Effect of the interval-symbol method with correct zero rewriting on the Δ-LLL algorithm

Abstract

We previously proposed the interval-symbol method with correct zero rewriting (ISCZ method) to reduce the amount of exact computations to obtain the exact results by aid of floating-point computations. Recently we have presented new ideas for reducing time and memory of executing the ISCZ method. In this paper, we apply the new ISCZ method to the Δ-LLL algorithm, which is a generalization of the Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm. By Maple experiments, we confirm its superiority over the original ISCZ method, and in the irrational case we show its great effect on the Δ-LLL algorithm in the sense that it is much more efficient than the purely exact approach.