Check whether T is a group (tools/is_group.hpp)

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• Last update: 2024-03-23 15:55:12+09:00
• Include: #include "tools/is_group.hpp"

template <typename G>
struct is_group {
  static constexpr bool value;
};

template <typename G>
inline constexpr bool is_group_v = is_group<G>::value;

If <G> satisfies the following conditions, tools::is_group<G>::value is true.

• typename G::T exists.
• The static member function typename G::T G::op(typename G::T, typename G::T) exists.
• The static member function typename G::T G::e() exists.
• The static member function typename G::T G::inv(typename G::T) exists.

Otherwise, it is false.

Constraints

• None

Time Complexity

• Not applicable

License

• CC0

Author

• anqooqie

Required by

• 2D cumulative sum (tools/cumsum2d.hpp)
• Precompute $n! \pmod{P}$ for $0 \leq n < P \approx 10^9$ (tools/large_fact_mod_cache.hpp)
• Online cumulative sum (tools/online_cumsum.hpp)
• Online difference array (tools/online_imos.hpp)
• Shift of sampling points of polynomial (tools/sample_point_shift.hpp)
• Twelvefold way (tools/twelvefold_way.hpp)

Verified with

• tests/bigdecimal/cast_to_long_long.test.cpp
• tests/cartesian_tree/interval.test.cpp
• tests/cumsum2d.test.cpp
• tests/is_group.test.cpp
• tests/large_fact_mod_cache/binomial.test.cpp
• tests/large_fact_mod_cache/fact.test.cpp
• tests/online_cumsum.test.cpp
• tests/online_imos.test.cpp
• tests/sample_point_shift.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_unrestricted.test.cpp

Code

#ifndef TOOLS_IS_GROUP_HPP
#define TOOLS_IS_GROUP_HPP

#include <type_traits>
#include <utility>

namespace tools {

  template <typename G, typename = void>
  struct is_group : ::std::false_type {};

  template <typename G>
  struct is_group<G, ::std::enable_if_t<
    ::std::is_same_v<typename G::T, decltype(G::op(::std::declval<typename G::T>(), ::std::declval<typename G::T>()))> &&
    ::std::is_same_v<typename G::T, decltype(G::e())> &&
    ::std::is_same_v<typename G::T, decltype(G::inv(::std::declval<typename G::T>()))>
  , void>> : ::std::true_type {};

  template <typename G>
  inline constexpr bool is_group_v = ::tools::is_group<G>::value;
}

#endif

#line 1 "tools/is_group.hpp"



#include <type_traits>
#include <utility>

namespace tools {

  template <typename G, typename = void>
  struct is_group : ::std::false_type {};

  template <typename G>
  struct is_group<G, ::std::enable_if_t<
    ::std::is_same_v<typename G::T, decltype(G::op(::std::declval<typename G::T>(), ::std::declval<typename G::T>()))> &&
    ::std::is_same_v<typename G::T, decltype(G::e())> &&
    ::std::is_same_v<typename G::T, decltype(G::inv(::std::declval<typename G::T>()))>
  , void>> : ::std::true_type {};

  template <typename G>
  inline constexpr bool is_group_v = ::tools::is_group<G>::value;
}

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