也谈四元消法的增根与减根问题

On the problem of extraneous and lost roots of elimination of equations in the Method of the Four Elements

四元消法是中国传统数学的重要成果之一,对于四元消法的增根与减根问题,李兆华先生曾经讨论过.笔者指出了四元消法可能产生增根和减根的原因及途径,并从四元消法法则的统一表示出发,把四元细草用吴消元法的笔算算法写出,用代数方程理论讨论四元消法的增根与减根问题,为准确认识与评价四元消法给出一个新视角.

The method of element elimination in Four Elements equations is one of important results in Chinese traditional mathematics. The problem of crention or loss of roots in this method was discussed by Li Zhaohua in Tianjin Normal College. In this paper, it is studied by the theory of algebra equation. The paper presents a new point of view to understand and evaluate this method.