in " the nine chapters on the mathematical art ," which was written in the early ancient period (before the first century a .d .) , four arithmetic operations for negative numbers were developed , and the book generally succeeded in introducing pluralistic simultaneous linear equations based on the results of those operations; gaussian elimination was also introduced . 早くも古代（後1世紀以前）に成立した『九章算術』では、負の数の四則演算を扱い、その成果に基づいて多元連立一次方程式を一般的に扱うことに成功し、ガウスの消去法を導入している。
earlier , both girolamo cardano in his ars magna (1580 ) and hui yang (of china , c .1238 - 1298 ) had used the same method of calculating determinants that seki later used to find the root of pluralistic simultaneous linear equations with two unknown coefficients; yang ' s findings were recorded in " xiangjie jiuzhang suanfa " (a mathematical treatise in which yang acknowledged that his method of finding square roots and cubic roots had been invented by another mathematician ). 先立って、楊輝（中国、1238年?～1298年）は『詳解九章算術』で、ジェロラモ・カルダーノは Ars Magna（1580）の中で数字係数の二元連立一次方程式の解を行列式と同様の計算式であたえている。
