1) reduced minimum polynomial
可约极小多项式
3) minimal polynomial
极小多项式
1.
An algorithm for minimal polynomials of polynomials in idempotent matrices;
幂等矩阵的多项式的极小多项式的算法
2.
Based on the theory of cyclotomic polynomial over finite field GF(q),a fast algorithm was derived for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q~np~m,where p and q are prime numbers,and q is a primitive root modulo p~2.
基于有限域GF(q)上的分圆多项式理论,提出和证明了求周期为qnpm的GF(q)上序列的线性复杂度和极小多项式的一个快速算法,这里p与q均为素数,且q是模p2的本原根。
3.
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of sequences over GF(pm) with the period kn,where p is a prime,gcd(n,pm-1)=1,pm-1=kt,and n,k and t are integers.
提出和证明了求GF(pm)上周期为kn的序列线性复杂度和极小多项式的一个快速算法,其中p是素数,gcd(n,pm-1)=1且pm-1=kt,n,k与t均为正整数。
4) minimum polynomial
极小多项式
1.
Searching arithmetic about minimum polynomial of commutative fields has been given.
借助于计算功能强大的数学软件Mathematica求出了一类有限域,它们具有相同的极小多项式,由此算法求出了一类有限域,并讨论了算法复杂性。
2.
The period of the generalized Geffe shrinking sequence is proved and its linear complexity,minimum polynomials are presented in this paper.
广义Geffe缩减生成器是有限域GF(q)上q+1个LFSR s的简单组合,它是Geffe提出的Geffe生成器的推广,证明了广义Geffe缩减序列周期的猜想,并给出其线性复杂度和极小多项式。
5) Irreducible polynomial
不可约多项式
1.
For a wide range of integers n (n is the product of prime number and prime number or 1),a necessary and sufficient condition is given for a polynomial of degree n over the finite field F_p being an irreducible polynomial or primitive polynomial.
对于一大类整数n(n为素数乘于素数或1的积),分别给出有限域Fp上n次多项式是不可约多项式与本原多项式的一个充要条件,该条件可通过O(n3)次Fp上乘法加以验证,易于硬件实现。
2.
In this paper, we discuss the number of irreducible polynomials over F q of degree m and period l, moreover, we describle a principle of obtaining new irreducible polynomials from known ones.
主要利用较文献 [4]更为简明的方法证明了有关有限域 Fq(q为一个素数幂 )上的以 l为周期的 n次不可约多项式的个数的结论 ,另外 ,本文结合初等数论知识得到了前面这个结论的几个推论 ,并对利用低次不可约多项式构造高次不可约多项式进行了研究 。
6) common minimal polynomial
公共极小多项式
1.
Al- gorithms for computing the minimal polynomial and common minimal polynomial of this kind of matrices over any field are presented by means of the Grbner basis of the ideal in the polynomial ring,and two algorithms for finding the inverses of such matrices are also presented.
本文引入了任意域上置换因子循环矩阵,利用多项式环的理想的Gr(?)bner基的算法给出了任意域上置换因子循环矩阵的极小多项式和公共极小多项式的算法,同时给出了这类矩阵逆矩阵的两种算法最后,利用Schur补给出了任意域上具有置换因子循环矩阵块的分块矩阵逆的一个算法,在有理数域或模素数剩余类域上,这一算法可由代数系统软件CoCoA4。
2.
Algorithms for computing the minimal polynomial and common minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gr(o).
研究了域上首尾和r-循环矩阵,利用多项式环的理想的Gr bner基的算法给出了任意域上首尾和r-循环矩阵的极小多项式和公共极小多项式的一种算法。
补充资料：多项式乘多项式法则
Image:1173836820929048.jpg
多项式乘多项式法则
先用一个多项式的每一项乘以另一个多项式的每一项，再把所得的积相加。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。