KoniecznyTraits< Element >

template<typename Element>
struct libsemigroups::KoniecznyTraits< Element >

Template Parameters

Element

the type of the elements.

See also

Konieczny

Public Types
using	const_element_type
	The type of const elements of a Konieczny instance.
using	Degree = ::libsemigroups::Degree<element_type>
	Adapter for the degree of an element.
using	element_type = typename detail::BruidhinnTraits<Element>::value_type
	The type of the elements of a Konieczny instance with const removed.
using	ElementHash = ::libsemigroups::Hash<element_type>
	Adapter for hashing.
using	EqualTo = ::libsemigroups::EqualTo<element_type>
	Adapter for testing equality.
using	Lambda = ::libsemigroups::Lambda<element_type, lambda_value_type>
	Adapter for the action on LambdaValue's.
using	lambda_orb_type
using	lambda_value_type
using	Less = ::libsemigroups::Less<element_type>
	Adapter for comparisons.
using	One = ::libsemigroups::One<element_type>
	Adapter for the identity element of the given type.
using	Product = ::libsemigroups::Product<element_type>
	Adapter for the product of two elements.
using	Rank = ::libsemigroups::Rank<element_type, rank_state_type>
	Adapter for calculating ranks.
using	rank_state_type = typename ::libsemigroups::RankState<element_type>
	Alias for RhoValue with template parameter element_type.
using	Rho = ::libsemigroups::Rho<element_type, rho_value_type>
	Adapter for the action on RhoValue's.
using	rho_orb_type
using	rho_value_type
	Alias for RhoValue with template parameter element_type.
using	Swap = ::libsemigroups::Swap<element_type>
	Adapter for swapping.

Member Typedef Documentation

const_element_type

template<typename Element>

using const_element_type

Initial value:

 
        typename detail::BruidhinnTraits<Element>::const_value_type

Degree

template<typename Element>

using Degree = ::libsemigroups::Degree<element_type>

Defined in adapters.hpp.

Specialisations of this struct should be stateless trivially default constructible with a call operator of signature size_t operator()(Element const& x) const (possibly noexcept, inline and/or constexpr also).

The return value of the call operator ought to indicate the degree of a Element instance which may or may not depend on the parameter x. The degree of a permutation, for instance, would be the the number of points it acts on, the degree of a matrix is its dimension, and so on. This is used, for example, by SchreierSimsTraits in some member functions to determine whether it is known a priori that a permutation does not belong to the object, because it acts on too many points.

Template Parameters

Element

the type of the elements of a semigroup.

The second template parameter exists for SFINAE.

Used by:

• FroidurePinTraits
• KoniecznyTraits
• SchreierSimsTraits

Example

template <>
struct Degree<BMat8> {
  constexpr inline size_t operator()(BMat8 const&) const noexcept {
    return 8;
  }
};

ElementHash

template<typename Element>

using ElementHash = ::libsemigroups::Hash<element_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with a call operator of signature size_t operator()(Value const&) for use with, for example, std::unordered_map.

Template Parameters

Value

the type of objects to compare.

The second template parameter exists for SFINAE.

Used by:

• ActionTraits
• FroidurePinTraits
• SchreierSimsTraits

EqualTo

template<typename Element>

using EqualTo = ::libsemigroups::EqualTo<element_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with a call operator of signature bool operator()(Value const&, Value const&) (possibly noexcept, inline and/or constexpr also) for use with, for example, std::unordered_map.

Template Parameters

Value

the type of objects to compare.

The second template parameter exists for SFINAE.

Used by:

• ActionTraits
• FroidurePinTraits
• SchreierSimsTraits

Lambda

template<typename Element>

using Lambda = ::libsemigroups::Lambda<element_type, lambda_value_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with an operator of signature void operator()(Point&, Element const&), which should modify the first argument in-place to contain the lambda value of the second argument. The kernel of the lambda function should be Green's \(\mathscr{L}\)-relation on the semigroup in question.

Template Parameters

Element	the type of elements.
Point	the type of the lambda points.

The third template parameter exists for SFINAE.

Used by:

• KoniecznyTraits.

lambda_orb_type

template<typename Element>

using lambda_orb_type

Initial value:

 RightAction<element_type,
                      lambda_value_type,
                      ImageRightAction<element_type, lambda_value_type>>

The type of the orbit of the lambda values under ImageRightAction.

See also

ImageRightAction and RightAction

lambda_value_type

template<typename Element>

using lambda_value_type

Initial value:

 
        typename ::libsemigroups::LambdaValue<element_type>::type

Alias for LambdaValue with template parameter element_type.

Less

template<typename Element>

using Less = ::libsemigroups::Less<element_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with a call operator of signature bool operator()(Value const&, Value const&) (possibly noexcept, inline and/or constexpr also) which defines a linear order on the objects of type Value.

