alexander polynomial

alexander polynomial的基本解释

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亚历山大多项式

与alexander polynomial相关的网络例句 [注：此内容来源于网络，仅供参考]

In contrast, Diogenes, one of Antisthenes most famous followers carried the cynical philosophy to its farthest extreme. Diogenes was not known merely as one of "The Dog Philosophers," his personal nickname was "The Dog" and Plato referred to him as "Socrates gone mad." He denied all physical wealth and pleasure; he lived in a barrel and his only possessions were a robe to cover himself and a walking stick. There is an antecdote of questionable historical accuracy that demonstrates the character of Diogenes: One day Diogenes was sitting on a hill next to his barrel enjoying the warm rays of the sun when he was approached by Alexander the Great. Alexander asked Diogenes if he was the infamous Diogenes of whom the Athenians had spoken. Diogenes replied that he was. Alexander asked Diogenes if it was true that he had no desire for anything. Diogenes looked up at Alexander and said that he only wanted one thing, with that he asked Alexander to move a little to one side because he was blocking the sun. After the encounter, Alexander reportedly stated that if he could be anyone other than Alexander he would want to be Diogenes. Although Diogenes' behavior was sometimes amusing, he was not well liked in Athens primarily because of his writings encouraging incest and cannibalism.

和他形成对比的是带奥珍妮丝，他最著名的一个把犬儒哲学发扬到极致的追随者，带奥珍妮丝不光被看成犬儒哲学家，他自己的外号是狗并且柏拉图称他为疯了的苏格拉底，他漠视一切身体健康和愉悦，他住在一个罐子里，所有的财产是用来遮盖自己的一挂长袍，和一只拐杖，曾有一个轶闻能够体现带奥珍妮丝的性格，尽管历史准确性存在争论：有一天带奥珍妮丝坐在小山坡上，身边是他的罐子，正在沐浴和煦的阳光，这是亚历山大王走到他的身边，亚历山大问带奥珍妮丝是不是雅典人所热论的那个声名不佳的带奥珍妮丝，带奥珍妮丝回答是，亚历山大接着问你什么东西都不想要是否属实，带奥珍妮丝抬头看看亚历山大王，说道，除了一样东西，说着，他请亚历山大挪开一点因为他挡住了他正在享受的阳光，据传言，这次邂逅以后，亚历山大说过，如果给他一个不是亚历山大的机会，他愿意成为带奥珍妮丝，尽管带奥珍妮丝所为有时趣味横生，但是他还不是很见爱于雅典人，主要是因为他的著述里面提倡乱伦和食人

Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

本文先叙述了对最小多项式和特征多项式的国内外的研究历史和现状，然后给出了已有的计算常数矩阵特征多项式、多项式矩阵的特征多项式和常数矩阵最小多项式的主要算法及其复杂性。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

与alexander polynomial相关的网络解释 [注：此内容来源于网络，仅供参考]

alexander polynomial：亚历山大多项式

alexander matrix 亚历山大阵 | alexander polynomial 亚历山大多项式 | algebra 代数学