dedekind::algebra::IsVectorSpace Concept Reference

The Gold Standard: A Module where the Scalar is a Field. More...

Concept definition

template<typename V, typename F, typename AddV std::plus<V>, typename AddF std::plus<F>, typename MultF std::multiplies<F>, typename Act std::multiplies<>>
concept dedekind::algebra::IsVectorSpace =  IsModule<V, F, AddV, AddF, MultF, Act> &&
                        dedekind::category::IsField<F, AddF, MultF>

Detailed Description

The Gold Standard: A Module where the Scalar is a Field.

Template Parameters

V	The vector carrier.
F	The scalar field carrier.
AddV	Additive law on V (defaults to std::plus<V>).
AddF	Additive law on F (defaults to std::plus<F>).
MultF	Multiplicative law on F (defaults to std::multiplies<F>).
Act	External action witness F x V -> V (defaults to std::multiplies<>).

Uses dedekind::category::IsField (axiomatic, no division-operator requirement) so that primitive scalar carriers like bool under (std::bit_xor, std::bit_and) work without needing a division surface. The operator-level field witness dedekind::algebra::IsField composes additionally with IsDivisionRing; code that needs the division surface on the scalar side should check that separately.