algebraic number

1. Many parents simply abdicate all responsibility for their children.
   许多父母对孩子简直是完全撒手不管。
2. PARI is a fast-running C library of symbolic functions for factorization, algebraic number theory, elliptic curves, matrices, and transcendental functions.
   PARI是快速运行的符号函数C语言库，用于因素分解、代数数论、椭圆曲线、矩阵和超越函数。
3. Two classes of boolean functions with optimum algebraic immunity in odd number of variables
   两类具有最优代数免疫阶的奇变元布尔函数位某一数列中一个数目的位置
4. Excel Method for Calculation Roots of High Order Real Algebraic Equations; Methods of exploring the real number roots of a real coefficient polynomial function are procedurally given.
   求解高次实系数代数方程的Excel算法较程序化地给出了实系数多项式函数实数根的求法。
5. Ideal is one of the most important concepts in abstract algebra, especially the theory of commutative ring. It is also an indispensable basic tool to study algebraic number theory.
   理想概念是现代抽象代数学特别是交换环理论最核心的概念之一，也是研究代数数论学科必不可少的基本工具。
6. Then he considers the case of algebraic numbers and obtains some results like the following: Every real algebraic number field of finite degree is non-inductive;
   然后着重在代数范围内进行讨论，得到下列的结果：每个有限次实代数数域都不是归纳域；
7. Properties and Representations of Generalized Inverse on Algebraic Perturbation and Minimal Property of Condition Number on Drazin Inverse
   广义逆在代数扰动理论中的性质、表示及矩陈Drazin逆条件数的极小性质
8. In the paper, taking the degree 4 real algebraic number 2+ 3 as example, for a kind of real algebraic numbers, we give an algorithm to compute their ordinary continued fractions.
   现以2+3这个四次实代数数为例，给出一类实代数数简单连分数展开式的算法。
9. On the calculation of integer's cyclic convolution over algebraic number fields
   用实数卷积计算代数数域上整数卷积
10. Imbedding theorems and the large sieve method in algebraic number fields
    嵌入定理与代数数域上的大筛法
11. The finite extension K of Q is called algebraic number field.
    有理数域Q的有限次扩域K叫作代数数域，数域K的所有代数整数构成一个环，称为K的代数整数环，记作ZK。
12. Also, it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts.
    还证明了很多有限次代数数域不与上述的超积初等等价。
13. The mean value theorem in algebraic number fields
    代数数域中的均值定理
14. New algebraic algorithm for computing the Euler number of 3-D images
    三维数字图象Euler数新的有效计算法
15. On exponential sums over an algebraic number field
    代数数域上的指数和的估值
16. An algorithm for continued fractions of algebraic number
    一类代数数的连分数表示的一个算法
17. Simpler proofs of some theorems in algebraic number theory
    代数数论中若干定理的简化证明
18. We now complete directly the two proofs neither turning to the formula of transitivity of norms nor taking the norm of an ideal, thus simplifying the proofs of the two important theorems in algebraic number theory.
    不取范而直接给出关于整理想加群结构定理的证明，从而简化了代数数论中这两个重要定理的证明。
19. The reduction of two classes of algebraic number field
    两类代数数域的化简
20. The Euler function is generalized over the full matrix ring M ( Ok, n), where Ok is the integral number ring of the algebraic number field K.
    主要把欧拉函数推广到全矩阵环M（Ok，n）上，其中Ok为代数数域K的整数环。
21. Computation of the Algebraic Square Root for the Number Field Sieve
    数域筛法中代数平方根的计算
22. The algebraic number more or the transcendental number?
    代数数多还是超越数多？
23. The k-times norm of the algebraic number field extension
    数域扩张中的K次范
24. A rapid digits expansion algorithm of algebraic number was built to calculate stream cipher using Sturm's tool and dichotomy.
    利用Sturm定理和二分法，给出一类代数数的快速展开计算密钥流的算法。
25. On the Degree of Extensions of Algebraic Number Field
    关于代数数域的扩张次数
26. The HJB equation is then reduced to a set of recursive algebraic equations and yields a closed-loop controller with a finite number of terms.
    HJB方程简化为一组递归的代数方程，求得一个有限项的闭环控制器。
27. Tokyo version of "algebraic number" field of the contents of the overall arrangement in line with the version of the North division, such as the integral understanding of knowledge points in the 1-4 grades.
    东京版数与代数领域的内容安排整体跟北师版一致，如整数的认识，知识点安排在1-4年级上。
28. As an important algebraic subject, Ring theory is the base of Algebraic Geometry and Algebraic Number Theory.
    环论作为一门重要的代数学科，它是代数几何和代数数论的基础。
29. In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.
    十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。
30. For the algebraic attack, as the round number increases, the number of equations will rise, thus the equations are difficult to be solved.
    对于代数攻击，随着轮数的增加，方程的数目也不断增加，求解方程也就更加困难。

noun

1. root of an algebraic equation with rational coefficients