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Factoring polynomials with rational coefficients   总被引:55,自引:0,他引:55  
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Let i(L), i(L*) denote the successive minima of a latticeL and its reciprocal latticeL *, and let [b1,..., b n ] be a basis ofL that is reduced in the sense of Korkin and Zolotarev. We prove that and, where and j denotes Hermite's constant. As a consequence the inequalities are obtained forn7. Given a basisB of a latticeL in m of rankn andx m , we define polynomial time computable quantities(B) and(x,B) that are lower bounds for 1(L) and(x,L), where(x,L) is the Euclidean distance fromx to the closest vector inL. If in additionB is reciprocal to a Korkin-Zolotarev basis ofL *, then 1(L) n * (B) and.The research of the second author was supported by NSF contract DMS 87-06176. The research of the third author was performed at the University of California, Berkeley, with support from NSF grant 21823, and at AT&T Bell Laboratories.  相似文献
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