Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

Grant Olney Passmore

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arXiv · 1506.04863

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

Grant Olney Passmore

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Abstract

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.

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Grant Olney Passmore. 2015-06-16. Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers. https://arxiv.org/abs/1506.04863

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