Properties of Spaces

Tools to reflect on whether types expose other types typically associated with various spaces. More...

Classes
struct	sequoia::maths::commutative_ring_type_of< ConvexSpace >
	Helper to extract the commutative ring type of the free module associated with a convex space. More...

Variables
template<class T >
constexpr bool	sequoia::maths::has_commutative_ring_type_v
	Compile time constant reflecting whether a type exposes a nested type named commutative_ring_type which satisifes the weak_commutative_ring concept.
template<class T >
constexpr bool	sequoia::maths::has_field_type_v
	Compile time constant reflecting whether a type exposes a nested type named field_type which satisifes the weak_field concept.
template<class T >
constexpr bool	sequoia::maths::defines_commutative_ring_v {has_commutative_ring_type_v<T> || has_field_type_v<T>}
	Compile time constant reflecting whether a type exposes a nested type with the properties of a commutative ring.
template<class T >
constexpr bool	sequoia::maths::defines_field_v
	Reports whether a type exposes a nested type with the properties of a field.
template<class T >
constexpr bool	sequoia::maths::has_dimension_v
	Compile time constant reflecting whether a type exposes a nested value, dimension, convertible to a std::size_t.
template<class T >
constexpr bool	sequoia::maths::has_set_type_v
	Compile time constant reflecting whether a type exposes a nested type named set_type.
template<class T >
constexpr bool	sequoia::maths::has_vector_space_type_v
	Compile time constant reflecting whether a type exposes a nested vector_space_type which satisfies the vector_space concept.
template<class T >
constexpr bool	sequoia::maths::has_free_module_type_v
	Compile time constant reflecting whether a type exposes a nested free_modul_type which satisfies the vector_space concept.
template<convex_space ConvexSpace>
constexpr std::size_t	sequoia::maths::dimension_of {free_module_type_of_t<ConvexSpace>::dimension}
	Helper to extract the dimension of the free module associated with a convex space.

Detailed Description

Tools to reflect on whether types expose other types typically associated with various spaces.

Variable Documentation

defines_commutative_ring_v

template<class T >

constexpr bool sequoia::maths::defines_commutative_ring_v {has_commutative_ring_type_v<T> || has_field_type_v<T>}

inlineconstexpr

Compile time constant reflecting whether a type exposes a nested type with the properties of a commutative ring.

The point here is that a field is a special case of a ring. Therefore, anything which defines a field is implicitly defining a ring.

defines_field_v

template<class T >

constexpr bool sequoia::maths::defines_field_v

inlineconstexpr

Initial value:

{
        has_field_type_v<T>
    || requires { 
          typename T::commutative_ring_type;
          requires weak_field<typename T::commutative_ring_type>;
        }
  }

Reports whether a type exposes a nested type with the properties of a field.

The point here is to capture the case where a type exposes a nested type commutative_ring_type but the latter satisfies not just the weak_commutative_ring concept but also the strong weak_field concept.

has_commutative_ring_type_v

template<class T >

constexpr bool sequoia::maths::has_commutative_ring_type_v

inlineconstexpr

Initial value:

{
    requires { 
      typename T::commutative_ring_type;
      requires weak_commutative_ring<typename T::commutative_ring_type>;
    }
  }

Compile time constant reflecting whether a type exposes a nested type named commutative_ring_type which satisifes the weak_commutative_ring concept.

has_dimension_v

template<class T >

constexpr bool sequoia::maths::has_dimension_v

inlineconstexpr

Initial value:

{
    requires { { T::dimension } -> std::convertible_to<std::size_t>; }
  }

Compile time constant reflecting whether a type exposes a nested value, dimension, convertible to a std::size_t.

has_field_type_v

template<class T >

constexpr bool sequoia::maths::has_field_type_v

inlineconstexpr

Initial value:

{
    requires { 
      typename T::field_type;
      requires weak_field<typename T::field_type>;
    }
  }

Compile time constant reflecting whether a type exposes a nested type named field_type which satisifes the weak_field concept.

has_free_module_type_v

template<class T >

constexpr bool sequoia::maths::has_free_module_type_v

inlineconstexpr

Initial value:

{
    requires {
      typename T::free_module_type;
      requires free_module<typename T::free_module_type>;
    }
  }

Compile time constant reflecting whether a type exposes a nested free_modul_type which satisfies the vector_space concept.

has_set_type_v

template<class T >

constexpr bool sequoia::maths::has_set_type_v

inlineconstexpr

Initial value:

{
    requires { typename T::set_type; }
  }

Compile time constant reflecting whether a type exposes a nested type named set_type.

has_vector_space_type_v

template<class T >

constexpr bool sequoia::maths::has_vector_space_type_v

inlineconstexpr

Initial value:

{
    requires {
      typename T::vector_space_type;
      requires vector_space<typename T::vector_space_type>;
    }
  }

Compile time constant reflecting whether a type exposes a nested vector_space_type which satisfies the vector_space concept.