1) greatest common factor
最大公因式
1.
By some properties of elementary transformations of matrix,this paper solved the polynomial quotient and complement in the general division algorithm,the greatest common factor between two polynomials,and judged if there are multiple factors a polynomial are obtaine
应用矩阵初等变换的一些性质解决了求带余除法中的商和余式、求两个多项式的最大公因式以及判定一个多项式有无重因式等问题。
2.
The use of the elementary transformation matrix discussed the one yuan polynomial greatest common factor the matrix law.
本文利用矩阵的初等变换讨论了一元多项式最大公因式的求法。
3.
In this paper,the greatest common factors of polynomials in several indeterminaters over a number filed are studied.
探讨了数域上多元多项式的最大公因式,给出了两个多元多项式与其最大公因式的若干关系式,并获得了两个多元多项式互素的等价条件。
2) the greatest common factor
最大公因式
1.
In this paper,we give the applications of matrix elementary transformation in obtaining the greatest common factor and coefficients polynomial,orthonornal basisl.
给出了矩阵的初等变换在求多项式的最大公因式及其组合系数多项式,求标准正交基问题中的应用。
2.
In the paper,a coefficients changing method of resulting unary multinomial division is put forward,its application in finding the greatest common factor and deciding whether two unary multinomial are relatively prime are popularized,and the examples are given by the author.
文章提出了一种求解两个一元多项式除法的系数变换法,并推广到求取一元多项式的最大公因式及判别两个多项式是否互素等问题上,给出了该方法的应用实例。
3.
After converting polynomials into a number matrix,we can simplify the number matrix by applying the conversion of oblique elementary of matrix or the second oblique elementary of matrix,and then the algorithm for solving the greatest common factor,which is based on the conversion of oblique elementary operation,can be achieved.
把多项式组转为系数矩阵表示后,通过矩阵的第一斜消变换、第二斜消变换化简矩阵,得到利用斜消变换求解最大公因式的算法实现。
3) Greatest common divisor
最大公因式
1.
This paper summarizes the applications of elementary transformation of matrix in solving the rank of a matrix or a set of vectors,calculating inverse matrix or system of linear equations,and solving the system of linear equations and the greatest common divisor of polynomials with examples,furthermore,it introduces the thought and application of generalized elementary transformation.
文章总结了初等变换在求矩阵的秩、向量组的秩、逆矩阵,求解线性方程组和多项式的最大公因式等方面的应用,并通过实例加以说明,进而介绍了广义初等变换的思想方法和应用。
2.
It is proved that the elementary transformation of matrix can be used to obtain the greatest common factor of several integers and the greatest common divisor of multinomial.
证明了可以用矩阵的初等变换来求若干个正整数的最大公因数和若干个多项式的最大公因式,并通过具体实例来验证该方法。
3.
In this paper, a method simpler than Euclidean algorithm, namely the method of matrix transformation for solving the greatest common divisor of a group of polynomial, is given, and the algorithm according to this method has been designed.
给出求多项式组的最大公因式的一种简单方法——矩阵变换的方法 ,并给出算法 。
4) the greatest common divisor
最大公因式
1.
In this paper,the matrix method of calculating the greatest common divisor of several polynomials is given by using the row elementary operation,and so is the concrete application of this method.
数域F上任意几个多项式的最大公因式是存在的,但很难求得,利用多项式矩阵的列初等变换给出了求几个多项式的最大公因式的新方法,并给出了这种方法的具体应用。
2.
In this paper,we obtain several solutions to the greatest common divisor of polynomial of one indeterminate by using the division algorithm and elementary transformation and oblique elementary transformation of matrix.
文章从辗转相除、矩阵的初等变换以及矩阵的斜消变换等不同角度给出了一元多项式的最大公因式的不同求法。
3.
By using the row elementary opration the matrix method of calculating the greatest common divisor of several polynomials is given with concrete applications.
利用多项式矩阵的行初等变换给出了求几个多项式的最大公因式的新方法,并给出了这种方法的具体应用。
5) greatest common formula
最大公因式
1.
Matrix method for obtaining the greatest common formula of multinomial;
求多项式最大公因式的矩阵变换方法
2.
Division algorithm is a common method to evaluate the greatest common formula of multinomial.
求多项式最大公因式通常是用辗转相除法 ,当多项式次数较高时 ,计算较复杂 ,而推广到多个多项式的情形计算量更大 。
6) highest common factor(H.C.F)
最大公因子;最高公因式;最高公因子
补充资料：公因式
多项式各项都含有的公共的因式叫做这个多项式各项的公因式.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条