An exact real algebraic arithmetic with equality determination

Authors:
Namhyun Hur;James H. Davenport
Affiliations:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK;Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

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.