dedekind::numbers::PartialEmbedIntegerToRational< I > Struct Template Reference

Identity and Associativity traits for Rational arithmetic. More...

Public Types
using	value_type = Rational<I>
using	logic_species = Kleene

Public Member Functions
TernaryResult< Rational< I > >	operator() (I n) const noexcept

Detailed Description

template<IsInteger I>
struct dedekind::numbers::PartialEmbedIntegerToRational< I >

Identity and Associativity traits for Rational arithmetic.

Rational arithmetic over exact field operations satisfies:

• Kleene associativity: if both sides are defined, they are equal
• Kleene commutativity (for addition/multiplication)
• Partial identities: 0 for addition, 1 for multiplication

Specializations are declared in the dedekind::category namespace (see below).

Embedding transform: ℤ ↪ ℚ with Ternary acknowledgment.

The embedding of an integer Z into the rationals is exact: every integer n corresponds uniquely to n/1. This transform returns Ternary::True to signal no information loss.

See also

embed_ℤ_ℚ_ (below) — the same \(n\mapsto n/1\) as a categorical arrow over default_integer, carrying the monic/homomorphism/monotone registrations the tower S-leg needs. This Ternary transform is the Kleene surface; the two are distinct, not a redundant fork.

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

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