Template Parameters

Value

the type of objects to compare.

The second template parameter exists for SFINAE.

Used by:

• FroidurePinTraits

One

template<typename Element>

using One = ::libsemigroups::One<element_type>

Specialisations of this struct should be stateless trivially default constructible with two call operator of signatures:

1. Element operator()(size_t n) const (possibly noexcept, inline and/or constexpr also) returning a multiplicative identity element for the category Element and with Degree<Element>()(x) equal to the parameter n. For example, if Element is a type of n x n matrices, then this should return the n x n identity matrix.
2. Element operator()(T const&) const (possibly noexcept, inline and/or constexpr also). This could be implemented as:

   Element operator()(Element const& x) const noexcept {
     return this->operator()(Degree<Element>()(x));
   }

Template Parameters

Element

the type of the elements of a semigroup.

The second template parameter exists for SFINAE.

Used by:

• ActionTraits
• FroidurePinTraits
• SchreierSimsTraits

Example

template <typename T>
struct One<
    T,
    typename std::enable_if<std::is_base_of<PTransf16, T>::value>::type> {
  T operator()(size_t = 0) const noexcept {
    return T::one();
  }
 
  T operator()(T const&) const noexcept {
    return T::one();
  }
};

Product

template<typename Element>

using Product = ::libsemigroups::Product<element_type>

Defined in adapters.hpp.

Specialisations of this struct should be stateless trivially default constructible with a call operator of signature void operator()(Element&, Element const&, Element const&, size_t = 0) (possibly noexcept, inline and/or constexpr also).

The call operator should change xy in-place to be the product of x and y. The 4th parameter is optional and it can be used as an index for static thread local storage, that might be required for forming the product of x and y. The purpose of the 1st parameter is to avoid repeated allocations of memory to hold temporary products that are discarded soon after they are created.

Template Parameters

Element

the type of the elements of a semigroup.

The second template parameter exists for SFINAE.

Used by:

• ActionTraits
• FroidurePinTraits
• SchreierSimsTraits

Example

template <>
struct Product<size_t> {
  void operator()(size_t& xy, size_t x, size_t y, size_t = 0) const
  noexcept {
    xy = x * y;
  }
};

Rank

template<typename Element>

using Rank = ::libsemigroups::Rank<element_type, rank_state_type>

Defined in adapters.hpp.

This type should be default constructible and a call operator of signature size_t operator()(Element const&) if no additional data is required to compute the rank, or a call operator of signature size_t operator()(State<Element> const&, Element const&) if additional data is required.

The call operator should return the rank of the element given as argument. This must satisfy the following properties:

• \(\operatorname{rank}\) should agree with the \(D\)-order on the semigroup; that is, if \(D_x \leq D_y\), then \(\operatorname{rank}(x) \leq \operatorname{rank}(y)\),
• if \(D_x \leq D_y\) and \(\operatorname{rank}(x) = \operatorname{rank}(y)\), then \(D_x = D_y\).

Template Parameters

Element	the type of elements.
State	the type of the data required to compute ranks of Elements; defaults to RankState<Element>.

The third template parameter exists for SFINAE.

Used by:

• KoniecznyTraits.

Rho

template<typename Element>

using Rho = ::libsemigroups::Rho<element_type, rho_value_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with an operator of signature void operator()(Point&, Element const&), which should modify the first argument in-place to contain the rho value of the second argument. The kernel of the rho function should be Green's \(\mathscr{R}\)-relation on the semigroup in question.

Template Parameters

Element	the type of elements.
Point	the type of the rho points.

The third template parameter exists for SFINAE.

Used by:

• KoniecznyTraits.

rho_orb_type

template<typename Element>

using rho_orb_type

Initial value:

 LeftAction<element_type,
                     rho_value_type,
                     ImageLeftAction<element_type, rho_value_type>>

The type of the orbit of the rho values under ImageLeftAction

See also

ImageLeftAction and LeftAction

rho_value_type

template<typename Element>

using rho_value_type

Initial value:

 
        typename ::libsemigroups::RhoValue<element_type>::type

Swap

template<typename Element>

using Swap = ::libsemigroups::Swap<element_type>

Defined in adapters.hpp.

This type should be a stateless trivially default constructible with a call operator of signature void operator()(Value&, Value&) (possibly noexcept, inline and/or constexpr also) which swaps its arguments.

Template Parameters

Value

the type of objects to swap.

The second template parameter exists for SFINAE.

Used by:

• ActionTraits
• FroidurePinTraits
• SchreierSimsTraits

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

• /Users/jdm3/libsemigroups/include/libsemigroups/konieczny.hpp