However, at that time equations were neither written nor conceptualized in terms of such a place-value notation.
It was only much later that the concept and representation of equations begat a full-fledged place-value notation.
By that time, general equations of any degree were used and were represented by a full-fledged place-value notation.
This is an instance of a place-value notation, in which the position of a number in a numerical configuration has a mathematical meaning.
Jia's algorithm operated on a column of rows set up on the counting surface in such a way that it still involved a place-value notation for the underlying equations.
As soon as positive and negative powers of the indeterminates or too many mixed terms occurred, however, he had to use tricks that were in conflict with the principles of the place-value notation.
A science historian quoted here says the Babylonian creation of a "place-value notation system" -- a way of writing numbers, for example, with a place for ones, tens, hundreds, and so on -- was similar in impact to invention of the alphabet.
The following discussion of the evolution of mathematical subjects within the Chinese tradition emphasizes several common characteristics: an interest in general algorithms and the importance given to "position" (a place-value notation involving rods or counters), a specific part devoted to configurations of numbers, and the parallelisms between procedures.
Moreover, in setting up the algorithms, the divisors were arranged one above the other, yielding a place-value notation for the underlying equations: the row in which a number occurred was associated with the power of the unknown whose coefficient it was.
Rods were then no longer used as a counting tool, so perhaps Chinese algebraic place-value notations, deprived of the instrument on which they were based, could not be understood.
