surfaces_general.h

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/*
 * surfaces_general.h
 *
 *  Created on: Jun 26, 2021
 *      Author: betten
 */
 
#ifndef SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_GENERAL_SURFACES_GENERAL_H_
#define SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_GENERAL_SURFACES_GENERAL_H_
 
 
 
namespace orbiter {
namespace layer5_applications {
namespace applications_in_algebraic_geometry {
namespace cubic_surfaces_in_general {
 
 
// #############################################################################
// cubic_surface_activity_description.cpp
// #############################################################################
 
 
 
class cubic_surface_activity_description {
public:
 
    int f_report;
 
    int f_report_with_group;
 
    int f_export_points;
 
    int f_clebsch;
 
    int f_codes;
 
    int f_all_quartic_curves;
 
    int f_export_all_quartic_curves;
 
    int f_export_tritangent_planes;
 
    cubic_surface_activity_description();
    ~cubic_surface_activity_description();
    int read_arguments(
        int argc, std::string *argv,
        int verbose_level);
    void print();
 
};
 
// #############################################################################
// cubic_surface_activity.cpp
// #############################################################################
 
 
 
class cubic_surface_activity {
public:
 
    cubic_surface_activity_description *Descr;
    surface_create *SC;
 
 
    cubic_surface_activity();
    ~cubic_surface_activity();
    void init(
            cubic_surfaces_in_general::cubic_surface_activity_description *Cubic_surface_activity_description,
            surface_create *SC, int verbose_level);
    void perform_activity(int verbose_level);
};
 
 
 
 
// #############################################################################
// surface_clebsch_map.cpp
// #############################################################################
 
 
 
class surface_clebsch_map {
public:
 
    surface_object_with_action *SOA;
 
    int orbit_idx;
    int f, l, hds;
 
    algebraic_geometry::clebsch_map *Clebsch_map;
 
 
    surface_clebsch_map();
    ~surface_clebsch_map();
    void report(std::ostream &ost, int verbose_level);
    void init(surface_object_with_action *SOA, int orbit_idx, int verbose_level);
 
};
 
 
// #############################################################################
// surface_create.cpp
// #############################################################################
 
 
 
 
class surface_create {
 
public:
    surface_create_description *Descr;
 
    std::string prefix;
    std::string label_txt;
    std::string label_tex;
 
    int f_ownership;
 
    int q;
    field_theory::finite_field *F;
 
    int f_semilinear;
 
    algebraic_geometry::surface_domain *Surf;
 
    surface_with_action *Surf_A;
 
    algebraic_geometry::surface_object *SO;
 
    int f_has_group;
    groups::strong_generators *Sg;
    int f_has_nice_gens;
    data_structures_groups::vector_ge *nice_gens;
 
 
 
 
    surface_create();
    ~surface_create();
    void null();
    void freeself();
    void init_with_data(surface_create_description *Descr,
        surface_with_action *Surf_A,
        int verbose_level);
    void init(surface_create_description *Descr,
        surface_with_action *Surf_A,
        int verbose_level);
    void create_surface_from_description(int verbose_level);
    void override_group(std::string &group_order_text,
            int nb_gens, std::string &gens_text, int verbose_level);
    void create_Eckardt_surface(int a, int b, int verbose_level);
    void create_surface_G13(int a, int verbose_level);
    void create_surface_F13(int a, int verbose_level);
    void create_surface_bes(int a, int c, int verbose_level);
    void create_surface_general_abcd(int a, int b, int c, int d, int verbose_level);
    void create_surface_by_coefficients(std::string &coefficients_text,
            std::vector<std::string> &select_double_six_string,
            int verbose_level);
    void create_surface_by_coefficient_vector(int *coeffs20,
            std::vector<std::string> &select_double_six_string,
            int verbose_level);
    void create_surface_by_rank(std::string &rank_text, int defining_q,
            std::vector<std::string> &select_double_six_string,
            int verbose_level);
    void create_surface_from_catalogue(int iso,
            std::vector<std::string> &select_double_six_string,
            int verbose_level);
    void create_surface_by_arc_lifting(
            std::string &arc_lifting_text,
            int verbose_level);
    void create_surface_by_arc_lifting_with_two_lines(
            std::string &arc_lifting_text,
            std::string &arc_lifting_two_lines_text,
            int verbose_level);
    void create_surface_Cayley_form(
            int k, int l, int m, int n,
            int verbose_level);
    void create_surface_by_equation(
            std::string &name_of_formula,
            std::string &name_of_formula_tex,
            std::string &managed_variables,
            std::string &equation_text,
            std::string &equation_parameters,
            std::string &equation_parameters_tex,
            std::vector<std::string> &select_double_six_string,
            int verbose_level);
    void create_surface_by_double_six(
            std::string &by_double_six_label,
            std::string &by_double_six_label_tex,
            std::string &by_double_six_text,
            int verbose_level);
    void create_surface_by_skew_hexagon(
            std::string &given_label,
            std::string &given_label_tex,
            int verbose_level);
    void apply_transformations(
        std::vector<std::string> &transform_coeffs,
        std::vector<int> &f_inverse_transform,
        int verbose_level);
    void compute_group(
            projective_geometry::projective_space_with_action *PA,
            int verbose_level);
 
