中算数学机械化思想在和算中的发展——解伏题的机械化特征

和算解伏题是关于多元高次联立方程组求解问题,因其在世界数学史上首次导入了行列式算法而向为学术界所重视。文章从数学机械化这一视角对其提出新的认识,重新讨论和算解伏题的消元理论问题,认为和算解伏题是中算代数化几何与以元天术为核心的代数演算的机械化数学传统的后续发展,关孝和给出了多元高次方程组消元的一般性程序,从而构筑了和算后期计算几何发达的基础,比诸行列式理论,解伏题的数学机械化思想的价值更为重要。

The Development ofMathematics Mechanization Thought of Chinese Mathematics in Japanese Mathematics

The problem of kaifukudai in Wasan is a method for solving system of equations with high degrees.The method is always regarded seriously in the academia because the determinant algorithm is produced by it for the first time in the history of mathematics.This paper reexamines the theory of elimination in the method of kaifukudai in Wasan and puts forward some new understandings about the method from the visual angle of mathematics mechanization.It is considered that the method of kaifukudai in Wasan is the development of the mechanical mathematics tradition in ancient China.Seki Takakazu invented a general program for solving system of equations with high degrees.For this reason,calculating geometry was highly developed later in Wasan.The paper holds that the mechanical thought in the method for kaifukudai is much more important than the determinant theory.