lajos R\\'onyai, P\\'eter Kutas","submitted_at":"2015-08-31T10:22:07Z","abstract_excerpt":"We propose a polynomial time $f$-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over $\\mathbb{F}_q$) for computing an isomorphism (if there is any) of a finite dimensional $\\mathbb{F}_q(x)$-algebra $A$ given by structure constants with the algebra of $n$ by $n$ matrices with entries from $\\mathbb{F}_q(x)$. The method is based on computing a finite $\\mathbb{F}_q$-subalgebra of $A$ which is the intersection of a maximal $\\mathbb{F}_q[x]$-order and a maximal $R$-order, where $R$ is the subring of $\\mathbb{F}_q(x)$ consisting of fractions of polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07755","kind":"arxiv","version":3},"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"}