presentation-examples.hpp

//
// libsemigroups - C++ library for semigroups and monoids
// Copyright (C) 2022-2026 Murray T. Whyte
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
//
// This file contains declarations of functions for constructing various
// standard examples of presentations.
 
#ifndef LIBSEMIGROUPS_PRESENTATION_EXAMPLES_HPP_
#define LIBSEMIGROUPS_PRESENTATION_EXAMPLES_HPP_
 
#include <cstddef>  // for size_t
#include <vector>   // for vector
 
#include "presentation.hpp"  // for Presentation
#include "types.hpp"         // for word_type
 
namespace libsemigroups {
  namespace presentation::examples {
 
#ifdef LIBSEMIGROUPS_PARSED_BY_DOXYGEN
    // Forward declarations of the functions so they appear first in the
    // documentation
    Presentation<word_type> abacus_jones_monoid(size_t n, size_t d);
    Presentation<word_type> alternating_group(size_t n);
    Presentation<word_type> brauer_monoid(size_t n);
    Presentation<word_type> braid_group(size_t n);
    Presentation<word_type> catalan_monoid(size_t n);
    Presentation<word_type> chinese_monoid(size_t n);
    Presentation<word_type> cyclic_inverse_monoid(size_t n);
    Presentation<word_type> dual_symmetric_inverse_monoid(size_t n);
    Presentation<word_type> fibonacci_semigroup(size_t r, size_t n);
    Presentation<word_type> full_transformation_monoid(size_t n);
    Presentation<word_type> hypo_plactic_monoid(size_t n);
    Presentation<word_type> monogenic_semigroup(size_t m, size_t r);
    Presentation<word_type> motzkin_monoid(size_t n);
    Presentation<word_type> not_renner_type_B_monoid(size_t l, int q);
    Presentation<word_type> not_renner_type_D_monoid(size_t l, int q);
    Presentation<word_type> not_symmetric_group(size_t n);
    Presentation<word_type> order_preserving_cyclic_inverse_monoid(size_t n);
    Presentation<word_type> order_preserving_monoid(size_t n);
    Presentation<word_type> orientation_preserving_monoid(size_t n);
    Presentation<word_type> orientation_preserving_reversing_monoid(size_t n);
    Presentation<word_type> partial_brauer_monoid(size_t n);
    Presentation<word_type> partial_isometries_cycle_graph_monoid(size_t n);
    Presentation<word_type> partial_transformation_monoid(size_t n);
    Presentation<word_type> partition_monoid(size_t n);
    Presentation<word_type> plactic_monoid(size_t n);
    Presentation<word_type> rectangular_band(size_t m, size_t n);
    Presentation<word_type> renner_type_B_monoid(size_t l, int q);
    Presentation<word_type> renner_type_D_monoid(size_t l, int q);
    Presentation<word_type>
    sigma_plactic_monoid(std::vector<size_t> const& sigma);
    Presentation<word_type> singular_brauer_monoid(size_t n);
    Presentation<word_type> special_linear_group_2(size_t q);
    Presentation<word_type> stellar_monoid(size_t l);
    Presentation<word_type> stylic_monoid(size_t n);
    Presentation<word_type> symmetric_group(size_t n);
    Presentation<word_type> symmetric_inverse_monoid(size_t n);
    Presentation<word_type> temperley_lieb_monoid(size_t n);
    Presentation<word_type> uniform_block_bijection_monoid(size_t n);
    Presentation<word_type> zero_rook_monoid(size_t n);
#endif


    [[nodiscard]] Presentation<word_type> abacus_jones_monoid_AJP25(size_t n,
                                                                    size_t d);

    [[nodiscard]] Presentation<word_type> alternating_group_Moo97(size_t n);

    [[nodiscard]] Presentation<word_type> braid_group_Art25(size_t n);

    [[nodiscard]] Presentation<word_type> catalan_monoid_Sol96(size_t n);

    [[nodiscard]] Presentation<word_type> brauer_monoid_KM07(size_t n);

    [[nodiscard]] Presentation<word_type> chinese_monoid_CEKNH01(size_t n);

    [[nodiscard]] Presentation<word_type>
    cyclic_inverse_monoid_Fer22_a(size_t n);

    [[nodiscard]] Presentation<word_type>
    cyclic_inverse_monoid_Fer22_b(size_t n);

    [[nodiscard]] Presentation<word_type>
    dual_symmetric_inverse_monoid_EEF07(size_t n);

    [[nodiscard]] Presentation<word_type> fibonacci_semigroup_CRRT94(size_t r,
                                                                     size_t n);

    [[nodiscard]] Presentation<word_type>
    full_transformation_monoid_Aiz58(size_t n);

    [[nodiscard]] Presentation<word_type>
    full_transformation_monoid_II74(size_t n);

    [[nodiscard]] Presentation<word_type>
    full_transformation_monoid_MW24_a(size_t n);

