{"paper":{"title":"Detecting Simultaneous Integer Relations for Several Real Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT"],"primary_cat":"cs.SC","authors_text":"Jingwei Chen, Jingzhong Zhang, Xiaolin Qin, Yong Feng","submitted_at":"2010-10-11T01:26:08Z","abstract_excerpt":"An algorithm which either finds an nonzero integer vector ${\\mathbf m}$ for given $t$ real $n$-dimensional vectors ${\\mathbf x}_1,...,{\\mathbf x}_t$ such that ${\\mathbf x}_i^T{\\mathbf m}=0$ or proves that no such integer vector with norm less than a given bound exists is presented in this paper. The cost of the algorithm is at most ${\\mathcal O}(n^4 + n^3 \\log \\lambda(X))$ exact arithmetic operations in dimension $n$ and the least Euclidean norm $\\lambda(X)$ of such integer vectors. It matches the best complexity upper bound known for this problem. Experimental data show that the algorithm is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1982","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"}