拓展对称与偏差数概念的形成及作用

域上欧氏几何中,把正交为换表为对称之积的问题,是几何中基本问题之一,二十世纪七十年代以后。环上几何学兴起,欧氏空间把正交变换表为对称之积,为人们所注意,如何将这一问题的结果,有效的转移到环上,转移过程中,出现一类对称叫拓展对称的问题,因此,欲将域上的结果有效的转到环上,首称必须解开拓展对称,在域上,开解正交变换表成对称之积,因子个数的多少,是用变换的剩余数来标定的,在环上,仅用剩余数却难于定出因子个数,于是创出一个偏差数的概念,用正交变换的偏差数和剩余数来标定因子个数,表明分解的长度。

The Formation and Function of Two Concepts of Extended Symmetry and Deviation Number

This paper discusses the solution of a kind of symmetry called"extended symmetry"in an effective transfer process of the symmetric product representation of orthogonal transformation from field to ring.Like the residue,number of transfrom in the field,a concept,a concept"deviation number"is created on account of that only using of residue,number is diffcult to demarcate the number of factors in the ring.This paper uses residue number and deviation number of orthogognal transformation together to demarcat the number of factors and show the length of decomposition in the ring,and meanwhile,discussed the application of extended symmetry in orthogognal transformation.