};
 
 
// #############################################################################
// surface_create_description.cpp
// #############################################################################
 
 
 
 
 
class surface_create_description {
 
public:
 
    int f_q;
    int q;
 
    int f_label_txt;
    std::string label_txt;
 
    int f_label_tex;
    std::string label_tex;
 
    int f_label_for_summary;
    std::string label_for_summary;
 
    int f_catalogue;
    int iso;
    int f_by_coefficients;
    std::string coefficients_text;
 
    int f_by_rank;
    std::string rank_text;
    int rank_defining_q;
 
    int f_family_Eckardt;
    int family_Eckardt_a;
    int family_Eckardt_b;
 
    int f_family_G13;
    int family_G13_a;
 
    int f_family_F13;
    int family_F13_a;
 
    int f_family_bes;
    int family_bes_a;
    int family_bes_c;
 
    int f_family_general_abcd;
    int family_general_abcd_a;
    int family_general_abcd_b;
    int family_general_abcd_c;
    int family_general_abcd_d;
 
    int f_arc_lifting;
    std::string arc_lifting_text;
    std::string arc_lifting_two_lines_text;
 
    int f_arc_lifting_with_two_lines;
    std::vector<std::string> select_double_six_string;
 
    int f_Cayley_form;
    int Cayley_form_k;
    int Cayley_form_l;
    int Cayley_form_m;
    int Cayley_form_n;
 
 
    int f_by_equation;
    std::string equation_name_of_formula;
    std::string equation_name_of_formula_tex;
    std::string equation_managed_variables;
    std::string equation_text;
    std::string equation_parameters;
    std::string equation_parameters_tex;
 
 
    int f_by_double_six;
    std::string by_double_six_label;
    std::string by_double_six_label_tex;
    std::string by_double_six_text;
 
    int f_by_skew_hexagon;
    std::string by_skew_hexagon_label;
    std::string by_skew_hexagon_label_tex;
 
    int f_override_group;
    std::string override_group_order;
    int override_group_nb_gens;
    std::string override_group_gens;
 
    std::vector<std::string> transform_coeffs;
    std::vector<int> f_inverse_transform;
 
 
 
    surface_create_description();
    ~surface_create_description();
    void null();
    void freeself();
    int read_arguments(int argc, std::string *argv,
        int verbose_level);
    void print();
    int get_q();
};
 
 
// #############################################################################
// surface_domain_high_level.cpp
// #############################################################################
 
 
 
 
class surface_domain_high_level {
 
public:
 
 
    surface_domain_high_level();
    ~surface_domain_high_level();
 
    void do_sweep_4_15_lines(
            projective_geometry::projective_space_with_action *PA,
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void do_sweep_F_beta_9_lines(
            projective_geometry::projective_space_with_action *PA,
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void do_sweep_6_9_lines(
            projective_geometry::projective_space_with_action *PA,
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void do_sweep_4_27(
            projective_geometry::projective_space_with_action *PA,
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
 
