top_level_geometry_global.cpp

Go to the documentation of this file.

/*
 * top_level_geometry_global.cpp
 *
 *  Created on: May 23, 2021
 *      Author: betten
 */
 
 
#include "orbiter.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer5_applications {
namespace apps_geometry {
 
 
top_level_geometry_global::top_level_geometry_global()
{
 
}
 
top_level_geometry_global::~top_level_geometry_global()
{
 
}
 
 
void top_level_geometry_global::set_stabilizer_projective_space(
        projective_geometry::projective_space_with_action *PA,
        int intermediate_subset_size,
        std::string &fname_mask, int nb, std::string &column_label,
        std::string &fname_out,
        int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
 
    if (f_v) {
        cout << "top_level_geometry_global::set_stabilizer_projective_space" << endl;
    }
 
    substructure_classifier *SubC;
 
    SubC = NEW_OBJECT(substructure_classifier);
 
    SubC->set_stabilizer_in_any_space(
            PA->A, PA->A, PA->A->Strong_gens,
            intermediate_subset_size,
            fname_mask, nb, column_label,
            fname_out,
            verbose_level);
 
 
    FREE_OBJECT(SubC);
    if (f_v) {
        cout << "top_level_geometry_global::set_stabilizer_projective_space done" << endl;
    }
 
}
 
 
void top_level_geometry_global::report_decomposition_by_group(
        projective_geometry::projective_space_with_action *PA,
        groups::strong_generators *SG, std::ostream &ost, std::string &fname_base,
        int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "projective_space_with_action::report_decomposition_by_group" << endl;
    }
 
    long int order;
 
 
    order = SG->group_order_as_lint();
 
 
#if 0
    ost << "The group generated by the element" << endl;
    ost << "$$" << endl;
    A->element_print_latex(Elt, ost);
    ost << "$$" << endl;
    ost << "has the following orbits:\\\\" << endl;
 
    ost << "Orbits on points:\\\\" << endl;
#endif
 
    groups::schreier *Sch1;
    groups::schreier *Sch2;
 
    Sch1 = NEW_OBJECT(groups::schreier);
    Sch2 = NEW_OBJECT(groups::schreier);
 
    PA->A->all_point_orbits_from_generators(*Sch1,
            SG,
            0 /* verbose_level */);
 
 
    //ost << "Orbits on lines:\\\\" << endl;
 
    Sch2 = NEW_OBJECT(groups::schreier);
    PA->A_on_lines->all_point_orbits_from_generators(*Sch2,
            SG,
            0 /* verbose_level */);
    //Sch->print_orbit_lengths_tex(ost);
 
 
 
 
    ost << "Considering the group generated by" << endl;
    SG->print_generators_tex(ost);
 
    if (Sch1->nb_orbits == 1 && Sch2->nb_orbits == 1) {
        ost << "The group is transitive on points and on lines.\\\\" << endl;
        std::vector<int> Orb1;
        std::vector<int> Orb2;
        Sch1->get_orbit_in_order(Orb1, 0 /* orbit_idx */, verbose_level);
        Sch2->get_orbit_in_order(Orb2, 0 /* orbit_idx */, verbose_level);
 
        int *Inc;
        orbiter_kernel_system::file_io Fio;
        string fname;
 
        fname.assign(fname_base);
        fname.append("_incma_transitive.csv");
 
        PA->P->make_incidence_matrix(Orb1, Orb2, Inc, verbose_level);
 
        Fio.int_matrix_write_csv(fname, Inc, Orb1.size(), Orb2.size());
 
        FREE_int(Inc);
 
    }
 
 
 
    ost << "Orbits on points:\\\\" << endl;
    Sch1->print_orbit_lengths_tex(ost);
 
    ost << "Orbits on lines:\\\\" << endl;
    Sch2->print_orbit_lengths_tex(ost);
 
    ost << "Fixed points:\\\\" << endl;
    Sch1->print_fixed_points_tex(ost);
 
    ost << "Fixed lines:\\\\" << endl;
    Sch2->print_fixed_points_tex(ost);
 
 
    if (PA->f_has_action_on_planes) {
        groups::schreier *Sch3;
        Sch3 = NEW_OBJECT(groups::schreier);
        PA->A_on_planes->all_point_orbits_from_generators(*Sch3,
                SG,
                0 /*verbose_level*/);
        ost << "Fixed planes:\\\\" << endl;
        Sch3->print_fixed_points_tex(ost);
 
