Computing a Separating Element for a Zero Dimensional Parametric Algebraic Variety

This paper presents an efficient algorithm for computing a separating element of a zero dimensional parametric algebraic variety. By converting the computations on rational function filed into computations on the base filed, we reduce the problem to finding a separating element for a zero dimensional algebraic variety without parameters. Thus, the computational complexity is reduced efficiently. The algorithm has been implemented and the examples reported in this paper show the algorithm is of practical value.