代数整数

Different from previously presented threshold RSA signature schemes, this new scheme can effectively avoid computation of any element\'s inverse in any algebraic structure such as Z_(φ and Z_N, which makes the complicated algebraic extension, parameter constraint and inversion pre-computation all unnecessary.

该体制基于整数矩阵运算，不需要对任何非域代数结构中的元素求逆，为构造高效实用的门限RSA签名方案奠定了基础。

Software Description: XICalc is an integer calculator program with the following features: multiple precision integers with millions of digits; uses Hartley Transform to speed-up long multiplies; separate input and outputnotation, base 2 to base 36; greatest common divisor function; Modulo arithmetic options; Bernoullinumbers, Euler Numbers; Boolean functions; random number generator; prime factor algorithm using theElliptic Curve Method; number theoretic functions phi, sigma and tau; prime testing and searching using the Adleman function; algebraic notation; if-then-else statement; go-to statement; can run XICalc code from files; hot help from F1 key; and it抯 written in Microsoft Visual C#.

XICalc 是一款带有如下功能的综合性计算器软件：带有百万数位的多精度整数；使用 Hartley Transform 加速长整型多样化计算；以2到36为基数分隔输入和输出符号；最大公约数函数；模数算法选项；Bernoulli 数字；Euler 数字；布尔函数；随机数字生成器；使用圆周曲线算法的主要因素运算法则；π，τ，Σ的数字理论函数；使用 Adleman 函数的最初测试和搜索功能；代数符号；if-then-else 语法结构声明；go-to 语法结构声明；来自于文件的XICalc 代码；F1键的热点帮助；并且该软件是采用适用于 Windows 操作系统的微软 Visual C#。

Factoring integers ; algorithm ; algebraic number field

整数分解；算法；代数数域

According to algebraic number theory,all solutions of Pocklington equation in a ring of integers of a quadratic imaginary field are determined,which implies that the equation has only several solutions in the ring.

利用代数数论的理论与方法，决定了一个重要的不定方程在一个特殊的虚二次域整数环中的解，从而指出这个方程在比整数环更大的环中也仅有有限个解。

You need an arithmetic progression, just like the built-in function range, but with float values.

你需要一个代数表达式，就象内建函数range一样。但是它要的是浮点数（range仅仅在整数上工作

Let n ≥ 4 be a fixed integer, R be a unital commutative ring of characteristic not 2, and D_n be a D_n-type classical Lie algebra over R.

假设n是一个大于等于4的整数，R是特征非2的有单位元的交换环，D_n是环R上的D_n型李代数，N是D_n的一个极大幂零子代数。

31 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Table 3-2 Distributivity Idempotency Absorption laws 分配律同一律吸收律 a=ab+ac a+= a+a=a aa=a a+ab=a a=a'=a'b''=a'+b' DeMorgan's laws德摩根定理计算机专业英语 3-32 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Since a finite set of n elements has exactly 2n subsets, and it can be shown that the finite Boolean algebras are precisely the finite set algebras, each finite Boolean algebra consists of exactly 2n elements for some integer n.

由于n个元素的有限集有且只有个子集由于个元素的有限集有且只有2n个子集，而且很显然有限布个元素的有限集有且只有个子集，尔代数一定是有限集合代数，所以对某个整数n而言而言，尔代数一定是有限集合代数，所以对某个整数而言，每个有限布尔代数也有且只有2n个元素。例如，上文定义的集合T的限布尔代数也有且只有个元素。

In vector algebra, addition are defined to add coordinates entries respectively,and this system of operation is the direct sum Z Z={|a,b are integers} of integers ring Z,the operations are+=,=.

向量代数加法就是这样按照分量加法在运算，再加上按照分量的乘法，这个运算体系就是整数环Z的直和Z Z={|a，b为整数}，其上的运算就是+=，=。

The primary theory of numbers aspect related integer property basic content.

摘要本论文主要讨论了整数的离散性、代数性质、有序性、整除性、最大公因数与最小公倍数、素因子分解、同余等初等数论方面的有关整数性质的基本内容。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。