正规升列在参数代数方程组求解中的应用

The Application of Normal Ascending Set in Solving System of Parametric Algebraic Equations

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法．对于给定的的代数方城组,通过正规分解,可以得到一组具有三角形式的分解．根据这种三角形式,我们可以给出代数方程组的所有解．而对于带有参数方程组,将给出方程组有解时参数需满足的条件．进一步,对于给定的参数值,正规分解中得到三角形式仍然保持,通过求解三角形式的方程组从而得出原参数方程组的解．

In this paper, we present a method to solve system of algebraic equations or system of parametric algebraic equations by computing the normal zero decomposition of polynomial systems. For a system of algebraic equations, we can get a zero decomposition of triangular systems. We can get all the solutions of the algebraic system by computing the solutions of the triangular systems. For a system of parametric algebraic equations, we will give the conditions which the parametric should satisfy such that the algebraic system has solutions. Furthermore, the triangular systems in the normal decomposition still keep the triangular form for the specializations of the parameters. All the solutions of the parametric system can be got by computing the solutions of the triangular systems.