基于运算提升的超群的构造验证算法

The verification algorithm of hypergroupconstruction based on operation upgrade

文章主要对H.S.Wall提出的基于运算提升的超群做进一步的研究,重点探讨了如何利用计算机验证所构造的超群是否合理的问题。首先利用超群的定义和特征,将数学语言转化为计算机语言,得到了超群的等价定义。然后再利用该等价定义,给出了一种验证超群构造是否合理的同构优化算法。最后借助编程软件平台,利用该算法改正了文献中的错误并构造出新的例子,证明了该优化算法的可行性和实用性。

This paper makes a further study of the hypergroup based on operation upgrade proposed by H.S.Wall, and focuses on how to use a computer to verify whether or not the hypergroup constructed is reasonable. First, by using the definition and characteristics of the hypergroup, the mathematical language is transformed into computer language, and we get the equivalent definition of the hypergroup.Then, using the equivalence definition, we give an isomorphism optimization algorithm to verify the rationality of the construction of the hypergroup. Finally, with the aid of the programming software platform, the algorithm is used to correct the errors in the literature and to construct a new example, which proves the feasibility and practicability of the optimization algorithm.