        FREE_OBJECT(Sch3);
    }
 
 
 
 
    {
        geometry::incidence_structure *Inc;
        data_structures::partitionstack *Stack;
 
        actions::action_global AG;
 
        if (f_v) {
            cout << "projective_space_with_action::report_decomposition_by_group before AG.compute_decomposition_based_on_orbit_length" << endl;
        }
        AG.compute_decomposition_based_on_orbit_length(PA->P,
                    Sch1, Sch2,
                    Inc, Stack, 0 /*verbose_level*/);
        if (f_v) {
            cout << "projective_space_with_action::report_decomposition_by_group after AG.compute_decomposition_based_on_orbit_length" << endl;
        }
 
 
 
        while (TRUE) {
 
            int ht0, ht1;
 
            ht0 = Stack->ht;
 
            if (f_v) {
                cout << "process_single_case before refine_column_partition_safe" << endl;
            }
            Inc->refine_column_partition_safe(*Stack, verbose_level - 2);
            if (f_v) {
                cout << "process_single_case after refine_column_partition_safe" << endl;
            }
            if (f_v) {
                cout << "process_single_case before refine_row_partition_safe" << endl;
            }
            Inc->refine_row_partition_safe(*Stack, verbose_level - 2);
            if (f_v) {
                cout << "process_single_case after refine_row_partition_safe" << endl;
            }
            ht1 = Stack->ht;
            if (ht1 == ht0) {
                break;
            }
        }
 
        int f_labeled = TRUE;
 
        Inc->print_partitioned(cout, *Stack, f_labeled);
        Inc->get_and_print_decomposition_schemes(*Stack);
        Stack->print_classes(cout);
 
 
        int f_print_subscripts = FALSE;
        ost << "Decomposition based on orbit lengths:\\\\" << endl;
        ost << "Row scheme:\\\\" << endl;
        Inc->get_and_print_row_tactical_decomposition_scheme_tex(
            ost, TRUE /* f_enter_math */,
            f_print_subscripts, *Stack);
        ost << "Column scheme:\\\\" << endl;
        Inc->get_and_print_column_tactical_decomposition_scheme_tex(
            ost, TRUE /* f_enter_math */,
            f_print_subscripts, *Stack);
 
 
 
        FREE_OBJECT(Inc);
        FREE_OBJECT(Stack);
    }
 
 
 
 
 
    {
        geometry::incidence_structure *Inc;
        data_structures::partitionstack *Stack;
 
        actions::action_global AG;
 
        if (f_v) {
            cout << "projective_space_with_action::report_decomposition_by_group before AG.compute_decomposition_based_on_orbits" << endl;
        }
        AG.compute_decomposition_based_on_orbits(PA->P,
                    Sch1, Sch2,
                    Inc, Stack, 0 /*verbose_level*/);
        if (f_v) {
            cout << "projective_space_with_action::report_decomposition_by_group after AG.compute_decomposition_based_on_orbits" << endl;
        }
 
 
        int f_print_subscripts = FALSE;
        ost << "Decomposition based on orbits:\\\\" << endl;
        ost << "Row scheme:\\\\" << endl;
        Inc->get_and_print_row_tactical_decomposition_scheme_tex(
            ost, TRUE /* f_enter_math */,
            f_print_subscripts, *Stack);
        ost << "Column scheme:\\\\" << endl;
        Inc->get_and_print_column_tactical_decomposition_scheme_tex(
            ost, TRUE /* f_enter_math */,
            f_print_subscripts, *Stack);
 
 
 
        FREE_OBJECT(Inc);
        FREE_OBJECT(Stack);
    }
 
 
 
