Using the Interval-Symbol Method with Zero Rewriting to Factor Polynomials over Algebraic Number Fields

Abstract

The ISZ method (Interval-Symbol method with Zero rewriting) based on stabilization theory was proposed to reduce the amount of exact computations as much as possible but obtain the exact results by aid of floating-point computations. In this paper, we applied the ISZ method to Trager's algorithm which factors univariate polynomials over algebraic number fields. By Maple experiments, we show the efficiency of the ISZ method over the purely exact approach which uses exact computations throughout the execution of the algorithm. Furthermore, we propose a new method called the ISZ* method, which is similar to the ISZ method but beforehand excludes insufficient precisions of floating-point approximation by checking the correctness of the obtained supports. We confirmed that the ISZ* method is more effective than the ISZ method when the initially set precision is not sufficiently high.