在高等代数教课书中，关于多项式的除法运算中余项的确定是以余式定理为依据且利用带余除法进行的，这是大家所熟悉的。
In the textbook of higher algebra, it is familiar to us that the remainder in the division operation of polynomial is on the basis of residue theorem and operated through division algorithm.
系统地讨论了代数多项式的算术-几何均值定理，并对原型几何规划理论作出了简明的推导与分析。
This paper discussed the theorem of the average arithmetic geometric mean of algebraic polynomials systematically, then derived and analyzed the original geometric programming (GP) briefly.
最后，基于此定理，给出了选址问题的一个多项式2近似算法。
Finally, based on the theorem, a polynomial 2 approximation algorithm for the location problem is presented.
本文在复数域上证明了哈密尔顿-凯莱定理，并给出方阵A的特征多项式的全部矩阵根。
The paper proved the Hamilton-Cayley theorem in complex number space, and indicated the all matrix root of the sign multinomial of matrix A.
探讨整值多项式及其恒因子，并给出费马小定理的一种证明方法。
This paper investigates the integral valued polynomial and its identity factors, also gives a new proof for Fermat's little theorem.
多项式，包括二次求根，三次方程式，余部定理。
Polynomials, including relationships involving the roots of quadratic and cubic equations, the remainder theorem.
利用矩阵的秩给出一元多项式整除性的判定定理，同时给出商式的简便求法。
This text that make use of the order of matrix gives outs the unitary polynomials divide exactly theorem of judgment; And give a simple and convenient method about quotients type at the same time.
本文将其中的常数推广为多项式，证明了相的唯一性定理。
The constants is generalized to polynomial in this paper, establish a corresponding unicity theorem.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
讨论了广义V_-多项式的基本定理，可乘性、拓扑不变性的充要条件以及广义二元色多项式及其应用。
Some basic theorems, multiplicability and topological invariance of the extended V-functions as well as extended dichromatic polynomials are discussed.
证明解稀疏多项式方程组特征值方法的第二等价性定理，并给出方程组的解与特征值的关系。
In this paper, the second equivalence theorem of eigenvalue method for solving sparse polynomial equations is proved.
对广义罗尔定理进行了证明，并应用广义罗尔定理讨论了勒让德多项式的零点。
This paper demonstrates the generalized Rolle theorem and discussed the zero of Legendre polynomials.
介绍了用多项式根的性质与导数极限定理求分段函数在分界点的导数的简单方法。
The paper introduces the property theorem about roots of polynomial and the derivate limit theorem, by which we can study the derived number of a break point of piecewise function.
利用光滑模和K -泛函给出了一类多元三角多项式算子同时逼近的正逆定理。
Using the modulus of smoothness and K-functional, direct and inverse theorems of simultaneous approximation for a kind of multivariate trigonometric polynomial operators are established.
本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。
It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.
应用勒让德多项式的加法定理和类似于求傅里叶系数的方法，导出了新展式中系数的普遍表达式。
The method, which we use to derive the general expressions for the new coefficients in the development of gravity anomaly Ag(m, a), is analogous to Fourier's.
研究特征多项式的降阶定理以及它在高阶矩阵方面的应用。
This paper introduces the reduced order theory of characteristic polynomial and its application in the higher order matrix aspects are presented.
定理2.1：算法2.1是一个多项式时间近似方案定理2.2程序结束时每个要求所对应的两点之间的路径是唯一的。
Theorem2.1: Algorithm2.1 is a Polynomial time approximation scheme Theorem2.2 When Algorithm2.1 end, the path between each node pairs which.
通过研究多项式的系数来确定整系数多项式的有理根，进而得出整系数多项式的有理根的一个判定定理和根的存在定理。
The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.
通过研究多项式的系数来确定整系数多项式的有理根，进而得出整系数多项式的有理根的一个判定定理和根的存在定理。
The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.
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