linalg::VectorSpace Concept Reference

Legacy vector-space expression contract for a registered space. More...

#include <space_concepts.hpp>

Concept definition

template<class Space>
concept linalg::VectorSpace = 
    requires(const space_point_t<Space>& x, const space_point_t<Space>& y,
             const space_type_t<Space>& alpha) {
      { x + y } -> std::convertible_to<space_point_t<Space>>;
      { x - y } -> std::convertible_to<space_point_t<Space>>;
      { alpha * x } -> std::convertible_to<space_point_t<Space>>;
      { alpha * (x + y) } -> std::convertible_to<space_point_t<Space>>;
      { alpha * x + alpha * y } -> std::convertible_to<space_point_t<Space>>;
      {
        space_type_t<Space>(1) * x
      } -> std::convertible_to<space_point_t<Space>>;
    }

Detailed Description

Legacy vector-space expression contract for a registered space.

The registered Point type must support addition, subtraction, and scalar multiplication by the registered value_type. The distributive expressions are checked for type compatibility. As with other C++ concepts, this verifies syntax and result types rather than proving the vector-space axioms.

New element-coordinate modeling should use Space and CoordinatizedSpace; this concept remains for APIs expressed through the legacy space_point_t/space_type_t vocabulary.

Definition at line 31 of file space_concepts.hpp.