测试二元运算乘法表是否构成群表的算法设计

对计算机测试二元运算乘法表是否构成群表的算法进行研究 ,一个乘法表构成群表的充要条件是乘法表具有两个性质·在测试乘法表构成群表的第一性质中提出了直接逐行、逐列测试G中所有元素 ,按行、按列搜索相同元素及相异元素计数三种算法 ;在第二性质测试中 ,对搜索与单位元 1构成矩形的同行、同列元素中提出自然升序法、外推法及小段优先三种算法 ;在遍历整个二维乘法表判别矩形第 4顶点元素特性中 ,提出了单个矩形移动、按行(列 ) (n-1 )个矩形同时移动、(n -1 ) 2 个矩形同时移动及改进的单个矩形移动四种算法 ;讨论了主要算法的复杂性 ;用VisualC ++6.0实现了算法的程序设计 ;用所设计...

Algorithmic Design of Testing with Computer whether the Multiplication Table of Binary Operation Forms Group Table

An computer algorithm was developed to examine whether the multiplication table of binary operation forms the group table. Three algorithms of searching for all elements in group G row by row,searching for same elements and counting dissimilar elements line by line and row by row,were raised in testing the first sufficient necessary condition of the group table formed by multiplication table. Three algorithms,extrapolation method, small segment precedence method and natural ascending order,were given to search for elements in the same line and row of rectangle with unit 1 in testing the second sufficient necessary condition; Four algorithms,single rectangle moving, simultaneous moving of ( n-1 ) rectangle line by line(column), simultaneous moving of ( n-1 ) 2 rectangles and the moving of improved single rectangle,were raised to distinguish the 4th vertex element characteristic of the rectangle by ransacking the entire two dimensional multiplication table; The complexity of main algorithms was discussed. The algorithm was programmed with Visual C++6.0. Several multiplication tables were tested by the designed software.