 
    void classify_surfaces_with_double_sixes(
            projective_geometry::projective_space_with_action *PA,
            poset_classification::poset_classification_control *Control,
            cubic_surfaces_and_double_sixes::surface_classify_wedge *&SCW,
            int verbose_level);
    void prepare_surface_classify_wedge(
            field_theory::finite_field *F,
            projective_geometry::projective_space_with_action *PA,
            poset_classification::poset_classification_control *Control,
            algebraic_geometry::surface_domain *&Surf, surface_with_action *&Surf_A,
            cubic_surfaces_and_double_sixes::surface_classify_wedge *&SCW,
            int verbose_level);
    void do_study_surface(field_theory::finite_field *F, int nb, int verbose_level);
    void do_classify_surfaces_through_arcs_and_two_lines(
            projective_geometry::projective_space_with_action *PA,
            poset_classification::poset_classification_control *Control_six_arcs,
            int f_test_nb_Eckardt_points, int nb_E,
            int verbose_level);
    void do_classify_surfaces_through_arcs_and_trihedral_pairs(
            projective_geometry::projective_space_with_action *PA,
            poset_classification::poset_classification_control *Control1,
            poset_classification::poset_classification_control *Control2,
            poset_classification::poset_classification_control *Control_six_arcs,
            int f_test_nb_Eckardt_points, int nb_E,
            int verbose_level);
    void do_six_arcs(
            projective_geometry::projective_space_with_action *PA,
            poset_classification::poset_classification_control *Control_six_arcs,
            int f_filter_by_nb_Eckardt_points, int nb_Eckardt_points,
            int verbose_level);
    void do_cubic_surface_properties(
            projective_geometry::projective_space_with_action *PA,
            std::string &fname_csv, int defining_q,
            int column_offset,
            int verbose_level);
    void do_cubic_surface_properties_analyze(
            projective_geometry::projective_space_with_action *PA,
            std::string &fname_csv, int defining_q,
            int verbose_level);
    void report_singular_surfaces(std::ostream &ost,
            struct cubic_surface_data_set *Data, int nb_orbits, int verbose_level);
    void report_non_singular_surfaces(std::ostream &ost,
            struct cubic_surface_data_set *Data, int nb_orbits, int verbose_level);
    void report_surfaces_by_lines(std::ostream &ost,
            struct cubic_surface_data_set *Data, data_structures::tally &T, int verbose_level);
    void do_create_surface_reports(std::string &field_orders_text, int verbose_level);
    void do_create_surface_atlas(int q_max, int verbose_level);
    void do_create_surface_atlas_q_e(int q_max,
            struct table_surfaces_field_order *T, int nb_e, int *Idx, int nb,
            std::string &fname_report_tex,
            int verbose_level);
    void do_create_dickson_atlas(int verbose_level);
    void make_fname_surface_report_tex(std::string &fname, int q, int ocn);
    void make_fname_surface_report_pdf(std::string &fname, int q, int ocn);
 
};
 
 
// #############################################################################
// surface_object_with_action.cpp
// #############################################################################
 
 
 
 
class surface_object_with_action {
 
public:
 
    int q;
    field_theory::finite_field *F; // do not free
 
    algebraic_geometry::surface_domain *Surf; // do not free
    surface_with_action *Surf_A; // do not free
 
    algebraic_geometry::surface_object *SO; // do not free
    groups::strong_generators *Aut_gens;
        // generators for the automorphism group
 
    int f_has_nice_gens;
    data_structures_groups::vector_ge *nice_gens;
 
    groups::strong_generators *projectivity_group_gens;
    groups::sylow_structure *Syl;
 
    actions::action *A_on_points;
    actions::action *A_on_Eckardt_points;
    actions::action *A_on_Double_points;
    actions::action *A_on_the_lines;
    actions::action *A_single_sixes;
    actions::action *A_on_tritangent_planes;
    actions::action *A_on_Hesse_planes;
    actions::action *A_on_trihedral_pairs;
    actions::action *A_on_pts_not_on_lines;
 
 
    groups::schreier *Orbits_on_points;
    groups::schreier *Orbits_on_Eckardt_points;
    groups::schreier *Orbits_on_Double_points;
    groups::schreier *Orbits_on_lines;
    groups::schreier *Orbits_on_single_sixes;
    groups::schreier *Orbits_on_tritangent_planes;
    groups::schreier *Orbits_on_Hesse_planes;
    groups::schreier *Orbits_on_trihedral_pairs;
    groups::schreier *Orbits_on_points_not_on_lines;
 