    FREE_OBJECT(Sch1);
    FREE_OBJECT(Sch2);
 
 
    if (f_v) {
        cout << "projective_space_with_action::report_decomposition_by_group done" << endl;
    }
 
}
 
void top_level_geometry_global::report_decomposition_by_single_automorphism(
        projective_geometry::projective_space_with_action *PA,
        int *Elt, std::ostream &ost, std::string &fname_base,
        int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism" << endl;
    }
 
#if 0
    if (P->n != 3) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism P->n != 3" << endl;
        exit(1);
    }
#endif
    //projective_space *P3;
    int order;
 
    ring_theory::longinteger_object full_group_order;
    order = PA->A->element_order(Elt);
 
    full_group_order.create(order, __FILE__, __LINE__);
 
    //P3 = P;
 
    //ost << "Fixed Objects:\\\\" << endl;
 
 
#if 0
    ost << "The group generated by the element" << endl;
    ost << "$$" << endl;
    A->element_print_latex(Elt, ost);
    ost << "$$" << endl;
    ost << "has the following orbits:\\\\" << endl;
 
    ost << "Orbits on points:\\\\" << endl;
#endif
 
    groups::schreier *Sch1;
    groups::schreier *Sch2;
    geometry::incidence_structure *Inc;
    data_structures::partitionstack *Stack;
    data_structures::partitionstack S1;
    data_structures::partitionstack S2;
 
    Sch1 = NEW_OBJECT(groups::schreier);
    Sch2 = NEW_OBJECT(groups::schreier);
 
    PA->A->all_point_orbits_from_single_generator(*Sch1,
            Elt,
            0 /*verbose_level*/);
 
    //ost << "Orbits on lines:\\\\" << endl;
 
    Sch2 = NEW_OBJECT(groups::schreier);
    PA->A_on_lines->all_point_orbits_from_single_generator(*Sch2,
            Elt,
            0 /*verbose_level*/);
    //Sch->print_orbit_lengths_tex(ost);
 
 
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "before incidence_and_stack_for_type_ij" << endl;
    }
    PA->P->incidence_and_stack_for_type_ij(
        1 /* row_type */, 2 /* col_type */,
        Inc,
        Stack,
        0 /*verbose_level*/);
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "after incidence_and_stack_for_type_ij" << endl;
    }
 
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "before S1.allocate" << endl;
    }
    S1.allocate(PA->A->degree, 0 /* verbose_level */);
    S2.allocate(PA->A_on_lines->degree, 0 /* verbose_level */);
 
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "before Sch1->get_orbit_partition" << endl;
    }
    Sch1->get_orbit_partition(S1, 0 /*verbose_level*/);
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "before Sch2->get_orbit_partition" << endl;
    }
    Sch2->get_orbit_partition(S2, 0 /*verbose_level*/);
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                "after Sch2->get_orbit_partition" << endl;
    }
    int i, j, sz;
 
    for (i = 1; i < S1.ht; i++) {
        if (f_v) {
            cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                    "before Stack->split_cell (S1) i=" << i << endl;
        }
        Stack->split_cell(
                S1.pointList + S1.startCell[i],
                S1.cellSize[i], verbose_level);
    }
    int *set;
    set = NEW_int(PA->A_on_lines->degree);
    for (i = 1; i < S2.ht; i++) {
        sz = S2.cellSize[i];
        Int_vec_copy(S2.pointList + S2.startCell[i], set, sz);
        for (j = 0; j < sz; j++) {
            set[j] += PA->A->degree;
        }
        if (f_v) {
            cout << "top_level_geometry_global::report_decomposition_by_single_automorphism "
                    "before Stack->split_cell (S2) i=" << i << endl;
        }
        Stack->split_cell(set, sz, 0 /*verbose_level*/);
    }
    FREE_int(set);
 
 
    ost << "Considering the cyclic group generated by" << endl;
    ost << "$$" << endl;
    PA->A->element_print_latex(Elt, ost);
    ost << "$$" << endl;
 
    if (Sch1->nb_orbits == 1 && Sch2->nb_orbits == 1) {
        ost << "The group is transitive on points and on lines.\\\\" << endl;
        std::vector<int> Orb1;
        std::vector<int> Orb2;
        Sch1->get_orbit_in_order(Orb1, 0 /* orbit_idx */, verbose_level);
        Sch2->get_orbit_in_order(Orb2, 0 /* orbit_idx */, verbose_level);
 
        int *Inc;
        orbiter_kernel_system::file_io Fio;
        string fname;
 
        fname.assign(fname_base);
        fname.append("_incma_cyclic.csv");
 
