quartic_curves.h

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/*
 * quartic_curves.cpp
 *
 *  Created on: May 25, 2021
 *      Author: betten
 */
 
#ifndef SRC_LIB_TOP_LEVEL_QUARTIC_CURVES_QUARTIC_CURVES_CPP_
#define SRC_LIB_TOP_LEVEL_QUARTIC_CURVES_QUARTIC_CURVES_CPP_
 
 
 
 
namespace orbiter {
namespace layer5_applications {
namespace applications_in_algebraic_geometry {
namespace quartic_curves {
 
 
// #############################################################################
// quartic_curve_activity_description.cpp
// #############################################################################
 
 
 
class quartic_curve_activity_description {
public:
 
    int f_report;
 
    int f_report_with_group;
 
    int f_export_points;
 
    int f_create_surface;
 
 
    quartic_curve_activity_description();
    ~quartic_curve_activity_description();
    int read_arguments(
        int argc, std::string *argv,
        int verbose_level);
    void print();
 
};
 
 
// #############################################################################
// quartic_curve_activity.cpp
// #############################################################################
 
 
 
class quartic_curve_activity {
public:
 
    quartic_curve_activity_description *Descr;
    quartic_curve_create *QC;
 
 
    quartic_curve_activity();
    ~quartic_curve_activity();
    void init(quartic_curve_activity_description *Quartic_curve_activity_description,
            quartic_curve_create *QC, int verbose_level);
    void perform_activity(int verbose_level);
    void do_report(
            quartic_curve_create *QC,
            int verbose_level);
 
};
 
 
 
 
// #############################################################################
// quartic_curve_create_description.cpp
// #############################################################################
 
 
 
 
 
class quartic_curve_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_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_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;
 
 
 
    quartic_curve_create_description();
    ~quartic_curve_create_description();
    void null();
    void freeself();
    int read_arguments(int argc, std::string *argv,
        int verbose_level);
    void print();
    int get_q();
};
 
 
 
// #############################################################################
// quartic_curve_create.cpp
// #############################################################################
 
 
 
 
class quartic_curve_create {
 
public:
    quartic_curve_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;
 
 
    projective_geometry::projective_space_with_action *PA;
 
    quartic_curve_domain_with_action *QCDA;
 
    algebraic_geometry::quartic_curve_object *QO;
 
    quartic_curve_object_with_action *QOA;
 
    int f_has_group;
    groups::strong_generators *Sg;
    int f_has_nice_gens;
    data_structures_groups::vector_ge *nice_gens;
 
 
 
 
    quartic_curve_create();
    ~quartic_curve_create();
    void null();
    void freeself();
    void init_with_data(
            quartic_curve_create_description *Descr,
            projective_geometry::projective_space_with_action *PA,
            quartic_curve_domain_with_action *QCDA,
            int verbose_level);
    void init(
            quartic_curve_create_description *Descr,
            projective_geometry::projective_space_with_action *PA,
            quartic_curve_domain_with_action *QCDA,
            int verbose_level);
    void create_quartic_curve_from_description(quartic_curve_domain_with_action *DomA, int verbose_level);
    void override_group(std::string &group_order_text,
            int nb_gens, std::string &gens_text, int verbose_level);
    void create_quartic_curve_by_coefficients(std::string &coefficients_text,
            int verbose_level);
    void create_quartic_curve_by_coefficient_vector(int *eqn15,
            int verbose_level);
    void create_quartic_curve_from_catalogue(quartic_curve_domain_with_action *DomA,
            int iso,
            int verbose_level);
    void create_quartic_curve_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,
            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);
 
};
 
 
// #############################################################################
// quartic_curve_domain_with_action.cpp
// #############################################################################
 
 
 
 
class quartic_curve_domain_with_action {
 
public:
 
 
    projective_geometry::projective_space_with_action *PA;
 
    int f_semilinear;
 
    algebraic_geometry::quartic_curve_domain *Dom; // do not free
 
    actions::action *A; // linear group PGGL(3,q)
 
 
    actions::action *A_on_lines; // linear group PGGL(3,q) acting on lines
 
    int *Elt1;
 
    induced_actions::action_on_homogeneous_polynomials *AonHPD_4_3;
 
 
    quartic_curve_domain_with_action();
    ~quartic_curve_domain_with_action();
    void init(algebraic_geometry::quartic_curve_domain *Dom,
            projective_geometry::projective_space_with_action *PA,
            int verbose_level);
 
