projective_space.h

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/*
 * projective_space.h
 *
 *  Created on: Mar 28, 2021
 *      Author: betten
 */
 
#ifndef SRC_LIB_TOP_LEVEL_PROJECTIVE_SPACE_PROJECTIVE_SPACE_H_
#define SRC_LIB_TOP_LEVEL_PROJECTIVE_SPACE_PROJECTIVE_SPACE_H_
 
 
 
namespace orbiter {
namespace layer5_applications {
namespace projective_geometry {
 
 
 
// #############################################################################
// canonical_form_classifier_description.cpp
// #############################################################################
 
 
 
 
 
class canonical_form_classifier_description {
 
public:
 
    std::string fname_mask;
    int nb_files;
 
    int f_fname_base_out;
    std::string fname_base_out;
 
    int f_degree;
    int degree;
 
    int f_algorithm_nauty;
    int f_algorithm_substructure;
 
    int substructure_size;
 
    projective_space_with_action *PA;
 
    canonical_form_classifier *Canon_substructure;
 
 
 
    canonical_form_classifier_description();
    ~canonical_form_classifier_description();
};
 
 
// #############################################################################
// canonical_form_classifier.cpp
// #############################################################################
 
 
 
 
 
class canonical_form_classifier {
 
public:
 
    canonical_form_classifier_description *Descr;
 
 
    ring_theory::homogeneous_polynomial_domain *Poly_ring;
 
    induced_actions::action_on_homogeneous_polynomials *AonHPD;
 
    int nb_objects_to_test;
 
    // nauty stuff:
 
    data_structures::classify_bitvectors *CB;
    int canonical_labeling_len;
    long int *alpha;
    int *gamma;
 
    // substructure stuff:
 
 
    // needed once for the whole classification process:
    substructure_classifier *SubC;
 
 
    // needed once for each object:
    canonical_form_substructure **CFS_table; // [nb_objects_to_test]
 
 
 
    int *Elt;
    int *eqn2;
 
 
    int counter;
    int *Canonical_forms; // [nb_objects_to_test * Poly_ring->get_nb_monomials()]
    long int *Goi; // [nb_objects_to_test]
 
    data_structures::tally_vector_data *Classification_of_quartic_curves;
        // based on Canonical_forms, nb_objects_to_test
 
    // transversal of the isomorphism types:
    int *transversal;
    int *frequency;
    int nb_types; // number of isomorphism types
 
 
    canonical_form_classifier();
    ~canonical_form_classifier();
    void count_nb_objects_to_test(int verbose_level);
    void classify(canonical_form_classifier_description *Descr,
            int verbose_level);
    void classify_nauty(int verbose_level);
    void classify_with_substructure(int verbose_level);
    void main_loop(int verbose_level);
    void classify_curve_nauty(int cnt, int row,
            int *eqn,
            int sz,
            long int *pts,
            int nb_pts,
            long int *bitangents,
            int nb_bitangents,
            int *canonical_equation,
            int *transporter_to_canonical_form,
            int verbose_level);
    void write_canonical_forms_csv(
            std::string &fname_base,
            int verbose_level);
    void generate_source_code(
            std::string &fname_base,
            data_structures::tally_vector_data *Classification_of_quartic_curves,
            int verbose_level);
    void report(std::string &fname, int verbose_level);
    void report2(std::ostream &ost, std::string &fname_base, int verbose_level);
 
};
 
 
// #############################################################################
// canonical_form_nauty.cpp
// #############################################################################
 
 
 
 
 
class canonical_form_nauty {
 
public:
 
    int idx;
    int *eqn;
    int sz;
 
    long int *Pts_on_curve;
    int sz_curve;
 
    long int *bitangents;
    int nb_bitangents;
 
    int nb_rows, nb_cols;
    data_structures::bitvector *Canonical_form;
    long int *canonical_labeling;
    int canonical_labeling_len;
 
 
    groups::strong_generators *SG_pt_stab;
 
    orbit_of_equations *Orb;
 
    groups::strong_generators *Stab_gens_quartic;
 
 
    canonical_form_nauty();
    ~canonical_form_nauty();
    void quartic_curve(
            projective_space_with_action *PA,
            ring_theory::homogeneous_polynomial_domain *Poly4_x123,
            induced_actions::action_on_homogeneous_polynomials *AonHPD,
            int idx, int *eqn, int sz,
            long int *Pts_on_curve, int sz_curve,
            long int *bitangents, int nb_bitangents,
            int *canonical_equation,
            int *transporter_to_canonical_form,
            groups::strong_generators *&gens_stab_of_canonical_equation,
            int verbose_level);
 