    [[nodiscard]] Presentation<word_type>
    full_transformation_monoid_MW24_b(size_t n);

    [[nodiscard]] Presentation<word_type> hypo_plactic_monoid_Nov00(size_t n);

    [[nodiscard]] Presentation<word_type> motzkin_monoid_PHL13(size_t n);

    [[nodiscard]] Presentation<word_type>
    not_renner_type_B_monoid_Gay18(size_t l, int q);

    [[nodiscard]] Presentation<word_type>
    not_renner_type_D_monoid_God09(size_t l, int q);

    [[nodiscard]] Presentation<word_type> not_symmetric_group_GKKL08(size_t n);

    [[nodiscard]] Presentation<word_type>
    order_preserving_cyclic_inverse_monoid_Fer22(size_t n);

    [[nodiscard]] Presentation<word_type>
    order_preserving_monoid_AR00(size_t n);

    [[nodiscard]] Presentation<word_type>
    orientation_preserving_monoid_AR00(size_t n);

    [[nodiscard]] Presentation<word_type>
    orientation_preserving_reversing_monoid_AR00(size_t n);

    [[nodiscard]] Presentation<word_type> partial_brauer_monoid_KM07(size_t n);

    [[nodiscard]] Presentation<word_type>
    partial_isometries_cycle_graph_monoid_FP22(size_t n);

    [[nodiscard]] Presentation<word_type>
    partial_transformation_monoid_MW24(size_t n);

    [[nodiscard]] Presentation<word_type>
    partial_transformation_monoid_Shu60(size_t n);

    [[nodiscard]] Presentation<word_type> partition_monoid_Eas11(size_t n);

    [[nodiscard]] Presentation<word_type> partition_monoid_HR05(size_t n);

    [[nodiscard]] Presentation<word_type> plactic_monoid_Knu70(size_t n);

    [[nodiscard]] Presentation<word_type> rectangular_band_ACOR00(size_t m,
                                                                  size_t n);

    [[nodiscard]] Presentation<word_type> renner_type_B_monoid_Gay18(size_t l,
                                                                     int    q);

    [[nodiscard]] Presentation<word_type> renner_type_D_monoid_Gay18(size_t l,
                                                                     int    q);

    [[nodiscard]] Presentation<word_type>
    sigma_plactic_monoid_AHMNT24(std::vector<size_t> const& sigma);

    [[nodiscard]] Presentation<word_type> singular_brauer_monoid_MM07(size_t n);

    [[nodiscard]] Presentation<word_type> special_linear_group_2_CR80(size_t q);

    [[nodiscard]] Presentation<word_type> stellar_monoid_GH19(size_t l);

    [[nodiscard]] Presentation<word_type> stylic_monoid_AR22(size_t n);

    [[nodiscard]] Presentation<word_type> symmetric_group_Bur12(size_t n);

    [[nodiscard]] Presentation<word_type> symmetric_group_Car56(size_t n);

    [[nodiscard]] Presentation<word_type> symmetric_group_Moo97_a(size_t n);

    [[nodiscard]] Presentation<word_type> symmetric_group_Moo97_b(size_t n);

    // TODO(1) rename this function and/or include the presentation
    // from Joel's thesis (Example 7.1.2).
    [[nodiscard]] Presentation<word_type>
    symmetric_inverse_monoid_Sol04(size_t n);

    [[nodiscard]] Presentation<word_type>
    symmetric_inverse_monoid_MW24(size_t n);

    [[nodiscard]] Presentation<word_type>
    symmetric_inverse_monoid_Shu60(size_t n);

    [[nodiscard]] Presentation<word_type> temperley_lieb_monoid_Eas21(size_t n);

    [[nodiscard]] Presentation<word_type>
    uniform_block_bijection_monoid_Fit03(size_t n);
 
    // TODO(1) add okada_monoid
    // TODO(1) add free_semilattice

    // When q = 0, the a_i^2 = 1 relations from the C+M symmetric group
    // presentation are replaced with a_i^2 = a_i. See Definition 4.1.1 in
    // Joel Gay's thesis https://theses.hal.science/tel-01861199
    //
    //  This could also be called the RennerTypeAMonoid
    [[nodiscard]] Presentation<word_type> zero_rook_monoid_Gay18(size_t n);



    [[nodiscard]] inline Presentation<word_type> alternating_group(size_t n) {
      return alternating_group_Moo97(n);
    }

    [[nodiscard]] inline Presentation<word_type> brauer_monoid(size_t n) {
      return brauer_monoid_KM07(n);
    }

    [[nodiscard]] inline Presentation<word_type> chinese_monoid(size_t n) {
      return chinese_monoid_CEKNH01(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    cyclic_inverse_monoid(size_t n) {
      return cyclic_inverse_monoid_Fer22_b(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    dual_symmetric_inverse_monoid(size_t n) {
      return dual_symmetric_inverse_monoid_EEF07(n);
    }

