以下为句子列表：
英文: Chun-Chih Peng and Chung-Huang Yang , Design and Implementation for Integer Factorization and Primality Testing Tools with Elliptic Curve on Windows Platforms,2007 Symposium on Cryptography and Information Security, Sasebo, Japan, January 2007.
中文: 张家瀚、杨中皇，支援链结机制之标准化时戳实作，2007知识社群与资讯安全研讨会，文化大学，2007年5月。
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英文: The concept of row (column) transposed matrix and row (column) symmetric matrix is given, their basic property is studied, and the formula for full rank factorization and orthogonal diagonal factorization of row (column) symmetric matrix are presented, wh
中文: 摘要提出了行（列）转置矩阵与行（列）对称矩阵的概念，研究了其性质，给出了行（列）对称矩阵的满秩分解和正交时角分解公式，极大地减少了行（列）对称矩阵的满秩分解和正交对角分解的计算量与存储量，且没有降低数值精度。
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英文: The relationship between the eigenvalue, eigenvector and the rank of the product of matrices AB and BA is discussed, and the factorization of the singular values of matrix A is obtained.
中文: 摘要讨论了矩阵乘积AB与BA的特征值、特征向量及秩等的关系，并得到了矩阵的奇异值分解。
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英文: By using the factorization of meromorphic functions and the growth estimation of the modual,we obtain precise estimation of the order of growth and hyper-order of solutions of the equations.
中文: 通过应用亚纯函数的分解和模的增长估计,得到了该类方程解的级及其超级的精确估计。
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英文: Its result is exactly the same as that of the rescursive cyclotomic factorization algorithm (RCFA) which Martens (98) proposed by using polynomial algebra theory. So it has the advantages of simple structure and high efficiency.
中文: 它与马滕斯(Martens)利用多项式代数理论导出的递归割圆因式分解算法(RCFA)结果完全相同,具有结构简单、计算效率高的优点。
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