Minkowski's theorem - Wikipedia
网页In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin).
Minkowski's Theorem and Its Applications - CMU
网页Theorem.(Minkowski's theorem) Suppose C to be a symmetric, convex, bounded subset Rd. If vol( C ) > 2d, then C contains at least one lattice point other than 0. Proof. Take C0= 1 2 C = 1 2 x : x 2 C , then vol( C0) > 1. Then we claim that There exists a nonzero integral vector v 2 Zdnf 0g, such that v 2 C0C0.
格密码1.4 最短距离与Minkowski's theorem - 知乎 - 知乎专栏
网页二、Minkowski's theorem. 本节估计 \lambda 的上界，一个显然的上界是 \min_i{\mathbf{b}_i} ，但这个上界与基的选取有关。 定义 1 Hermite factor of a lattice： n 维格 \Lambda 的赫米特因子是 \gamma(\Lambda)=(\lambda(\Lambda)/det(\Lambda)^{1/n})^2 。
Minkowski theorem - Encyclopedia of Mathematics
网页2014年11月15日 · Minkowski's theorem on convex bodies is the most important theorem in the geometry of numbers, and is the basis for the existence of the geometry of numbers as a separate division of number theory. It was established by H. Minkowski in 1896 (see [1]).
闵可夫斯基不等式 - 维基百科，自由的百科全书
网页在数学中，闵可夫斯基不等式（ Minkowski inequality）表明L p 空间是一个赋范向量空间。 设 S {\displaystyle S} 是一个 测度空间 ， 1 ≤ p ≤ ∞ , f , g ∈ L p ( S ) {\displaystyle 1\leq p\leq \infty ,f,g\in L^{p}(S)} ，那么 f + g ∈ L p ( S ) {\displaystyle f+g\in L^{p}(S)} ，我们有：
闵可夫斯基定理 - 百度百科
网页验证推导. 任取一个关于原点对称且面积大于1的封闭凸图形，一定存在两点，使横纵坐标之差为整数。. 设其中一点坐标为 (x0,y0)，另一点为 (x0+k,y0+b) (k,b∈Z)，并且 (x0,y0)、 (x0+k,y0+b)都在图形内。. 因图形关于原点对称，所以对于任意点 (x,y)，若其在图形中，则 ...
闵可夫斯基格点定理证明(Minkowski Lattice Therorem) - 知乎
网页当在该空间中有一个体积为S的中心在原点且中心对称的凸体，只要这个凸体的体积 大于 由相临的格点组成的平行多面体（2维就是平行四边形）的体积的2^n倍，那么这个凸体中必然包含除了原点之外的某个 格点。. 在2维的情形下读者可以自行画图去验证这个 ...
Minkowski's bound - Wikipedia
网页In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field K. It is named for the mathematician Hermann Minkowski .
网页Minkowski’s Theorem. SVP is hard to approximate within any constant factor√ unless NP = RP. CVP is hard to approximate within nO(1/loglogn). Approximation within the factor n is in NP ∩co-NP. 4 Lattice basis reduction We will show a polynomial time algorithm to approximately solve the SVP within a factor of 2O(n). Because
网页Minkowski’s Theorem guarantees R contains a lattice point if R satisfies a set of requirements set forth by the theorem. We will discuss Pick’s Theorem and Minkowski’s Theorem more after a brief introduc-tion to lattices. We will then give an overview of the steps we will need to take to prove Pick’s Theorem and Minkowski’s Theorem.