Title

A Study on the History of the Positive-Negative Root Extraction Algorithm in Ancient China

Author

Rong-bin Wang

Genre

Article  

Pages

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Key words

mathematics in ancient China, the Positive Negative Root Extraction Algorithm, Liu Yi, Jia Xian

Abstract

      By examining the records of Jia Xian’s (fl.1023-1050) and Liu Yi’s (c.1080) methods for root extraction quoted by Yang Hui (fl. 1261-1275), the author of this paper has the following ideas for the developing course of the Positive-Negative Root Extraction Algorithm in ancient China.

    About in the later half of the 10th century, ancient Chinese Mathematicians invented the ZengCheng method and the ZengCheng Root Extraction Algorithm. The ZengCheng Root Extraction Algorithm is a kind of mechanized algorithm and could be easily extended to the general method for solving algebraic equations with positive coefficients of and degree. And in the course of continuously using this algorithm, the ancient Chinese mathematicians found Table of the Origin of he Method for Root Extraction.

    About in the 11th century, Liu Yi improved the method for root extraction to the Positive Negative Root Extraction algorithm. The method of estimating roots in this algorithm is very difficult, and mainly owing to th is difficult problem, the theory of algebraic equations was far developed in the mid-Qing Dynasty.