新四元数系

与“正统”的Hamilton四元数不同，按作者的n元数运算统一规律，详细列举了新的四元数运算公式；如同对三元数的讨论方式，引进四元数的特征变换，论证了四元数特征与四元数的一致对应关系，从而得到四元数运算的另一等价形式即特征形式，据此可明了四元数与实数，复数以及三元数之间的密切联系，利用四维算术空间的特征轴和特征面，阐明了四元数运算的几何意义，利用引进的四元数的权值概念，建立了四元数的乘积定律，通过与Hamilton四元数运算的比较，确立了新四元数应有的地位。

The system of new four-ary number

The new four-ary number, is different with the orthodox ideas of Hamilton's quarternions.According to the writers' unified pattern of operation on n-ary number,the formulas of operation for four-ary number are listed in detailed. Like the way discussed for three-ary number, it introduced the characteristic transfermation to four-ary number，and proved the identical corresponding relationship between four-ary number and its characteristic,and get out another equal form of operation for four-ary number,i.e. the characteristic form. On it,the close connection among four-ary number with real number, complex number and three-ary number may be going clear.Use the characteristic axis and the characteristic plane of four-dimention arithmetic space, the geometric meaning of the operation of four-ary number is described clearly. Using the concept of weight value is introduced,set up the new ideas of product law of four-ary number.Through comparing on operation of four-ary number with Hamilton's quarternions,it established the position that new four-ary number ought to have.