Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu

Abstract

This paper is a sequel to our paper ``Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu''. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper \cite{6}, we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials $p(a, b, c)$ where $a, b, c$ are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables $a, b, c$.