};
 
 
 
// #############################################################################
// canonical_form_substructure.cpp
// #############################################################################
 
 
 
 
class canonical_form_substructure {
 
public:
 
    std::string fname_case_out;
 
    canonical_form_classifier *Canonical_form_classifier;
        // has substructure_classifier *SubC
 
 
    int cnt;
    int row;
    int counter;
    int *eqn;
    int sz;
    long int *pts;
    int nb_pts;
    long int *bitangents;
    int nb_bitangents;
 
    long int *canonical_pts;
 
 
    substructure_stats_and_selection *SubSt;
 
 
 
 
 
    compute_stabilizer *CS;
 
    groups::strong_generators *Gens_stabilizer_original_set;
    groups::strong_generators *Gens_stabilizer_canonical_form;
 
 
    orbit_of_equations *Orb;
 
    groups::strong_generators *gens_stab_of_canonical_equation;
 
    int *trans1;
    int *trans2;
    int *intermediate_equation;
 
 
 
    int *Elt;
    int *eqn2;
 
    int *canonical_equation;
    int *transporter_to_canonical_form;
 
 
    canonical_form_substructure();
    ~canonical_form_substructure();
    void classify_curve_with_substructure(
            canonical_form_classifier *Canonical_form_classifier,
            int counter, int cnt, int row,
            std::string &fname_case_out,
            int *eqn,
            int sz,
            long int *pts,
            int nb_pts,
            long int *bitangents,
            int nb_bitangents,
            ring_theory::longinteger_object &go_eqn,
            int verbose_level);
    void handle_orbit(
            int *transporter_to_canonical_form,
            groups::strong_generators *&Gens_stabilizer_original_set,
            groups::strong_generators *&Gens_stabilizer_canonical_form,
            int verbose_level);
 
 
};
 
 
 
// #############################################################################
// object_in_projective_space_with_action.cpp
// #############################################################################
 
 
 
 
 
class object_in_projective_space_with_action {
 
public:
 
    geometry::object_with_canonical_form *OwCF;
        // do not free
    groups::strong_generators *Aut_gens;
        // generators for the automorphism group
    long int ago;
    int nb_rows, nb_cols;
    int *canonical_labeling;
 
 
    object_in_projective_space_with_action();
    ~object_in_projective_space_with_action();
    void null();
    void freeself();
    void init(
            geometry::object_with_canonical_form *OwCF,
            long int ago,
            groups::strong_generators *Aut_gens,
            int *canonical_labeling,
            int verbose_level);
    void print();
    void report(std::ostream &fp,
            projective_space_with_action *PA, int max_TDO_depth, int verbose_level);
 
};
 
 
 
// #############################################################################
// projective_space_activity_description.cpp
// #############################################################################
 
 
 
class projective_space_activity_description {
public:
 
 
    int f_export_point_line_incidence_matrix;
 
    int f_table_of_cubic_surfaces_compute_properties;
    std::string table_of_cubic_surfaces_compute_fname_csv;
    int table_of_cubic_surfaces_compute_defining_q;
    int table_of_cubic_surfaces_compute_column_offset;
 
    int f_cubic_surface_properties_analyze;
    std::string cubic_surface_properties_fname_csv;
    int cubic_surface_properties_defining_q;
 
    int f_canonical_form_of_code;
    std::string canonical_form_of_code_label;
    std::string canonical_form_of_code_generator_matrix;
    combinatorics::classification_of_objects_description *Canonical_form_codes_Descr;
 
    int f_map;
    std::string map_label;
    std::string map_parameters;
 
    int f_analyze_del_Pezzo_surface;
    std::string analyze_del_Pezzo_surface_label;
    std::string analyze_del_Pezzo_surface_parameters;
 
    int f_cheat_sheet_for_decomposition_by_element_PG;
    int decomposition_by_element_power;
    std::string decomposition_by_element_data;
    std::string decomposition_by_element_fname;
 
    int f_decomposition_by_subgroup;
    std::string decomposition_by_subgroup_label;
    groups::linear_group_description * decomposition_by_subgroup_Descr;
 
 
    int f_define_object;
    std::string define_object_label;
    geometry::geometric_object_description *Object_Descr;
 
