FroidurePinTraits< Element, State >

template<typename Element, typename State = typename FroidurePinState<Element>::type>
struct libsemigroups::FroidurePinTraits< Element, State >

Defined in froidure-pin.hpp.

This is a traits class for use with FroidurePin.

Template Parameters

Element	the type of the elements.
State	the type of the state (if any, defaults to void, meaning none).

See also

FroidurePinBase and FroidurePin.

Public Types
using	Complexity = ::libsemigroups::Complexity<element_type>
	Adapter for the complexity of multiplication.
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 FroidurePin instance.
using	EqualTo = ::libsemigroups::EqualTo<element_type>
	Adapter for testing equality.
using	Hash = ::libsemigroups::Hash<element_type>
	Adapter for hashing.
using	IncreaseDegree = ::libsemigroups::IncreaseDegree<element_type>
	Adapter for increasing the degree of an element.
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	state_type = State
	The type of the state (if any).
using	Swap = ::libsemigroups::Swap<element_type>
	Adapter for swapping.

Member Typedef Documentation

Complexity

template<typename Element, typename State = typename FroidurePinState<Element>::type>

using Complexity = ::libsemigroups::Complexity<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 approximate complexity of multiplying two instances of Element, which may or may not depend on the parameter x. This is used, for example, by FroidurePin in some member functions to determine whether it is better to multiply elements or to follow a path in the Cayley graph.

Template Parameters

Element

the type of the elements of a semigroup.

The second template parameter exists for SFINAE.

Used by:

• FroidurePinTraits

Example

template <>
struct Complexity<KBE> {
  constexpr size_t operator()(KBE const&) const noexcept {
    return LIMIT_MAX;
  }
};

Degree

template<typename Element, typename State = typename FroidurePinState<Element>::type>

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;
  }
};

element_type

template<typename Element, typename State = typename FroidurePinState<Element>::type>

using element_type = typename detail::BruidhinnTraits<Element>::value_type

This type has const removed, and if Element is a pointer to const, then the second const is also removed.

EqualTo

template<typename Element, typename State = typename FroidurePinState<Element>::type>

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

Hash

template<typename Element, typename State = typename FroidurePinState<Element>::type>

using Hash = ::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

IncreaseDegree

template<typename Element, typename State = typename FroidurePinState<Element>::type>

using IncreaseDegree = ::libsemigroups::IncreaseDegree<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& x, size_t n) const (possibly noexcept, inline and/or constexpr also).

The call operator should change the first argument in-place so that if m = Degree<Element>()(x), then after the call to IncreaseDegree<Element>()(x, n), Degree<Element>()(x) returns m + n. This only makes sense for certain types of elements, such as permutations, transformations, or matrices, and not for other types of object. In the latter case, the call operator should simply do nothing. This is used, for example, in the member function FroidurePin::closure, when one of the generators being added has degree larger than the existing generators.

Template Parameters

Element

the type of the elements of a semigroup.

The second template parameter exists for SFINAE.

Used by:

• FroidurePinTraits

Example

template <typename Integral>
struct IncreaseDegree<
    Integral,
    typename std::enable_if<std::is_integral<Integral>::value>::type>
    {
  void operator()(Integral&, size_t) const noexcept {
  }
};

Less

template<typename Element, typename State = typename FroidurePinState<Element>::type>

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, typename State = typename FroidurePinState<Element>::type>

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, typename State = typename FroidurePinState<Element>::type>

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;
  }
};

state_type

template<typename Element, typename State = typename FroidurePinState<Element>::type>

using state_type = State

This type can be used to store some state that might be required in an FroidurePin instance.

Swap

template<typename Element, typename State = typename FroidurePinState<Element>::type>

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/jdm/libsemigroups/include/libsemigroups/froidure-pin.hpp