 
 
    surface_object_with_action();
    ~surface_object_with_action();
    void null();
    void freeself();
    void init_equation(surface_with_action *Surf_A, int *eqn,
            groups::strong_generators *Aut_gens, int verbose_level);
    void init_with_group(surface_with_action *Surf_A,
        long int *Lines, int nb_lines, int *eqn,
        groups::strong_generators *Aut_gens,
        int f_find_double_six_and_rearrange_lines,
        int f_has_nice_gens,
        data_structures_groups::vector_ge *nice_gens,
        int verbose_level);
    void init_with_surface_object(surface_with_action *Surf_A,
            algebraic_geometry::surface_object *SO,
            groups::strong_generators *Aut_gens,
            int f_has_nice_gens,
            data_structures_groups::vector_ge *nice_gens,
            int verbose_level);
    void init_surface_object(surface_with_action *Surf_A,
            algebraic_geometry::surface_object *SO,
            groups::strong_generators *Aut_gens, int verbose_level);
    void compute_projectivity_group(int verbose_level);
    void compute_orbits_of_automorphism_group(int verbose_level);
    void init_orbits_on_points(int verbose_level);
    void init_orbits_on_Eckardt_points(int verbose_level);
    void init_orbits_on_Double_points(int verbose_level);
    void init_orbits_on_lines(int verbose_level);
    void init_orbits_on_half_double_sixes(int verbose_level);
    void init_orbits_on_tritangent_planes(int verbose_level);
    void init_orbits_on_Hesse_planes(int verbose_level);
    void init_orbits_on_trihedral_pairs(int verbose_level);
    void init_orbits_on_points_not_on_lines(int verbose_level);
    void print_generators_on_lines(
            std::ostream &ost,
            groups::strong_generators *Aut_gens,
            int verbose_level);
    void print_elements_on_lines(
            std::ostream &ost,
            groups::strong_generators *Aut_gens,
            int verbose_level);
    void print_automorphism_group(std::ostream &ost,
        int f_print_orbits, std::string &fname_mask,
        graphics::layered_graph_draw_options *Opt,
        int verbose_level);
    void cheat_sheet_basic(std::ostream &ost, int verbose_level);
    void cheat_sheet(std::ostream &ost,
            std::string &label_txt,
            std::string &label_tex,
            int f_print_orbits, std::string &fname_mask,
            graphics::layered_graph_draw_options *Opt,
            int verbose_level);
    void print_automorphism_group_gnerators(std::ostream &ost, int verbose_level);
    void investigate_surface_and_write_report(
            graphics::layered_graph_draw_options *Opt,
            actions::action *A,
            surface_create *SC,
            cubic_surfaces_and_arcs::six_arcs_not_on_a_conic *Six_arcs,
            int verbose_level);
    void investigate_surface_and_write_report2(
            std::ostream &ost,
            graphics::layered_graph_draw_options *Opt,
            actions::action *A,
            surface_create *SC,
            cubic_surfaces_and_arcs::six_arcs_not_on_a_conic *Six_arcs,
            std::string &fname_mask,
            std::string &label,
            std::string &label_tex,
            int verbose_level);
    void all_quartic_curves(
            std::string &surface_prefix,
            std::ostream &ost,
            std::ostream &ost_quartics,
            int verbose_level);
    void export_all_quartic_curves(
            std::string &surface_prefix,
            std::ostream &ost_quartics_csv,
            int verbose_level);
    void print_full_del_Pezzo(std::ostream &ost, int verbose_level);
};
 
// #############################################################################
// surface_study.cpp
// #############################################################################
 
 
class surface_study {
public:
    int q;
    int nb;
    int *rep;
    std::string prefix;
    field_theory::finite_field *F;
    algebraic_geometry::surface_domain *Surf;
 
    int nb_lines_PG_3;
 
    int *data;
    int nb_gens;
    int data_size;
    std::string stab_order;
 
    actions::action *A;
    actions::action *A2;
    groups::sims *S;
    long int *Lines;
    int *coeff;
 
    int f_semilinear;
 
    data_structures_groups::set_and_stabilizer *SaS;
 
 
    // line orbits:
    int *orbit_first;
    int *orbit_length;
    int *orbit;
    int nb_orbits;
 
 
    // orbit_on_lines:
    actions::action *A_on_lines;
    groups::schreier *Orb;
    int shortest_line_orbit_idx;
 
