is a Chinese system of algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

 for polynomial

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

 equations created in the 13th century. It is first known from the writing of Li Zhi

Li Zhi (mathematician)

Li Zhi , later Li Ye , was a Chinese mathematician and scholar, who published and improved the tian yuan shu method for solving polynomial equations of one variable.- Name :...

 (Li Ye), though it was created earlier.

The mathematical culture in which it was created was lost due to war and general suspiciousness during the Ming dynasty

Ming Dynasty

The Ming Dynasty, also Empire of the Great Ming, was the ruling dynasty of China from 1368 to 1644, following the collapse of the Mongol-led Yuan Dynasty. The Ming, "one of the greatest eras of orderly government and social stability in human history", was the last dynasty in China ruled by ethnic...

 of knowledge from the (Mongolian) Yuan dynasty

Yuan Dynasty

The Yuan Dynasty , or Great Yuan Empire was a ruling dynasty founded by the Mongol leader Kublai Khan, who ruled most of present-day China, all of modern Mongolia and its surrounding areas, lasting officially from 1271 to 1368. It is considered both as a division of the Mongol Empire and as an...

. The writings of Li Zhi

Li Zhi (mathematician)

Li Zhi , later Li Ye , was a Chinese mathematician and scholar, who published and improved the tian yuan shu method for solving polynomial equations of one variable.- Name :...

, Qin Jiushao, Zhu Shijie

Zhu Shijie

Zhu Shijie , courtesy name Hanqing , pseudonym Songting , was one of the greatest Chinese mathematicians lived during the Yuan Dynasty....

 and others could no longer be fully understood, until the arrival of western mathematics in China.

Meanwhile tian yuan shu arrived in Japan where it is called . The book Suanxue qimeng by Zhu Shijie

Zhu Shijie

Zhu Shijie , courtesy name Hanqing , pseudonym Songting , was one of the greatest Chinese mathematicians lived during the Yuan Dynasty....

, was deciphered and was important in the development of Japanese mathematics

Japanese mathematics

denotes a distinct kind of mathematics which was developed in Japan during the Edo Period . The term wasan, from wa and san , was coined in the 1870s and employed to distinguish native Japanese mathematics theory from Western mathematics .In the history of mathematics, the development of wasan...

 (wasan) in the 17th and 18th centuries.

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 (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.