dedekind::linear_algebra::SemimoduleVec< S, N, Orientation > Struct Template Reference

An N-entry semimodule vector over the semiring S, read as an index→scalar arrow. IsColumnVector / IsCovector by the default (semimodule) contract: ⊕ and the two-sided scalar ⊗ action, but no negation (a dioid has none). Ket (ColumnOrientation, |v⟩) and Bra (RowOrientation, ⟨w|) are its two orientations — the bra·ket language of :transfer made first-class carriers, the "matrix column/row @b is a vector" slogan for a semiring. One carrier, orientation as a template parameter (the tag is the only difference between a column and a row). More...

Collaboration diagram for dedekind::linear_algebra::SemimoduleVec< S, N, Orientation >:

Public Types
using	scalar_type = S
using	orientation = Orientation
using	dimension_type = dedekind::sets::Finite
using	Domain = std::size_t
	A vector is an index→scalar arrow, so Ket / Bra are IsArrow — they feed :transfer's inner_product / OuterProduct directly, retiring the ad-hoc bra/ket structs.
using	Codomain = S

Public Member Functions
constexpr S	operator() (std::size_t i) const
constexpr S	operator[] (std::size_t i) const

Public Attributes
std::array< S, N >	c {}

Static Public Attributes
static constexpr std::size_t	dimension = N
template<typename Op>
static constexpr bool	is_associative_v
	The additive monoid (·, ⊕) inherits the scalar's laws (§4 property distribution): the elementwise ⊕ is associative / commutative exactly when the base ⊕ is, and only for the vector's own std::plus — an arbitrary Op is not certified. Totality distributes separately (is_saturating below).
template<typename Op>
static constexpr bool	is_commutative_v

Friends
constexpr bool	operator== (const SemimoduleVec &, const SemimoduleVec &)=default
constexpr SemimoduleVec	operator+ (const SemimoduleVec &a, const SemimoduleVec &b)
constexpr SemimoduleVec	operator* (const S &s, const SemimoduleVec &a)
constexpr SemimoduleVec	operator* (const SemimoduleVec &a, const S &s)

Detailed Description

template<typename S, std::size_t N, typename Orientation>
struct dedekind::linear_algebra::SemimoduleVec< S, N, Orientation >

An N-entry semimodule vector over the semiring S, read as an index→scalar arrow. IsColumnVector / IsCovector by the default (semimodule) contract: ⊕ and the two-sided scalar ⊗ action, but no negation (a dioid has none). Ket (ColumnOrientation, |v⟩) and Bra (RowOrientation, ⟨w|) are its two orientations — the bra·ket language of :transfer made first-class carriers, the "matrix column/row @b is a vector" slogan for a semiring. One carrier, orientation as a template parameter (the tag is the only difference between a column and a row).

Member Data Documentation

is_associative_v

template<typename S, std::size_t N, typename Orientation>

template<typename Op>

bool dedekind::linear_algebra::SemimoduleVec< S, N, Orientation >::is_associative_v

staticconstexpr

Initial value:

=
      std::same_as<Op, std::plus<SemimoduleVec>> &&
      dedekind::category::associative<S>(
          typename dedekind::algebra::semiring_ops<S>::add{})

The additive monoid (·, ⊕) inherits the scalar's laws (§4 property distribution): the elementwise ⊕ is associative / commutative exactly when the base ⊕ is, and only for the vector's own std::plus — an arbitrary Op is not certified. Totality distributes separately (is_saturating below).

is_commutative_v

template<typename S, std::size_t N, typename Orientation>

template<typename Op>

bool dedekind::linear_algebra::SemimoduleVec< S, N, Orientation >::is_commutative_v

staticconstexpr

Initial value:

=
      std::same_as<Op, std::plus<SemimoduleVec>> &&
      dedekind::category::commutative<S>(
          typename dedekind::algebra::semiring_ops<S>::add{})

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

• src/main/modules/dedekind/linear_algebra/matnxn.cppm