Adapter types

This page contains the documentation for adapters for the SchreierSims class.

using libsemigroups::SchreierSims::Action = typename TTraits::Action

Alias for TTraits::Action.

See Action for further details.

using libsemigroups::SchreierSims::Degree = typename TTraits::Degree

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::SchreierSims::EqualTo = typename TTraits::EqualTo

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::SchreierSims::Inverse = typename TTraits::Inverse

Adapter for the inverse of an element.

Defined in adapters.hpp.

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

The call operator should return the inverse of the element x under the assumption that x has an inverse (in the sense of groups). For example, if x is a permutation, then this would return its inverse. If x is a permutation matrix of type BMat8, then this operator would return its transpose.

The second template parameter exists for SFINAE.

Used by:

Example

template <>
struct Inverse<BMat8> {
  inline BMat8 operator()(BMat8 const& x) const noexcept {
    LIBSEMIGROUPS_ASSERT(x * x.transpose() == x.one());
    return x.transpose();
  }
};

Template Parameters

TElementType – the type of the elements of a semigroup.

using libsemigroups::SchreierSims::One = typename TTraits::One

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:

  1. 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.

  2. 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::SchreierSims::Product = typename TTraits::Product

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::SchreierSims::Swap = typename TTraits::Swap

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.