关孝和行列式展开算法中之错误的改正(英文)

A correction of SEKI′s error in the expansion of determinants

讨论算学家关孝和(1642?—1708)对于超过一个未知量的方程组的辅助变量的行列式的消元法。认为由于在5阶行列式展开中的一个错误,他的理论没有得到应有的肯定,且迄今为止所有的修改方案都不能令人信服。为此,提出一个新的改正。

SEKI Takakazu(1642?-1708) is a Japanese mathematician who introduced determinants and resultants as a means of eliminating an auxiliary indeterminate from systems of algebraic equations with more than one indeterminates.Unfortunately his theory has not received due respects because of his error in the expansion of determinants of order 5.Since none of the socalled corrections are persuasive,a new one is proposed here.