};
 
 
// #############################################################################
// quartic_curve_from_surface.cpp
// #############################################################################
 
 
 
 
class quartic_curve_from_surface {
 
public:
 
    cubic_surfaces_in_general::surface_object_with_action *SOA;
 
    int pt_orbit;
    int equation_nice[20]; // equation after transformation
    int *transporter; // the transformation that maps the point off the lines to (1,0,0,0)
 
    int v[4]; // = (1,0,0,0)
    int pt_A; // = SOA->SO->SOP->Pts_not_on_lines[i];
    int pt_B; // = SOA->Surf->rank_point(v);
 
    long int *Lines_nice; // lines after transformation
    int nb_lines;
 
    long int *Bitangents;
    int nb_bitangents; // = nb_lines + 1
 
 
    // computed by split_nice_equation starting from the equation of the cubic surface:
    int *f1; // terms involving X0^2, with X0^2 removed (linear)
    int *f2; // terms involving X0, with X0 removed (quadratic)
    int *f3; // terms free of X0 (cubic)
 
    long int *Pts_on_surface; // points on the transformed surface
    int nb_pts_on_surface;
 
    // the equation of the quartic curve:
    int *curve; // poly1 + poly2 = f2^2 - 4 * f1 * f3
    int *poly1; // f2 * f2
    int *poly2; // -4 * f1 * f3
    int two, four, mfour; // 2, 4, -4 in F
 
    int *tangent_quadric; // = 2 * x_0 * f_1 + f_2
    long int *Pts_on_tangent_quadric; // = SOA->Surf->Poly2_4->enumerate_points(tangent_quadric)
    int nb_pts_on_tangent_quadric;
 
    //int *line_type;
    //int *type_collected;
 
    //int *Class_pts;
    //int nb_class_pts;
    //long int *Pts_intersection;
    //int nb_pts_intersection;
 
    long int *Pts_on_curve; // = SOA->Surf->Poly4_x123->enumerate_points(curve)
    int sz_curve;
 
#if 0
    strong_generators *gens_copy;
    set_and_stabilizer *moved_surface;
    //strong_generators *stab_gens_moved_surface;
    strong_generators *stab_gens_P0;
#endif
 
    groups::strong_generators *Stab_gens_quartic;
 
 
 
    quartic_curve_from_surface();
    ~quartic_curve_from_surface();
    void init(cubic_surfaces_in_general::surface_object_with_action *SOA, int verbose_level);
    void quartic(std::string &surface_prefix, int pt_orbit, int f_TDO, int verbose_level);
    void compute_quartic(int pt_orbit,
        int *equation, long int *Lines, int nb_lines,
        int verbose_level);
    void compute_stabilizer(int verbose_level);
    void cheat_sheet_quartic_curve(
            std::string &surface_prefix,
            std::ostream &ost,
            std::ostream &ost_curves,
            int f_TDO,
            int verbose_level);
 
};
 
 
 
 
// #############################################################################
// quartic_curve_object_with_action.cpp
// #############################################################################
 
 
 
 
class quartic_curve_object_with_action {
 
public:
 
    field_theory::finite_field *F; // do not free
 
    quartic_curve_domain_with_action *DomA;
 
    algebraic_geometry::quartic_curve_object *QO; // 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;
 
    groups::schreier *Orbits_on_points;
 
    quartic_curve_object_with_action();
    ~quartic_curve_object_with_action();
    void init(quartic_curve_domain_with_action *DomA,
            algebraic_geometry::quartic_curve_object *QO,
            groups::strong_generators *Aut_gens,
            int verbose_level);
 
};
 
 
 
 
 
}}}}
 
 
 
#endif /* SRC_LIB_TOP_LEVEL_QUARTIC_CURVES_QUARTIC_CURVES_CPP_ */