 
    int f_define_surface;
    std::string define_surface_label;
    applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *Surface_Descr;
 
    int f_table_of_quartic_curves;
        // based on knowledge_base
 
    int f_table_of_cubic_surfaces;
        // based on knowledge_base
 
    int f_define_quartic_curve;
    std::string define_quartic_curve_label;
    applications_in_algebraic_geometry::quartic_curves::quartic_curve_create_description *Quartic_curve_descr;
 
    int f_classify_surfaces_with_double_sixes;
    std::string classify_surfaces_with_double_sixes_label;
    poset_classification::poset_classification_control *classify_surfaces_with_double_sixes_control;
 
 
    int f_classify_surfaces_through_arcs_and_two_lines;
    int f_test_nb_Eckardt_points;
    int nb_E;
    int f_classify_surfaces_through_arcs_and_trihedral_pairs;
        int f_trihedra1_control;
        poset_classification::poset_classification_control *Trihedra1_control;
        int f_trihedra2_control;
        poset_classification::poset_classification_control *Trihedra2_control;
        int f_control_six_arcs;
        poset_classification::poset_classification_control *Control_six_arcs;
 
    int f_sweep;
    std::string sweep_fname;
 
    int f_sweep_4_15_lines;
    std::string sweep_4_15_lines_fname;
    applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *sweep_4_15_lines_surface_description;
 
    int f_sweep_F_beta_9_lines;
    std::string sweep_F_beta_9_lines_fname;
    applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *sweep_F_beta_9_lines_surface_description;
 
    int f_sweep_6_9_lines;
    std::string sweep_6_9_lines_fname;
    applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *sweep_6_9_lines_surface_description;
 
    int f_sweep_4_27;
    std::string sweep_4_27_fname;
    applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *sweep_4_27_surface_description;
 
    int f_six_arcs_not_on_conic;
    int f_filter_by_nb_Eckardt_points;
    int nb_Eckardt_points;
    int f_surface_quartic;
    int f_surface_clebsch;
    int f_surface_codes;
 
    int f_make_gilbert_varshamov_code;
    int make_gilbert_varshamov_code_n;
    int make_gilbert_varshamov_code_d;
 
 
    int f_spread_classify;
    int spread_classify_k;
    poset_classification::poset_classification_control *spread_classify_Control;
 
    int f_classify_semifields;
    semifields::semifield_classify_description *Semifield_classify_description;
    poset_classification::poset_classification_control *Semifield_classify_Control;
 
    int f_cheat_sheet;
 
    int f_classify_quartic_curves_nauty;
    std::string classify_quartic_curves_nauty_fname_mask;
    int classify_quartic_curves_nauty_nb;
    std::string classify_quartic_curves_nauty_fname_classification;
 
    int f_classify_quartic_curves_with_substructure;
    std::string classify_quartic_curves_with_substructure_fname_mask;
    int classify_quartic_curves_with_substructure_nb;
    int classify_quartic_curves_with_substructure_size;
    int classify_quartic_curves_with_substructure_degree;
    std::string classify_quartic_curves_with_substructure_fname_classification;
 
    int f_set_stabilizer;
    int set_stabilizer_intermediate_set_size;
    std::string set_stabilizer_fname_mask;
    int set_stabilizer_nb;
    std::string set_stabilizer_column_label;
    std::string set_stabilizer_fname_out;
 
    int f_conic_type;
    int conic_type_threshold;
    std::string conic_type_set_text;
 
    int f_lift_skew_hexagon;
    std::string lift_skew_hexagon_text;
 
    int f_lift_skew_hexagon_with_polarity;
    std::string lift_skew_hexagon_with_polarity_polarity;
 
    int f_arc_with_given_set_as_s_lines_after_dualizing;
    int arc_size;
    int arc_d;
    int arc_d_low;
    int arc_s;
    std::string arc_input_set;
    std::string arc_label;
 
    int f_arc_with_two_given_sets_of_lines_after_dualizing;
    int arc_t;
    std::string t_lines_string;
 
    int f_arc_with_three_given_sets_of_lines_after_dualizing;
    int arc_u;
    std::string u_lines_string;
 
    int f_dualize_hyperplanes_to_points;
    int f_dualize_points_to_hyperplanes;
    std::string dualize_input_set;
 
    int f_dualize_rank_k_subspaces;
    int dualize_rank_k_subspaces_k;
 
