Q is the rational field Rational<Z> — the canonical exact, dense, strongly-ordered coefficient carrier. Used to gate the real carriers (Cut, QuadraticReal): over \(\mathbb{Q}\) a nonsquare integer D has \(\sqrt D\notin\mathbb{Q}\) (a theorem), so those carriers are genuine (canonical representation, sound conjugate/norm) — which fails for a coefficient field that already contains \(\sqrt D\) (e.g. the degenerate QuadraticReal<2, QuadraticReal<2>>). More...

Concept definition

template<typename Q>
concept dedekind::numbers::IsRational = 
    detail_rational::is_rational<std::remove_cvref_t<Q>>::value

Detailed Description

Q is the rational field Rational<Z> — the canonical exact, dense, strongly-ordered coefficient carrier. Used to gate the real carriers (Cut, QuadraticReal): over \(\mathbb{Q}\) a nonsquare integer D has \(\sqrt D\notin\mathbb{Q}\) (a theorem), so those carriers are genuine (canonical representation, sound conjugate/norm) — which fails for a coefficient field that already contains \(\sqrt D\) (e.g. the degenerate QuadraticReal<2, QuadraticReal<2>>).