结式的若干应用

Some applications of the resultants

结式是多项式理论中的一个重要概念。本文从7个方面阐述了结式的应用,包括判断2个多项式的公共零点,判定多项式是否有重根,计算多项式的判别式,寻找代数数满足的方程,平面有理曲线的隐式化,非线性代数方程组求解和不等式机器证明中半代数系统边界曲面的获得等。

The resultant is an important concept over the theory of polynomials. In this paper, it s applications were explained from seven different fields, the common zeros of two polynomials, the multiplicities of roots and the discrimination of a polynomial, searching the equations suitable for a algebraic number, implicating a rational curve over the plane, computing the zeros of a nonlinear algebraic equation and gathering the discrimination surface of the SAS in automated theorem proving on inequalities.