    [[nodiscard]] inline Presentation<word_type> fibonacci_semigroup(size_t r,
                                                                     size_t n) {
      return fibonacci_semigroup_CRRT94(r, n);
    }

    [[nodiscard]] Presentation<word_type> full_transformation_monoid(size_t n);

    [[nodiscard]] inline Presentation<word_type> hypo_plactic_monoid(size_t n) {
      return hypo_plactic_monoid_Nov00(n);
    }

    [[nodiscard]] inline Presentation<word_type> catalan_monoid(size_t n) {
      return catalan_monoid_Sol96(n);
    }

    [[nodiscard]] Presentation<word_type> monogenic_semigroup(size_t m,
                                                              size_t r);

    [[nodiscard]] inline Presentation<word_type> motzkin_monoid(size_t n) {
      return motzkin_monoid_PHL13(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    not_renner_type_B_monoid(size_t l, int q) {
      return not_renner_type_B_monoid_Gay18(l, q);
    }

    [[nodiscard]] inline Presentation<word_type>
    not_renner_type_D_monoid(size_t l, int q) {
      return not_renner_type_D_monoid_God09(l, q);
    }

    [[nodiscard]] inline Presentation<word_type> not_symmetric_group(size_t n) {
      return not_symmetric_group_GKKL08(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    order_preserving_cyclic_inverse_monoid(size_t n) {
      return order_preserving_cyclic_inverse_monoid_Fer22(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    order_preserving_monoid(size_t n) {
      return order_preserving_monoid_AR00(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    orientation_preserving_monoid(size_t n) {
      return orientation_preserving_monoid_AR00(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    orientation_preserving_reversing_monoid(size_t n) {
      return orientation_preserving_reversing_monoid_AR00(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    partial_brauer_monoid(size_t n) {
      return partial_brauer_monoid_KM07(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    partial_isometries_cycle_graph_monoid(size_t n) {
      return partial_isometries_cycle_graph_monoid_FP22(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    partial_transformation_monoid(size_t n) {
      return partial_transformation_monoid_MW24(n);
    }

    [[nodiscard]] inline Presentation<word_type> partition_monoid(size_t n) {
      return partition_monoid_Eas11(n);
    }

    [[nodiscard]] inline Presentation<word_type> plactic_monoid(size_t n) {
      return plactic_monoid_Knu70(n);
    }

    [[nodiscard]] inline Presentation<word_type> rectangular_band(size_t m,
                                                                  size_t n) {
      return rectangular_band_ACOR00(m, n);
    }

    [[nodiscard]] inline Presentation<word_type> renner_type_B_monoid(size_t l,
                                                                      int q) {
      return renner_type_B_monoid_Gay18(l, q);
    }

    [[nodiscard]] inline Presentation<word_type> renner_type_D_monoid(size_t l,
                                                                      int q) {
      return renner_type_D_monoid_Gay18(l, q);
    }

    [[nodiscard]] inline Presentation<word_type>
    sigma_plactic_monoid(std::vector<size_t> const& sigma) {
      return sigma_plactic_monoid_AHMNT24(sigma);
    }

    [[nodiscard]] inline Presentation<word_type>
    singular_brauer_monoid(size_t n) {
      return singular_brauer_monoid_MM07(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    special_linear_group_2(size_t q) {
      return special_linear_group_2_CR80(q);
    }

    [[nodiscard]] inline Presentation<word_type> stellar_monoid(size_t l) {
      return stellar_monoid_GH19(l);
    }

    [[nodiscard]] inline Presentation<word_type> stylic_monoid(size_t n) {
      return stylic_monoid_AR22(n);
    }

    [[nodiscard]] inline Presentation<word_type> symmetric_group(size_t n) {
      return symmetric_group_Car56(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    symmetric_inverse_monoid(size_t n) {
      return symmetric_inverse_monoid_MW24(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    temperley_lieb_monoid(size_t n) {
      return temperley_lieb_monoid_Eas21(n);
    }

    [[nodiscard]] inline Presentation<word_type>
    uniform_block_bijection_monoid(size_t n) {
      return uniform_block_bijection_monoid_Fit03(n);
    }

    [[nodiscard]] inline Presentation<word_type> zero_rook_monoid(size_t n) {
      return zero_rook_monoid_Gay18(n);
    }

    [[nodiscard]] inline Presentation<word_type> abacus_jones_monoid(size_t n,
                                                                     size_t d) {
      return abacus_jones_monoid_AJP25(n, d);
    }

    [[nodiscard]] inline Presentation<word_type> braid_group(size_t n) {
      return braid_group_Art25(n);
    }

 
  }  // namespace presentation::examples
}  // namespace libsemigroups
#endif  // LIBSEMIGROUPS_PRESENTATION_EXAMPLES_HPP_