    int f_classify_arcs;
    apps_geometry::arc_generator_description *Arc_generator_description;
 
    int f_classify_cubic_curves;
 
    int f_latex_homogeneous_equation;
    int latex_homogeneous_equation_degree;
    std::string latex_homogeneous_equation_symbol_txt;
    std::string latex_homogeneous_equation_symbol_tex;
    std::string latex_homogeneous_equation_text;
 
    int f_lines_on_point_but_within_a_plane;
    long int lines_on_point_but_within_a_plane_point_rk;
    long int lines_on_point_but_within_a_plane_plane_rk;
 
    int f_rank_lines_in_PG;
    std::string rank_lines_in_PG_label;
 
    int f_unrank_lines_in_PG;
    std::string unrank_lines_in_PG_text;
 
    int f_move_two_lines_in_hyperplane_stabilizer;
    long int line1_from;
    long int line2_from;
    long int line1_to;
    long int line2_to;
 
    int f_move_two_lines_in_hyperplane_stabilizer_text;
    std::string line1_from_text;
    std::string line2_from_text;
    std::string line1_to_text;
    std::string line2_to_text;
 
 
    projective_space_activity_description();
    ~projective_space_activity_description();
    int read_arguments(
        int argc, std::string *argv,
        int verbose_level);
    void print();
 
 
};
 
 
// #############################################################################
// projective_space_activity.cpp
// #############################################################################
 
 
 
class projective_space_activity {
public:
 
    projective_space_activity_description *Descr;
 
    projective_space_with_action *PA;
 
 
    projective_space_activity();
    ~projective_space_activity();
    void perform_activity(int verbose_level);
    void do_rank_lines_in_PG(
            std::string &label,
            int verbose_level);
 
};
 
// #############################################################################
// projective_space_global.cpp
// #############################################################################
 
 
 
class projective_space_global {
public:
    void map(
            projective_space_with_action *PA,
            std::string &label,
            std::string &evaluate_text,
            int verbose_level);
    void analyze_del_Pezzo_surface(
            projective_space_with_action *PA,
            std::string &label,
            std::string &evaluate_text,
            int verbose_level);
    void analyze_del_Pezzo_surface_formula_given(
            projective_space_with_action *PA,
            expression_parser::formula *F,
            std::string &evaluate_text,
            int verbose_level);
    void do_create_surface(
            projective_space_with_action *PA,
            applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create_description *Surface_Descr,
            applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_with_action *&Surf_A,
            applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_create *&SC,
            int verbose_level);
    void conic_type(
            projective_space_with_action *PA,
            int threshold,
            std::string &set_text,
            int verbose_level);
    void do_lift_skew_hexagon(
            projective_space_with_action *PA,
            std::string &text,
            int verbose_level);
    void do_lift_skew_hexagon_with_polarity(
            projective_space_with_action *PA,
            std::string &polarity_36,
            int verbose_level);
    void do_classify_arcs(
            projective_space_with_action *PA,
            apps_geometry::arc_generator_description *Arc_generator_description,
            int verbose_level);
    void do_classify_cubic_curves(
            projective_space_with_action *PA,
            apps_geometry::arc_generator_description *Arc_generator_description,
            int verbose_level);
    void classify_quartic_curves_nauty(
            projective_space_with_action *PA,
            std::string &fname_mask, int nb,
            std::string &fname_classification,
            canonical_form_classifier *&Classifier,
            int verbose_level);
    void classify_quartic_curves_with_substructure(
            projective_space_with_action *PA,
            std::string &fname_mask, int nb, int substructure_size, int degree,
            std::string &fname_classification,
            canonical_form_classifier *&Classifier,
            int verbose_level);
    void classify_quartic_curves(
            projective_space_with_action *PA,
            std::string &fname_mask,
            int nb,
            int size,
            int degree,
            std::string &fname_classification,
            int verbose_level);
    void set_stabilizer(
            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);
 
};
 
 
 
 
// #############################################################################
// projective_space_with_action_description.cpp
// #############################################################################
 
 
 
class projective_space_with_action_description {
public:
 
    int n;
    std::string input_q;
    field_theory::finite_field *F;
 
    int f_use_projectivity_subgroup;
 
    projective_space_with_action_description();
    ~projective_space_with_action_description();
    int read_arguments(
        int argc, std::string *argv,
        int verbose_level);
    void print();
 
};
 
