:expressions predicate for one 2D halfspace a·x + b·y ≤ c. More...

Public Types
using	Domain = dedekind::linear_algebra::Vec2V<T>
using	cardinality_type = dedekind::sets::ℵ_0

Public Member Functions
constexpr bool	operator() (const Domain &p) const

Detailed Description

template<typename T, T a, T b, T c>
struct dedekind::optimization::Halfspace2DPredicate< T, a, b, c >

:expressions predicate for one 2D halfspace a·x + b·y ≤ c.

Halfspace meets as real :expressions Set DSL.

The §5 LP exhibit reads in the textbook frame F : ℚ×ℚ, U : F→ℚ, G ⊆ F, opt = argmax(G, U), with G being a genuine :expressions::Set<Vec2V<T>, Boole, P> instance — the same DSL §3 builds out of bound-scout comprehensions, applied to the 2D LP carrier:

constexpr auto G = halfspace_set(H1{}) & halfspace_set(H2{})
                 & halfspace_set(H3{}) & halfspace_set(H4{});
constexpr LinearFunctional<Rat, Rat{3L}, Rat{2L}> U{};
constexpr auto opt = argmax(G, U);   //  Vec2<Rat, Rat{2L}, Rat{2L}>
static_assert(G.contains(opt));      //  opt ∈ G via the Set DSL

The integration with :expressions rides on the existing structured_and customization point (the same one :order:halfspace uses to collapse one-dimensional halfspace meets to singletons / intervals / empty). :expressions::operator& discovers our structured_and overloads via ADL on the predicate types and produces a structurally-typed Set:

Set<Vec2V<T>, Boole,
    Polytope2DPredicate<T, H1, H2, H3, H4>>

carrying the halfspace pack inside the predicate's template parameter list — exactly what argmax extracts to call the kernel. Closes FIXME(#365) in the 2D-halfspace case: the meet is no longer a lambda fall-through, it's a structural reduction the DSL recognises.

Carries (a, b, c) as NTTPs (structural) and exposes a stateless operator() — the predicate Set DSL participants are built from. ADL through this type's namespace (:optimization) lets the structured_and overloads below intercept halfspace meets inside :expressions::operator& .

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

src/main/modules/dedekind/optimization/lp.cppm

Public Types

Public Member Functions

Detailed Description

Halfspace meets as real :expressions Set DSL.