dedekind::sets::ResidueClass< L > Struct Template Reference

The class \(\{x \in \mathbb{N} \mid x \equiv r \pmod n\}\), read analytically: the materialisation of ℕ | (π % n == r). More...

Public Member Functions
constexpr bool	operator== (const Ø< Cardinality, L > &) const
template<typename C>
constexpr bool	operator== (const 𝔸< Cardinality, L, C > &) const

Public Attributes
std::size_t	modulus
bool	inhabited

Friends
constexpr bool	operator== (const Ø< Cardinality, L > &e, const ResidueClass &s)
template<typename C>
constexpr bool	operator== (const 𝔸< Cardinality, L, C > &u, const ResidueClass &s)

Detailed Description

template<typename L>
struct dedekind::sets::ResidueClass< L >

The class \(\{x \in \mathbb{N} \mid x \equiv r \pmod n\}\), read analytically: the materialisation of ℕ | (π % n == r).

Both lattice-bound comparisons (Eqn 2) are decided without enumerating anything: since x % n lies in \([0, n)\), the class is inhabited exactly when r does (r itself is a member), and it is all of ℕ exactly when it is inhabited and \(n = 1\). The modulus is positive by construction: a negative constant meeting ℕ raises, and a division by the constant 0 is refused when the term is built.

Template Parameters

L	the species.

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

• src/main/modules/dedekind/numbers/natural.cppm