As a foundation, the definition of elementary integral transformation and the method to factorize an integral matrix with elementary integral transformation is proposed firstly.

• 文中首先给出初等整数变换的概念，之后借助初等整数变换对整数矩阵进行分解，并在此基础上给出从加模S-不变量中求取不可达见证向量的方法。