An exact real algebraic arithmetic with equality determination
Namhyun Hur, James H. Davenport · 2000
We describe a new arithmetic model for real algebraic numbers with an exact equality determination. The model represents a real algebraic number as a pair of an arbitrary precision numerical value and a symbolic expression. For the numerical part we currently (another representation could be used) use the dyadic exact real number and for the symbolic part we use a square-free polynomial for the real algebraic number. In this model we show that we can decide exactly the equality of real algebraic numbers.