@inproceedings{10.1007/978-3-319-21401-6_12,
    Abstract = {We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., ``{\$}{\$}x^n {\backslash}in {\backslash}mathbb {\{}Q{\}}{\$}{\$}'' and ``{\$}{\$}x^n {\backslash}in {\backslash}mathbb {\{}Z{\}}{\$}{\$}.'' Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.},
    Address = {Cham},
    Author = {Passmore, Grant Olney},
    BookTitle = {Automated Deduction - CADE-25},
    Editor = {Felty, Amy P. and Middeldorp, Aart},
    File = {Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers (0) - a - a - e.pdf},
    ISBN = {978-3-319-21401-6},
    Pages = {181--196},
    Publisher = {Springer International Publishing},
    Title = {Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers},
    Year = {2015},
    date-added = {2019-08-21 09:21:18 +0200},
    date-modified = {2019-08-21 09:21:18 +0200},
    doi = {10.1007/978-3-319-21401-6_12}
}

@inproceedings{10.1007/978-3-319-21401-6_12, Abstract = {We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., {\$}{\$}x^n {\backslash}in {\backslash}mathbb {\{}Q{\}}{\$}{\$}'' and, Address = {Cham}, Author = {Passmore, Grant Olney}, BookTitle = {Automated Deduction - CADE-25}, Editor = {Felty, Amy P. and Middeldorp, Aart}, File = {Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers (0) - a - a - e.pdf}, ISBN = {978-3-319-21401-6}, Pages = {181--196}, Publisher = {Springer International Publishing}, Title = {Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers}, Year = {2015}, date-added = {2019-08-21 09:21:18 +0200}, date-modified = {2019-08-21 09:21:18 +0200}, doi = {10.1007/978-3-319-21401-6_12} }}{\$}x^n {\backslash}in {\backslash}mathbb {{}Z{}}{\$}{\$}.'' Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.