 
 
// #############################################################################
// projective_space_with_action.cpp
// #############################################################################
 
 
 
 
 
 
 
class projective_space_with_action {
 
public:
 
    int n; // projective dimension
    int d; // n + 1
    int q;
    field_theory::finite_field *F; // do not free
    int f_semilinear;
    int f_init_incidence_structure;
 
    geometry::projective_space *P;
 
    // if n >= 3:
    projective_space_with_action *PA2;
 
 
    // if n == 2:
    algebraic_geometry::quartic_curve_domain *Dom;
    applications_in_algebraic_geometry::quartic_curves::quartic_curve_domain_with_action *QCDA;
 
 
    actions::action *A; // linear group PGGL(d,q) in the action on points
    actions::action *A_on_lines; // linear group PGGL(d,q) acting on lines
 
    int f_has_action_on_planes;
    actions::action *A_on_planes; // linear group PGGL(d,q) acting on planes
 
 
    int *Elt1;
 
 
    projective_space_with_action();
    ~projective_space_with_action();
    void null();
    void freeself();
    void init(field_theory::finite_field *F, int n, int f_semilinear,
        int f_init_incidence_structure, int verbose_level);
    void init_group(int f_semilinear, int verbose_level);
    void canonical_labeling(
            geometry::object_with_canonical_form *OiP,
        int *canonical_labeling,
        int verbose_level);
    void report_fixed_points_lines_and_planes(
        int *Elt, std::ostream &ost,
        int verbose_level);
    void report_orbits_on_points_lines_and_planes(
        int *Elt, std::ostream &ost,
        int verbose_level);
    void report_decomposition_by_single_automorphism(
        int *Elt, std::ostream &ost, std::string &fname_base,
        int verbose_level);
    int process_object(
        data_structures::classify_bitvectors *CB,
        geometry::object_with_canonical_form *OiP,
        int f_save_incma_in_and_out, std::string &prefix,
        int nb_objects_to_test,
        groups::strong_generators *&SG,
        long int *canonical_labeling,
        int verbose_level);
    void compute_group_of_set(long int *set, int set_sz,
            groups::strong_generators *&Sg,
            int verbose_level);
    void map(
            expression_parser::formula *Formula,
            std::string &evaluate_text,
            int verbose_level);
    void analyze_del_Pezzo_surface(
            expression_parser::formula *Formula,
            std::string &evaluate_text,
            int verbose_level);
    void do_cheat_sheet_for_decomposition_by_element_PG(
            int decomposition_by_element_power,
            std::string &decomposition_by_element_data, std::string &fname_base,
            int verbose_level);
    void do_cheat_sheet_for_decomposition_by_subgroup(std::string &label,
            groups::linear_group_description * subgroup_Descr, int verbose_level);
    void report(
        std::ostream &ost,
        graphics::layered_graph_draw_options *O,
        int verbose_level);
    void create_quartic_curve(
            applications_in_algebraic_geometry::quartic_curves::quartic_curve_create_description *Quartic_curve_descr,
            applications_in_algebraic_geometry::quartic_curves::quartic_curve_create *&QC,
            int verbose_level);
    void canonical_form_of_code(
            std::string &label,
            int *genma, int m, int n,
            combinatorics::classification_of_objects_description *Canonical_form_codes_Descr,
            int verbose_level);
    void table_of_quartic_curves(int verbose_level);
    void table_of_cubic_surfaces(int verbose_level);
    void conic_type(
            long int *Pts, int nb_pts, int threshold,
            int verbose_level);
    void cheat_sheet(
            graphics::layered_graph_draw_options *O,
            int verbose_level);
    void do_spread_classify(int k,
            poset_classification::poset_classification_control *Control,
            int verbose_level);
    void setup_surface_with_action(
            applications_in_algebraic_geometry::cubic_surfaces_in_general::surface_with_action *&Surf_A,
            int verbose_level);
    void report_decomposition_by_group(
            groups::strong_generators *SG, std::ostream &ost, std::string &fname_base,
        int verbose_level);
    void do_rank_lines_in_PG(
            std::string &label,
            int verbose_level);
    void do_unrank_lines_in_PG(
            std::string &text,
            int verbose_level);
 
 
};
 
 
 
}}}
 
 
 
 
 
#endif /* SRC_LIB_TOP_LEVEL_PROJECTIVE_SPACE_PROJECTIVE_SPACE_H_ */