本文引入循环函数的概念,研究其基本性质、判定、构造方法及应用。利用矩阵乘法研究了一次分式函数的循环性及其定义域的结构,得到判定这类常见循环函数的充要条件和求定义域的方法,纠正了某些文章中的错误。 全文分四部分:循环函数的定义;循环函数的基本性质;循环函数的判定与构造方法;循环函数的应用。 (一)循环函数的定义 This article introduces the concept of a circular function, and studies its basic properties, judgments, construction methods and applications. Using matrix multiplication to study the circularity of a fractional function and the structure of its domain, the necessary and sufficient conditions for the determination of such common circular functions and the way to define the domain are obtained, and the errors in some articles are corrected. The full text is divided into four parts: the definition of the circular function; the basic properties of the circular function; the determination and construction method of the circular function; the application of the circular function. (a) The definition of a circular function