Tian yuan shu instance of algebra
Tian yuan shu (simplified Chinese: 天元术; traditional Chinese: 天元術; pinyin: tiān yuán shù) is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dynasty and possibly before.Description
Tian yuan shu means "method of the heavenly element" or "technique of the celestial unknown". The "heavenly element" is the unknown variable, usually written x in modern notation.
It is a positional system of rod numerals to represent polynomial equations. For example, 2x2 + 18x − 316 = 0 is represented as
, which in Arabic numerals is 
The 元 (yuan) denotes the unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x2) term. The system accommodates arbitrarily high exponents of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented.
In later writings of Li Zhi and Zhu Shijie, the line order was reversed so that the first line is the lowest exponent.
type of example of manifestation of representation of