Abstract: Since the separable element algorithm of the rational univariate representation (RUR) for solving zerodimensional systems presented by Rouillier makes the size of the coefficients in this representation too long, an improved algorithm for finding separating elements is presented in this paper, which is implemented by confirmingthe separating element of the coordinates step by step. Results show that the size of the coefficientsin the RUR corresponding to the separating element selected by the new algorithm is obviously shorter than that by Rouillier’s. In addition, the average complexity of both the algorithms are close.

Key words: zerodimensional algebraic variety, rational univariate representation with short coefficients, separating element, algorithm