Algorithms for solving algebra problems?

Question

Are there algorithms for solving non-trivial problems of algebra, for example, to simplify the following expression:

2x^3 - 3x^2 + 3x - 4 -------------------- x-2 

The solution would be 2x ^ 2 + x + 5 + 6 / (x-2).

Are there also algorithms for factoring and other algebra-oriented mathematicians?

thanks

Answer 1

For the example you provided, simple polynomial separation is just done. You can get additional information:

http://en.wikipedia.org/wiki/Polynomial_long_division

Answer 2

Stephen Wolfram made a career in his Mathematica. There are other symbolic math programs, such as Maxima:

http://www.arachnoid.com/maxima/

Answer 3

There is something called the Horner Scheme - http://en.wikipedia.org/wiki/Horner_scheme

Is that what you meant?

Answer 4

Answer: yes, there are certain algorithms for solving such issues.

Take a look at SymPy . SymPy is an open source library library written in pure Python. It contains many of these algorithms, and the code is available on github . Writers tried to emphasize clarity for this particular situation.