        PA->P->make_incidence_matrix(Orb1, Orb2, Inc, verbose_level);
 
        Fio.int_matrix_write_csv(fname, Inc, Orb1.size(), Orb2.size());
 
        FREE_int(Inc);
 
        int p;
        for (p = 2; p < Orb1.size(); p++) {
 
            if ((Orb1.size() % p) == 0) {
 
                cout << "considering subgroup of index " << p << endl;
 
                int *v, *w;
                std::vector<int> Orb1_subgroup;
                std::vector<int> Orb2_subgroup;
                combinatorics::combinatorics_domain Combi;
 
                v = NEW_int(Orb1.size());
                w = NEW_int(Orb1.size());
                for (i = 0; i < Orb1.size(); i++) {
                    v[i] = Orb1[i];
                }
                Combi.int_vec_splice(v, w, Orb1.size(), p);
                for (i = 0; i < Orb1.size(); i++) {
                    Orb1_subgroup.push_back(w[i]);
 
                }
 
                for (i = 0; i < Orb1.size(); i++) {
                    v[i] = Orb2[i];
                }
                Combi.int_vec_splice(v, w, Orb1.size(), p);
                for (i = 0; i < Orb1.size(); i++) {
                    Orb2_subgroup.push_back(w[i]);
 
                }
                FREE_int(v);
                FREE_int(w);
 
                fname.assign(fname_base);
                fname.append("_incma_subgroup");
                char str[1000];
 
                sprintf(str, "_index_%d.csv", p);
                fname.append(str);
 
                PA->P->make_incidence_matrix(Orb1_subgroup, Orb2_subgroup, Inc, verbose_level);
 
                Fio.int_matrix_write_csv(fname, Inc, Orb1.size(), Orb2.size());
                FREE_int(Inc);
            }
        }
 
    }
 
 
 
    ost << "Orbits on points:\\\\" << endl;
    Sch1->print_orbit_lengths_tex(ost);
 
    ost << "Orbits on lines:\\\\" << endl;
    Sch2->print_orbit_lengths_tex(ost);
 
    ost << "Fixed points:\\\\" << endl;
    Sch1->print_fixed_points_tex(ost);
 
    ost << "Fixed lines:\\\\" << endl;
    Sch2->print_fixed_points_tex(ost);
 
 
    if (PA->f_has_action_on_planes) {
        groups::schreier *Sch3;
        Sch3 = NEW_OBJECT(groups::schreier);
        PA->A_on_planes->all_point_orbits_from_single_generator(*Sch3,
                Elt,
                0 /*verbose_level*/);
        ost << "Fixed planes:\\\\" << endl;
        Sch3->print_fixed_points_tex(ost);
 
        FREE_OBJECT(Sch3);
    }
 
 
    int f_print_subscripts = FALSE;
    ost << "Row scheme:\\\\" << endl;
    Inc->get_and_print_row_tactical_decomposition_scheme_tex(
        ost, TRUE /* f_enter_math */,
        f_print_subscripts, *Stack);
    ost << "Column scheme:\\\\" << endl;
    Inc->get_and_print_column_tactical_decomposition_scheme_tex(
        ost, TRUE /* f_enter_math */,
        f_print_subscripts, *Stack);
 
 
 
    FREE_OBJECT(Sch1);
    FREE_OBJECT(Sch2);
    FREE_OBJECT(Inc);
    FREE_OBJECT(Stack);
 
    if (f_v) {
        cout << "top_level_geometry_global::report_decomposition_by_single_automorphism done" << endl;
    }
}
 
 
}}}