    // for study_find_eckardt_points:
    int *Adj;
    int *R;
    long int *Intersection_pt;
    long int *Double_pts;
    int nb_double_pts;
    long int *Eckardt_pts;
    int nb_Eckardt_pts;
 
 
    void init(field_theory::finite_field *F, int nb, int verbose_level);
    void study_intersection_points(int verbose_level);
    void study_line_orbits(int verbose_level);
    void study_group(int verbose_level);
    void study_orbits_on_lines(int verbose_level);
    void study_find_eckardt_points(int verbose_level);
    void study_surface_with_6_eckardt_points(int verbose_level);
};
 
 
 
 
 
// #############################################################################
// surface_with_action.cpp
// #############################################################################
 
 
 
 
class surface_with_action {
 
public:
 
 
    projective_geometry::projective_space_with_action *PA;
 
    int f_semilinear;
 
    algebraic_geometry::surface_domain *Surf; // do not free
 
    actions::action *A; // linear group PGGL(4,q)
 
    actions::action *A_wedge; // linear group PGGL(4,q)
 
 
    actions::action *A2; // linear group PGGL(4,q) acting on lines
    actions::action *A_on_planes; // linear group PGGL(4,q) acting on planes
 
    int *Elt1;
 
    induced_actions::action_on_homogeneous_polynomials *AonHPD_3_4;
 
 
    cubic_surfaces_and_arcs::classify_trihedral_pairs *Classify_trihedral_pairs;
 
    spreads::recoordinatize *Recoordinatize;
    long int *regulus; // [regulus_size]
    int regulus_size; // q + 1
 
 
    surface_with_action();
    ~surface_with_action();
    void null();
    void freeself();
    void init(algebraic_geometry::surface_domain *Surf,
            projective_geometry::projective_space_with_action *PA,
            int f_recoordinatize,
            int verbose_level);
    long int apply_null_polarity(
        long int a, int verbose_level);
    long int apply_polarity(
        long int a, int *Polarity36, int verbose_level);
    void complete_skew_hexagon(
        long int *skew_hexagon,
        std::vector<std::vector<long int> > &Double_sixes,
        int verbose_level);
    void complete_skew_hexagon_with_polarity(
            std::string &label_for_printing,
        long int *skew_hexagon,
        int *Polarity36,
        std::vector<std::vector<long int> > &Double_sixes,
        int verbose_level);
    void create_regulus_and_opposite_regulus(
        long int *three_skew_lines, long int *&regulus, long int *&opp_regulus, int &regulus_sz,
        int verbose_level);
    int create_double_six_safely(
        long int *five_lines, long int transversal_line,
        long int *double_six, int verbose_level);
    int create_double_six_from_five_lines_with_a_common_transversal(
        long int *five_lines, long int transversal_line,
        long int *double_six, int verbose_level);
    void report_basics(std::ostream &ost);
    void report_double_triplets(std::ostream &ost);
    void report_double_triplets_detailed(std::ostream &ost);
    void create_surface(
            surface_create_description *Surface_Descr,
            surface_create *&SC,
            int verbose_level);
    void create_surface_and_do_report(
            surface_create_description *Surface_Descr,
            int f_has_control_six_arcs,
            poset_classification::poset_classification_control *Control_six_arcs,
            int verbose_level);
    void test_group(
            surface_create *SC,
            int verbose_level);
    void report_with_group(
            surface_create *SC,
            int f_has_control_six_arcs,
            poset_classification::poset_classification_control *Control_six_arcs,
            int verbose_level);
    void create_surface_object_with_action(
            surface_create *SC,
            surface_object_with_action *&SoA,
            int verbose_level);
    void export_points(
            surface_create *SC,
            int verbose_level);
    void do_report(
            surface_create *SC,
            int verbose_level);
    void sweep_4_15_lines(
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void sweep_F_beta_9_lines(
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void sweep_6_9_lines(
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void sweep_4_27(
            surface_create_description *Surface_Descr,
            std::string &sweep_fname,
            int verbose_level);
    void table_of_cubic_surfaces(int verbose_level);
    void table_of_cubic_surfaces_export_csv(long int *Table,
            int nb_cols,
            int q, int nb_cubic_surfaces,
            surface_create **SC,
            int verbose_level);
    void table_of_cubic_surfaces_export_sql(long int *Table,
            int nb_cols,
            int q, int nb_cubic_surfaces,
            surface_create **SC,
            int verbose_level);
 
};
 
 
 
}}}}
 
 
 
 
 
#endif /* SRC_LIB_TOP_LEVEL_SURFACES_SURFACES_GENERAL_SURFACES_GENERAL_H_ */