整系数多项式

本文研究整系数多项式的不可约因式，给出了低次不可约多项式的判别的一种方法和一些不可约问题的处理方法。

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 .

2cosnα可表为2cosα的整系数多项式，这一多项式的系数有一些有趣的性质。

Cos n α may be formulated as a multinomial with an integral coefficient of 2 cos α . There are some interesting qualities in the coefficient of the multinomial .

运用抽象代数的知识对整系数多项式进行摸p约化处理，得到了整系数多项式在有理数域Q上不可约的4个新判别法。

In this paper , We apply the knowledge of abstract algebra to study integral polynomials that are simplified by module p and obtain four new irreducibility tests for integral polynomials .

探讨如何运用计算机代数系统Maple对整系数多项式不可约的判别条件&Eisenstein判别法的程序设计。

This paper discusses how to make use of the computer algebra system Maple to distinguish the program design of the condition of the Eisenstein discretion method , which can 't invite the whole coefficient polynomial .

该程序能够测试任意整系数多项式是否可约，并给出了满足不可约整系数多项式的Eisenstein素数值。

This procedure not only can test whether arbitrarily whole coefficient polynomial can invite or not , but also can give the prime number to satisfy the Eisenstein prime .

对Eisenstein判别法作了进一步推广，给出了判定整系数多项式在有理数域上不可约的又一定理及其5个重要推论。

In this paper , we generalize Eisenstein 's Discriminatory Method and give another theorem and its five important inferences for discriminating the irreducibility of intergral polynomial over the rational number field .

本文有特色的主要工作如下：1、利用Fermat数变换（FNT）的循环卷积性质进行整系数多项式相乘，提高了运算的精度和速度。

These works are presented in this thesis : 1 , The multiplication-free Fermat number transform ( FNT ) with the cyclic convolution property is used for calculating the multiplication of two polynomials to improve speed and accuracy .

整系数多项式有理根的一个新求法

A New Method for Finding Rational Roots of Integral Coefficient Polynomials

关于整系数多项式有理根求法的注记

Notes on Algorithms for Finding Rational Roots of Polynomials with Integer Coefficients

整系数多项式有理根检验法的简化

Reduction of the Test Method of Rational Root of Integral Coefficients Polynomial

整系数多项式不可约的一个判别法

The criterion of the irreducible polynomial of integer coefficient

有关一个整系数多项式环定理的矩阵证明

A Matrix Proof of a Theorem about a Polynomial Ring with Entire Coefficient

整系数多项式的若干性质

Some Properties of Polynomial with Integer Coefficient

整系数多项式因式分解的一种矩阵方法及程序设计语言

A Matrix Method and Its Programming Language for the Factorization of Polynomial with Integral Coefficients

关于整系数多项式的因式分解

The factoring on the integral multinomial

这个算法还能很自然地推广成分解多元整系数多项式的算法。

This algorithm can be naturally generalized to be an algorithm for factoring multivariate polynomials with integral coefficients .

本文将高等代数中的整系数多项式扩展为另外变量的多项式，对含多个变量的多项式进行因式分解。

The article extends the integer coefficient of advanced algebra to another variable multinomial and factorizes the multinomial containing several variables .

最后，我们举例说明了所提出的罚方法在具有整系数多项式目标函数及约束函数的整数规划中的应用。

Finally we illustrate the application of the proposed penalty formulations in polynomial integer programming problem with integer-coefficient objective function and constraint functions .

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。

In this paper an efficient implementation of kuhn s algorithm for finding all the root of a polynomial with complex coefficients is proposed .

将一元整系数多项式有理根的一个结论在多元多项式上进行了推广，从而得到多元多项式因式分解的一种方法。

A conclusion on rational root of one variable polynomial with integer coefficient is generalized and a method on multivariate polynomial factorization is put forward .

给出了整系数多项式有理根的一个必要条件，从而得到整系数多项式有理根检验的一个简化方法，达到了简化整系数多项式有理根检验的目的。

According to the first and second references , a sufficiency and necessity condition on rational root of integral coefficients polynomial is put forward and a reduced method of testing the rational root is also shown in this paper .

完全找到整系数不可约多项式的一种新方法

A New Method to Thoroughly Find the Irreducible Polynomials of Integer Coefficient

关于整系数不可约多项式

Irreducible Polynomial of Integral Coefficient

本文给出几个判断整系数不可约多项式的定理，比文[1]给出的定理更具有一般性。

This paper offers several theorems on judging irreducible polynomial of integral coefficient , which has more generality than those given out in the article ( 1 ) .