{"paper":{"title":"Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Caleb Meier, Harry Dym, J. W. Helton","submitted_at":"2012-12-04T22:06:31Z","abstract_excerpt":"Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non-commutative polynomial p(X,Y) in two k x k matrix variables X and Y. Algorithms that will generically determine whether the given family P has a non-commutative representation and that will produce such a representation are developed. These algorithms will determine a non-commutative representation for families P that admit a a non-commutative representation in an open, dense subset of the vector space of non-commut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0891","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"}