Stateless type aliases¶

using libsemigroups::SchreierSimsTraits::Action = ::libsemigroups::ImageRightAction<TElementType, TPointType>¶

Adapter for the value of a right action.

Defined in adapters.hpp.

Specialisations of this struct should be stateless trivially default constructible with a call operator of signature:

void operator()(TPointType& res, TElementType const& x, TPointType const& pt) const (possibly noexcept, inline and/or constexpr also); or
TPointType operator()(TElementType const& x, TPointType const& pt) const (possibly noexcept, inline and/or constexpr also).

In form (1): the call operator should change res in-place to contain the image of the point pt under the right action of the element x. The purpose of the 1st parameter is to avoid repeated allocations of memory to hold temporary points that are discarded soon after they are created.

In form (2): the call operator should return the image of the point pt under the right action of the element x.

The third template parameter exists for SFINAE.

Used by:

Action (in form (1))
SchreierSimsTraits (in form (2))

Example

template <>
struct ImageLeftAction<BMat8, BMat8> {
  void operator()(BMat8& res, BMat8 pt, BMat8 x) const noexcept {
    res = (x * pt).row_space_basis();
  }
};

Template Parameters:

TElementType – the type of the elements of a semigroup.
TPointType – the type of the points acted on.

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

Adapter for the degree of an element.

Defined in adapters.hpp.

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

The return value of the call operator ought to indicate the degree of a TElementType 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.

Used by:

Example

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

Template Parameters:

TElementType – the type of the elements of a semigroup.
TSfinae – this template parameter can be used for SFINAE.

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

Adapter for testing equality.

Defined in adapters.hpp.

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

Used by:

Template Parameters:

TValueType – the type of objects to compare.
TSfinae – this template parameter can be used for SFINAE.

using libsemigroups::SchreierSimsTraits::Inverse = ::libsemigroups::Inverse<element_type>¶

Adapter for increasing the degree of an element.

Defined in adapters.hpp.

Specialisations of this struct should be stateless trivially default constructible with a call operator of signature void operator()(TElementType& 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<TElementType>()(x), then after the call to IncreaseDegree<TElementType>()(x, n), Degree<TElementType>()(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.

The second template parameter exists for SFINAE.

Used by:

FroidurePinTraits

Example

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

Template Parameters:: TElementType – the type of the elements of a semigroup.

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

Adapter for the identity element of the given type.

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

TElementType operator()(size_t n) const (possibly noexcept, inline and/or constexpr also) returning a multiplicative identity element for the category TElementType and with Degree<TElementType>()(x) equal to the parameter n. For example, if TElementType is a type of n x n matrices, then this should return the n x n identity matrix.

TElementType operator()(T const&) const (possibly noexcept, inline and/or constexpr also). This could be implemented as:

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

Used by:

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();
  }
};

Template Parameters:

TElementType – the type of the elements of a semigroup.
TSfinae – this template parameter can be used for SFINAE.

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

Adapter for the product of two elements.

Defined in adapters.hpp.

Specialisations of this struct should be stateless trivially default constructible with a call operator of signature void operator()(TElementType& xy, TElementType const& x, TElementType const& y, 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.

Used by:

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;
  }
};

Template Parameters:

TElementType – the type of the elements of a semigroup.
TSfinae – this template parameter can be used for SFINAE.

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

Adapter for swapping.

Defined in adapters.hpp.

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

Used by:

Template Parameters:

TValueType – the type of objects to compare.
TSfinae – this template parameter can be used for SFINAE.