查询词典 polynomial coefficient

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。

The division with surplus, the comprehensive division and Eisenstein Test applications on polynomial that can not be divided are mainly discussed; the sufficient condition of that polynomial with coefficient being integer has no integer root, that cubic polynomial with coefficient being integer is irreducible in rational domain and that polynomial with coefficient being integer has not two completely same roots are summed up.

主要论述了带余除法、综合除法及不可约多项式艾森斯坦判别法的应用；总结出了整系数多项式的无整数根的充分性，三次整系数多项式在有理数域上不可约的充分性，整系数多项式无重根的充分性。

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。

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。

This text from 艾森斯坦 because of distinguishing the relevant conclusion between method and number theory inside gaved a few and whole coefficient polynomial can't invite of judge the method, discussed at the same time not higher than four times whole coefficient polynomial can invite sex problem, get some three times, four times whole coefficient polynomial can invite sexual and simple judging the method.

本文由艾森斯坦因判别法及数论中的有关结论给出了几个整系数多项式不可约的判定方法，同时讨论了不高于四次的整系数多项式的可约性问题，得到了某些三次，四次整系数多项式可约性的简易判定方法。

It is proved that if'sparse NP complete sets under polynomial-time Turing reductions exist'then 'SAT is polynomial-time non-adaptively search reducible to decision', and that if 'P is not equal to NP'then either'SAT is not polynomial-time non-adaptively search reducible to decision'or'SAT is not polynomial-time truth-table reducible to bounded approximable sets', and that if'P is not equal to NP'then'sparse complete sets for NP under polynomial-time disjunctive reductions do not exist'.

因为用现有的证明技术不可能绝对地解决这个假设，本文研究了这个假设与其他关于SAT结构性质的假设之间的关系，证明了如果'NP有多项式时间图灵归约下的稀疏完全集'则'SAT是多项式时间并行地搜索归约为判定'，以及如果假设'P不等于NP'，则要么'SAT不是多项式时间并行地搜索归约为判定'，要么'SAT不能用多项式时间真值表归约归约为有界可近似集'。

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

讨论4种常用正交多项式在拟合卫星轨道与时间函数时的适用性；通过计算实例说明利用切比雪夫多项式和勒让德多项式做数据拟合时具有很高的精度；分析得出评定多项式拟合数据精度的适用阶数，实际应用中可降低工作量，提高计算效率；最后讨论同一多项式阶数下不同历元数对拟合结果的影响。

A new method that transforms bitlevel waveform polynomial to word-level polynomial model is given, allowing for simple composition This method offers an efficient way to determine whether two descriptions from different design levels are equivalent, so component reuse, synthesis and verification across design levels can be realized. In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，基于C语言本人设计开发了一个实验软件系统，该系统包括波形多项式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

From the results of different coefficient and similar coefficient,Schima superbashowed high total mean different coefficient and low total mean similar coefficient;Castanopsis chinensis showed high total mean different coefficient and media totalmean similar coefficient;Cryptocarya chinensis showed low total mean differentcoefficient and high total mean similar coefficient.

从相异系数和相似系数的计算看，荷木总平均相异系数最大，总平均相似系数最小；锥栗总平均相异系数大，总平均相似系数居中；厚壳桂总平均相异系数最小，总平均相似系数最大。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。