Writing A Program That Does Algebra For Me

I want to try and write a program that can solve algebra problems in C++, how would I go about doing this (I already know some C++, I just need a basic idea of how to go about using variables, constants, etc. to do algebra)?

get "algorithms in C++" by R. Sedgewick, it has a few good algorithms for mathmatical purposes; alternatively use "Numerical Recipies in C"(fucking old but still the best book for numerical computing).