安定化理論に基づく計算履歴法の代数体上の因数分解への適用

Abstract

The log method based on stabilization theory was proposed by Shirayanagi and Sweedler, to reduce the amount of exact computations as much as possible to obtain the exact results. This method is a floating-point interval method with zero rewriting and symbols. Zero rewriting rewrites an interval coefficient into the zero interval if the interval contains zero. Symbols are used to keep track of the execution path of the original algorithm with exact computations, so that the associated real coefficients can be found by evaluating the symbols. After the algorithm terminates, one evaluates the symbols of the output and get a result with exact coefficients. There are two kinds of the log methods: ISZ method and ISCZ method, depending on the treatment of zero rewriting for interval coefficients with symbols. In this paper, we show the efficiency of the ISZ method by applying it to the factorization of polynomials over algebraic number fields.