{"paper":{"title":"Towards Randomized Testing of $q$-Monomials in Multivariate Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Quanhai Yang, Shenshi Chen, Yaqing Chen","submitted_at":"2013-02-24T11:58:20Z","abstract_excerpt":"Given any fixed integer $q\\ge 2$, a $q$-monomial is of the format $\\displaystyle x^{s_1}_{i_1}x^{s_2}_{i_2}...x_{i_t}^{s_t}$ such that $1\\le s_j \\le q-1$, $1\\le j \\le t$. $q$-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and $q$-monomails for prime $q$ in multivariate polynomials relies on the property that $Z_q$ is a field when $q\\ge 2 $ is prime. When $q>2$ is not prime, it remains open whether the problem of testing $q$-monomials can be solved in some compatible complexity. In this paper, we present a randomized $O^*(7.15^k)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5898","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"}