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Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers (1506.04863v1)
Published 16 Jun 2015 in math.LO and cs.LO
Abstract: We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(xn \in \mathbb{Q})$ and $(xn \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.