{"paper":{"title":"Multivariate Polynomial Integration and Derivative Are Polynomial Time Inapproximable unless P=NP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bin Fu","submitted_at":"2010-12-10T20:51:16Z","abstract_excerpt":"We investigate the complexity of integration and derivative for multivariate polynomials in the standard computation model. The integration is in the unit cube $[0,1]^d$ for a multivariate polynomial, which has format $f(x_1,\\cdots, x_d)=p_1(x_1,\\cdots, x_d)p_2(x_1,\\cdots, x_d)\\cdots p_k(x_1,\\cdots, x_d)$, where each $p_i(x_1,\\cdots, x_d)=\\sum_{j=1}^d q_j(x_j)$ with all single variable polynomials $q_j(x_j)$ of degree at most two and constant coefficients. We show that there is no any factor polynomial time approximation for the integration $\\int_{[0,1]^d}f(x_1,\\cdots,x_d)d_{x_1}\\cdots d_{x_d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2377","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"}