dedekind::morphologies::ModularCongruence< N > Struct Template Reference

The binary congruence relation \(x \equiv y \pmod N\) on the integer carrier: the kernel of the reduction \(\mathbb{Z} \twoheadrightarrow \mathbb{Z}/N\mathbb{Z} =\) Modular<N>. More...

Public Types
using	machine_type = typename Modular<N>::machine_type

Public Member Functions
constexpr bool	operator() (machine_type a, machine_type b) const

Detailed Description

template<auto N>
struct dedekind::morphologies::ModularCongruence< N >

The binary congruence relation \(x \equiv y \pmod N\) on the integer carrier: the kernel of the reduction \(\mathbb{Z} \twoheadrightarrow \mathbb{Z}/N\mathbb{Z} =\) Modular<N>.

Where Congruence<N,R> is the unary residue-class predicate (the fiber over R), ModularCongruence<N> is the equivalence relation whose quotient is Modular<N> — the relation the H-leg rides (IsCongruenceQuotient, :algebra::quotient). It is a genuine congruence for + and × ( \(x \equiv x' \wedge y \equiv y' \Rightarrow x{+}y \equiv x'{+}y'\)), so Modular<N> is witnessed relationally as \(V/({\equiv}\bmod N)\) — the non-trivial companion to the int/(=) diagonal witness upstream.

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

• src/main/modules/dedekind/morphologies/cyclic.cppm