surfaces_and_double_sixes.h

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/*
 * surfaces_and_double_sixes.h
 *
 *  Created on: Jun 26, 2021
 *      Author: betten
 */
 
#ifndef SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_AND_DOUBLE_SIXES_SURFACES_AND_DOUBLE_SIXES_H_
#define SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_AND_DOUBLE_SIXES_SURFACES_AND_DOUBLE_SIXES_H_
 
 
namespace orbiter {
namespace layer5_applications {
namespace applications_in_algebraic_geometry {
namespace cubic_surfaces_and_double_sixes {
 
 
 
// #############################################################################
// classification_of_cubic_surfaces_with_double_sixes_activity_description.cpp
// #############################################################################
 
 
 
class classification_of_cubic_surfaces_with_double_sixes_activity_description {
public:
 
    int f_report;
    poset_classification::poset_classification_report_options *report_options;
 
    int f_identify_Eckardt;
 
    int f_identify_F13;
 
    int f_identify_Bes;
 
    int f_identify_general_abcd;
 
    int f_isomorphism_testing;
    cubic_surfaces_in_general::surface_create_description *isomorphism_testing_surface1;
    cubic_surfaces_in_general::surface_create_description *isomorphism_testing_surface2;
 
    int f_recognize;
    cubic_surfaces_in_general::surface_create_description *recognize_surface;
 
    int f_create_source_code;
 
    int f_sweep;
 
 
    classification_of_cubic_surfaces_with_double_sixes_activity_description();
    ~classification_of_cubic_surfaces_with_double_sixes_activity_description();
    int read_arguments(
        int argc, std::string *argv,
        int verbose_level);
    void print();
 
 
};
 
// #############################################################################
// classification_of_cubic_surfaces_with_double_sixes_activity.cpp
// #############################################################################
 
 
 
class classification_of_cubic_surfaces_with_double_sixes_activity {
public:
 
    classification_of_cubic_surfaces_with_double_sixes_activity_description *Descr;
    surface_classify_wedge *SCW;
 
    classification_of_cubic_surfaces_with_double_sixes_activity();
    ~classification_of_cubic_surfaces_with_double_sixes_activity();
    void init(
            classification_of_cubic_surfaces_with_double_sixes_activity_description *Descr,
            surface_classify_wedge *SCW,
            int verbose_level);
    void perform_activity(int verbose_level);
    void report(
            poset_classification::poset_classification_report_options *report_options,
            int verbose_level);
    void do_surface_identify_Eckardt(int verbose_level);
    void do_surface_identify_F13(int verbose_level);
    void do_surface_identify_Bes(int verbose_level);
    void do_surface_identify_general_abcd(int verbose_level);
    void do_surface_isomorphism_testing(
            cubic_surfaces_in_general::surface_create_description *surface_descr_isomorph1,
            cubic_surfaces_in_general::surface_create_description *surface_descr_isomorph2,
            int verbose_level);
    void do_recognize(
            cubic_surfaces_in_general::surface_create_description *surface_descr,
            int verbose_level);
    void do_write_source_code(int verbose_level);
    void do_sweep(
            int verbose_level);
 
 
};
 
 
// #############################################################################
// classify_double_sixes.cpp
// #############################################################################
 
 
 
class classify_double_sixes {
 
public:
 
    int q;
    field_theory::finite_field *F;
    actions::action *A;
 
    //linear_group *LG;
 
    cubic_surfaces_in_general::surface_with_action *Surf_A;
    algebraic_geometry::surface_domain *Surf;
 
 
    // pulled from surface_classify_wedge:
 
    actions::action *A2; // the action on the wedge product
    induced_actions::action_on_wedge_product *AW;
        // internal data structure for the wedge action
 
    int *Elt0; // used in identify_five_plus_one
    int *Elt1; // used in identify_five_plus_one
    int *Elt2; // used in upstep
    int *Elt3; // used in upstep
    int *Elt4; // used in upstep
 
    groups::strong_generators *SG_line_stab;
        // stabilizer of the special line in PGL(4,q)
        // this group acts on the set Neighbors[] in the wedge action
 
    int l_min;
    int short_orbit_idx;
 
    int nb_neighbors;
        // = (q + 1) * q * (q + 1)
 
    long int *Neighbors; // [nb_neighbors]
        // The lines which intersect the special line.
        // In wedge ranks.
        // The array Neighbors is sorted.
 
    long int *Neighbor_to_line; // [nb_neighbors]
        // The lines which intersect the special line.
        // In grassmann (i.e., line) ranks.
    long int *Neighbor_to_klein; // [nb_neighbors]
        // In orthogonal ranks (i.e., points on the Klein quadric).
 
