(untitled) (Communications in Mathematical Research, 2021)
This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univariate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial system and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational-representation sets.