{"paper":{"title":"Algebraic Independence and Blackbox Identity Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.CC","authors_text":"Johannes Mittmann, Malte Beecken, Nitin Saxena","submitted_at":"2011-02-14T15:00:16Z","abstract_excerpt":"Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials {f_1, ..., f_m} \\subset \\F[x_1, ..., x_n] are called algebraically independent if there is no non-zero polynomial F such that F(f_1, ..., f_m) = 0. The transcendence degree, trdeg{f_1, ..., f_m}, is the maximal number r of algebraically independent polynomials in the set. In this paper we design blackbox and efficient linear maps \\phi that reduce the number of variables from n to r but maintain trdeg{\\phi(f_i)}_i = r, assuming f_i's sparse and sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2789","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"}