A decidable Dedekind real: a principal rational cut or a rational radical \(\pm\sqrt{c}\). More...

Public Member Functions
constexpr	Cut ()=default
	The additive identity \(0\) (principal cut at \(0\)).
constexpr	Cut (Q value)
	A rational is a real: its principal cut. Implicit, so \(\mathbb{Q}\hookrightarrow\) `Cut` is spelled by ordinary assignment.
template<typename V> requires (!std::same_as<V, Q> && std::convertible_to<V, Q>)
constexpr	Cut (V v)
	Single-step implicit lift `V` `→` `Q` `→` `Cut` (e.g. an `int` literal names the principal cut at that integer).
constexpr Cut	operator- () const
	Additive reflection \(-x\): negate the rational, or flip the root's sign.
constexpr bool	contains (const Q &q) const
	Is the rational `q` strictly below this real ( \(q\in\) the lower cut)? The decidable membership query the cut is defined by: the χ of `lower_set(*this)`.

Static Public Member Functions
static constexpr Cut	sqrt (Q radicand)
	The radical real \(\sqrt{c}\) (requires \(c\ge 0\); a perfect square is admitted — it simply compares `==` to its rational root).

Friends
constexpr std::strong_ordering	operator<=> (const Cut &a, const Cut &b)
	The order on reals is cut-inclusion, decided exactly on the leaf shapes. Everything else (`<`, `>`, `<=`, `>=`, `==`) derives.
constexpr bool	operator== (const Cut &a, const Cut &b)

Detailed Description

template<typename Q = Rational<default_integer>>
requires IsRational<Q>
class dedekind::numbers::Cut< Q >

A decidable Dedekind real: a principal rational cut or a rational radical \(\pm\sqrt{c}\).

Template Parameters

Q	the rational scalar carrier (defaults to \(\mathbb{Q}\)). Only its ordered-ring surface is used (`*`, unary `-`, `<=>`, `Q{}`), so every decision is exact.

The documentation for this class was generated from the following file:

Public Types