On Liu Yi's positive-negative root extraction algorithm

Liu Yi (c. 1080), the Northern Song Dynasty mathematician, was the first who annulled the restriction that the coefficients of an equation must be positive and the leading coefficient be 1. It is commonly recognized that with the learning of four arithmetic operations for negative numbers thezeng cheng method for root extraction can be extended to the general method for solving an algebraic equation of any high degree with numerical coefficients arbitrarily positive, negative or zero, and because of that many of praises have been put on thezeng cheng method but the significance of Liu's work is not given enough attention. In order to argue about the above view, the present paper points out that conceptive innovation has occured in Liu's positive-negative algorithm and that Liu's work is a key in the field of ancient Chinese mathematician's research for solving higher numerical equations. Supported by China Postdoctoral Science Foundation Wang Rongbin: born in March, 1964, Ph. D