    //long int *Line_to_neighbor; // [Surf->nb_lines_PG_3]
 
    ring_theory::longinteger_object go, stab_go;
    groups::sims *Stab;
    groups::strong_generators *stab_gens;
 
    int *orbit;
    int orbit_len;
 
    long int pt0_idx_in_orbit;
    long int pt0_wedge;
    long int pt0_line;
    long int pt0_klein;
 
 
    int Basis[8];
    int *line_to_orbit; // [nb_lines_PG_3]
    long int *orbit_to_line; // [nb_lines_PG_3]
 
    long int *Pts_klein;
    long int *Pts_wedge;
    int nb_pts;
 
    long int *Pts_wedge_to_line; // [nb_pts]
    long int *line_to_pts_wedge; // [nb_lines_PG_3]
 
    actions::action *A_on_neighbors;
        // restricted action A2 on the set Neighbors[]
 
    poset_classification::poset_classification_control *Control;
    poset_classification::poset_with_group_action *Poset;
    poset_classification::poset_classification *Five_plus_one;
        // orbits on five-plus-one configurations
 
 
    int *u, *v, *w; // temporary vectors of length 6
    int *u1, *v1; // temporary vectors of length 6
 
    int len;
        // = gen->nb_orbits_at_level(5)
        // = number of orbits on 5-sets of lines
    int *Idx;
        // Idx[nb], list of orbits
        // for which the rank of the system is equal to 19
    int nb; // number of good orbits
    int *Po;
        // Po[Flag_orbits->nb_flag_orbits],
        //list of orbits for which a double six exists
 
    int *Pts_for_partial_ovoid_test; // [5*6]
 
 
    invariant_relations::flag_orbits *Flag_orbits;
 
    invariant_relations::classification_step *Double_sixes;
 
 
    classify_double_sixes();
    ~classify_double_sixes();
    void null();
    void freeself();
    void init(cubic_surfaces_in_general::surface_with_action *Surf_A,
            poset_classification::poset_classification_control *Control,
            int verbose_level);
    void compute_neighbors(int verbose_level);
    void make_spreadsheet_of_neighbors(data_structures::spreadsheet *&Sp,
        int verbose_level);
    void classify_partial_ovoids(
        int verbose_level);
    void report(std::ostream &ost,
            graphics::layered_graph_draw_options *draw_options,
            poset_classification::poset_classification_report_options *Opt,
            int verbose_level);
    void partial_ovoid_test_early(long int *S, int len,
        long int *candidates, int nb_candidates,
        long int *good_candidates, int &nb_good_candidates,
        int verbose_level);
    void test_orbits(int verbose_level);
    void make_spreadsheet_of_fiveplusone_configurations(
            data_structures::spreadsheet *&Sp,
        int verbose_level);
    void identify_five_plus_one(long int *five_lines, long int transversal_line,
        long int *five_lines_out_as_neighbors, int &orbit_index,
        int *transporter, int verbose_level);
    void classify(int verbose_level);
    void downstep(int verbose_level);
    void upstep(int verbose_level);
    void print_five_plus_ones(std::ostream &ost);
    void identify_double_six(long int *double_six,
        int *transporter, int &orbit_index, int verbose_level);
    void write_file(std::ofstream &fp, int verbose_level);
    void read_file(std::ifstream &fp, int verbose_level);
    int line_to_neighbor(long int line_rk, int verbose_level);
};
 
 
 
// #############################################################################
// surface_classify_wedge.cpp
// #############################################################################
 
