| 1. | An algorithm for finding the minimal polynomial of a fls r - circulant matrix
循环矩阵的极小多项式的算法 |
| 2. | Algorithms for finding the minimal polynomials and inverses of permutation factor circulant matrices
求置换因子循环矩阵的极小多项式和逆的算法 |
| 3. | Hence an algorithm for the minimal polynomial of a block circulant matrix over the field is presented
) bner基，从而给出了求块循环矩阵的极小多项式的算法。 |
| 4. | So finding the minimal polynomial of a block circulant matrix is transformed into computing the reduced grobner basis of a kernel of a ring homomorphism
因此，将求域上块循环矩阵的极小多项式转化为求一个环同态的核的简化gr ( |
| 5. | The aim of this paper is to study the applications of grobner bases in finding the minimal polynomial of a given matrix and its inverse if it is nonsingular and to discuss selfdualities over a polynomial ring
) bner基理论在求矩阵极小多项式，判定矩阵可逆性和求逆矩阵等方面的应用，并讨论了多项式环的分次自对偶问题。 |
| 6. | 4 . a fast algorithm for computing the linear complexity and the minimal polynomial of a binary sequence with period t ? m is proposed , and generalized one for determining the linear complexity of a sequence with period pmqfl over gf ( q )
提出确定周期为2 ~ np ~ m的二元序列的线性复杂度和极小多项式的一个快速算法，并推广为计算gf （ q ）上周期为p ~ mq ~ n序列的线性复杂度和极小多项式的快速算法。 |
| 7. | 5 . a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2pfl over gf ( q ) is proposed , and a new algorithm for determining the linear complexity of a sequence with period pfl over gf ( p ? ) is introduced
提出一个计算gf （ q ）上周期为2p ~ n序列的线性复杂度和极小多项式的快速算法；提出一个计算gf （ p ~ m ）上周期为p ~ n的序列的线性复杂度的新算法。 |
| 8. | Algorithms for the minimal polynomial and the inverse of a given block symmetric circulant matrix over a group algebra of a finite group over a field are presented . and a method of determining singularity of this block symmetric circulant matrix is given
?给出了求域上有限群的群代数上的块循环矩阵的极小多项式的算法，西安电子科技大学博士学位论文:多项式代数及其应用奇异性判别法及其逆矩阵的求法 |
| 9. | In this paper , based on wu ' s method and the estimation for maximal and minimal polynomials , we extend the real root isolation algorithm from univariant integral polynomial to multivariant integral polynomial systems . it gives the solutions of polynomial systems in the form of multi - dimensional boxes
我们利用吴方法和极大，极小多项式估计，推广多项式实根分离算法( realrootisolation )到多项式组的情形( mrealrootisolation ) ，该算法以空间中的矩形区域形式给出了多项式组的实解 |
| 10. | 2 . a characterization of the minimal polynomials generated a sequence with given minimal period is proved , the distribution of the linear complexity of periodic sequences is shown , and a new solving process of mathematical expectation and variance of linear complexity of periodic sequences is presented . randomness of minimal periodic sequences is discussed
给出生成给定最小周期序列的极小多项式的一个充分和必要条件；给出一般有限域上周期序列的线性复杂度的分布，并给出其数学期望和方差的一个新的求法，讨论了最小周期序列的随机性。 |
