四元消法的增根与减根问题

On Problems of Extraneous and Lost Roots of Equations in the Method of the Four Elements

四元消法是《四元玉鉴》（1303年）所载四元术之核心内容。该算法是中国传统数学的重要成果之一,历来给予充分的肯定。文章以行列式计算所得方程与原著由四元消法所给之方程比较,举例说明该算法可能产生增根或减根。作者试图为全面认识与评价四元消法给出一个新的视角。

As the core of the method of Four Elements recorded in Zhu Shijie's the Siyuan Yujian (Jade Mirror of the Four Elements, 1303) ,the elimination method is one of the important results of traditional mathematics in China. Through comparing equations found by determinant and Zhu's method, this paper points out that extraneous or lost roots possibly exist in the equations of Zhu Shijie. The author tries to supply new evidence in order to evaluate Zhu's work completely.