 
 
class surface_classify_wedge {
public:
    field_theory::finite_field *F;
    int q;
 
    std::string fname_base;
 
    actions::action *A; // the action of PGL(4,q) on points
    actions::action *A2; // the action on the wedge product
 
    algebraic_geometry::surface_domain *Surf;
    cubic_surfaces_in_general::surface_with_action *Surf_A;
 
    int *Elt0;
    int *Elt1;
    int *Elt2;
    int *Elt3;
 
    classify_double_sixes *Classify_double_sixes;
 
    // classification of surfaces:
    invariant_relations::flag_orbits *Flag_orbits;
 
    invariant_relations::classification_step *Surfaces;
 
 
 
    surface_classify_wedge();
    ~surface_classify_wedge();
    void null();
    void freeself();
    void init(
            cubic_surfaces_in_general::surface_with_action *Surf_A,
        poset_classification::poset_classification_control *Control,
        int verbose_level);
    void do_classify_double_sixes(int verbose_level);
    void do_classify_surfaces(int verbose_level);
    void classify_surfaces_from_double_sixes(int verbose_level);
    void downstep(int verbose_level);
    void upstep(int verbose_level);
    void derived_arcs(int verbose_level);
    void starter_configurations_which_are_involved(int iso_type,
        int *&Starter_configuration_idx, int &nb_starter_conf, int verbose_level);
    void write_file(std::ofstream &fp, int verbose_level);
    void read_file(std::ifstream &fp, int verbose_level);
 
    void identify_Eckardt_and_print_table(int verbose_level);
    void identify_F13_and_print_table(int verbose_level);
    void identify_Bes_and_print_table(int verbose_level);
    void identify_Eckardt(int *Iso_type, int *Nb_lines, int verbose_level);
    void identify_F13(
        int *Iso_type, int *Nb_lines, int verbose_level);
    void identify_Bes(
        int *Iso_type, int *Nb_lines, int verbose_level);
    int isomorphism_test_pairwise(
            cubic_surfaces_in_general::surface_create *SC1,
            cubic_surfaces_in_general::surface_create *SC2,
        int &isomorphic_to1, int &isomorphic_to2,
        int *Elt_isomorphism_1to2,
        int verbose_level);
    void identify_surface(int *coeff_of_given_surface,
        int &isomorphic_to, int *Elt_isomorphism,
        int verbose_level);
    void latex_surfaces(std::ostream &ost, int f_with_stabilizers, int verbose_level);
    void report_surface(std::ostream &ost, int orbit_index, int verbose_level);
    void generate_source_code(int verbose_level);
        // no longer produces nb_E[] and single_six[]
    void generate_history(int verbose_level);
    int test_if_surfaces_have_been_computed_already();
    void write_surfaces(int verbose_level);
    void read_surfaces(int verbose_level);
    int test_if_double_sixes_have_been_computed_already();
    void write_double_sixes(int verbose_level);
    void read_double_sixes(int verbose_level);
    void create_report(int f_with_stabilizers,
            graphics::layered_graph_draw_options *draw_options,
            poset_classification::poset_classification_report_options *Opt,
            int verbose_level);
    void report(std::ostream &ost, int f_with_stabilizers,
            graphics::layered_graph_draw_options *draw_options,
            poset_classification::poset_classification_report_options *Opt,
            int verbose_level);
    void create_report_double_sixes(int verbose_level);
    void test_isomorphism(
            cubic_surfaces_in_general::surface_create_description *Descr1,
            cubic_surfaces_in_general::surface_create_description *Descr2,
            int verbose_level);
    void recognition(
            cubic_surfaces_in_general::surface_create_description *Descr,
            int verbose_level);
    void sweep_Cayley(int verbose_level);
    void identify_general_abcd(
        int *Iso_type, int *Nb_lines, int verbose_level);
    void identify_general_abcd_and_print_table(int verbose_level);
 
};
 
 
}}}}
 
 
 
 
 
#endif /* SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_AND_DOUBLE_SIXES_SURFACES_AND_DOUBLE_SIXES_H_ */