six_arcs_not_on_a_conic.cpp

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// six_arcs_not_on_a_conic.cpp
// 
// Anton Betten
//
// March 6, 2018
//
 
 
#include "orbiter.h"
 
using namespace std;
 
namespace orbiter {
namespace layer5_applications {
namespace applications_in_algebraic_geometry {
namespace cubic_surfaces_and_arcs {
 
 
six_arcs_not_on_a_conic::six_arcs_not_on_a_conic()
{
    //P2 = NULL;
    Descr = NULL;
    PA = NULL;
    Gen = NULL;
    nb_orbits = 0;
    Not_on_conic_idx = NULL;
    nb_arcs_not_on_conic = 0;
    //null();
}
 
 
six_arcs_not_on_a_conic::~six_arcs_not_on_a_conic()
{
    freeself();
}
 
void six_arcs_not_on_a_conic::null()
{
}
 
void six_arcs_not_on_a_conic::freeself()
{
    if (Gen) {
        FREE_OBJECT(Gen);
    }
    if (Not_on_conic_idx) {
        FREE_int(Not_on_conic_idx);
    }
    null();
}
 
void six_arcs_not_on_a_conic::init(
        apps_geometry::arc_generator_description *Descr,
        projective_geometry::projective_space_with_action *PA,
    int f_test_nb_Eckardt_points, int nb_E,
    //algebraic_geometry::surface_domain *Surf,
    int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int level = 6;
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init" << endl;
    }
 
    if (PA->n != 2) {
        cout << "six_arcs_not_on_a_conic::init PA->n != 2" << endl;
        exit(1);
    }
 
    //six_arcs_not_on_a_conic::P2 = P2;
    six_arcs_not_on_a_conic::Descr = Descr;
    six_arcs_not_on_a_conic::PA = PA;
    
 
    
 
    Descr->f_target_size = TRUE;
    Descr->target_size = 6;
    Descr->f_d = TRUE;
    Descr->d = 2;
    //Descr->f_n = TRUE;
    //Descr->n = 3;
    Descr->f_conic_test = TRUE;
    Descr->f_test_nb_Eckardt_points = f_test_nb_Eckardt_points;
    Descr->nb_E = nb_E;
    //Descr->Surf = Surf;
 
 
 
 
    
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "before Gen->init" << endl;
    }
 
    Gen = NEW_OBJECT(apps_geometry::arc_generator);
 
 
    Gen->init(
            Descr,
            PA,
            PA->A->Strong_gens,
            verbose_level - 2);
 
 
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "after Gen->init" << endl;
    }
 
 
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "Classifying 6-arcs for q=" << PA->F->q << endl;
        cout << "six_arcs_not_on_a_conic::init before Gen->compute_starter" << endl;
    }
    
    Gen->compute_starter(verbose_level - 1);
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "Classifying 6-arcs for q=" << PA->F->q << endl;
        cout << "six_arcs_not_on_a_conic::init after Gen->compute_starter" << endl;
    }
 
 
    nb_orbits = Gen->gen->nb_orbits_at_level(level);
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "We found " << nb_orbits << " isomorphism types "
                "of 6-arcs" << endl;
    }
 
 
    
    long int Arc6[6];
    int h, j;
    
 
    nb_arcs_not_on_conic = 0;
 
    Not_on_conic_idx = NEW_int(nb_orbits);  
    
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::init "
                "testing the arcs" << endl;
    }
 
    for (h = 0; h < nb_orbits; h++) {
 
        if (f_v && (h % 10000) == 0) {
            cout << "six_arcs_not_on_a_conic::init "
                    "testing arc " << h << " / " << nb_orbits << endl;
        }
 
        
        Gen->gen->get_set_by_level(level, h, Arc6);
        
        
        long int **Pts_on_conic;
        int **Conic_eqn;
        int *nb_pts_on_conic;
        int len1;
 
        if (f_v && (h % 10000) == 0) {
            cout << "six_arcs_not_on_a_conic::init "
                    "testing arc " << h << " / " << nb_orbits << " : ";
            Lint_vec_print(cout, Arc6, 6);
            cout << endl;
        }
 
 
        
        if (f_v && (h % 10000) == 0) {
            cout << "six_arcs_not_on_a_conic::init "
                    "computing conic intersections:" << endl;
        }
        PA->P->conic_type(
            Arc6, 6, 
            6 /* threshold */,
            Pts_on_conic, Conic_eqn, nb_pts_on_conic, len1,
            0 /*verbose_level - 2*/);
        if (f_v && (h % 10000) == 0) {
            cout << "The arc intersects " << len1
                    << " conics in 6 or more points. " << endl;
        }
 
        if (len1 == 0) {
            Not_on_conic_idx[nb_arcs_not_on_conic++] = h;
        }
 
        for (j = 0; j < len1; j++) {
            FREE_lint(Pts_on_conic[j]);
            FREE_int(Conic_eqn[j]);
        }
        FREE_plint(Pts_on_conic);
        FREE_pint(Conic_eqn);
        FREE_int(nb_pts_on_conic);
    }
 
    if (f_v) {
        cout << "We found " << nb_arcs_not_on_conic << " isomorphism types "
                "of 6-arcs not on a conic, out of a total of "
                << nb_orbits << " isomorphism types of arcs" << endl;
    }
    
 
 
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::done" << endl;
    }
 
}
 
 
void six_arcs_not_on_a_conic::recognize(long int *arc6, int *transporter,
        int &orbit_not_on_conic_idx, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int orbit_at_level;
    data_structures::sorting Sorting;
 
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::recognize" << endl;
    }
 
    Gen->gen->identify(arc6, 6,
        transporter,
        orbit_at_level,
        0 /*verbose_level */);
 
 
    if (!Sorting.int_vec_search(Not_on_conic_idx,
        nb_arcs_not_on_conic, orbit_at_level,
        orbit_not_on_conic_idx)) {
        cout << "six_arcs_not_on_a_conic::recognize could not find orbit" << endl;
        exit(1);
    }
    if (f_v) {
        cout << "six_arcs_not_on_a_conic::recognize done" << endl;
    }
}
 
 
void six_arcs_not_on_a_conic::report_latex(ostream &ost)
{
    int h;
    
    ost << "\\subsection*{Classification of 6-arcs not on a conic "
            "in $\\PG(2," << PA->F->q << ")$}" << endl;
    
    ring_theory::longinteger_object go;
    ring_theory::longinteger_domain D;
    {
    PA->A->Strong_gens->group_order(go);
 
    ost << "The order of the group $" << PA->A->label_tex << "$ is ";
    go.print_not_scientific(ost);
    ost << endl;
 
    ost << "\\bigskip" << endl << endl;
    }
 
    ring_theory::longinteger_object ol, Ol;
    Ol.create(0, __FILE__, __LINE__);
    for (h = 0; h < nb_arcs_not_on_conic; h++) {
        data_structures_groups::set_and_stabilizer *R;
 
        R = Gen->gen->get_set_and_stabilizer(
                6 /* level */,
                Not_on_conic_idx[h] /* orbit_at_level */,
                0 /* verbose_level */);
        Gen->gen->orbit_length(
                Not_on_conic_idx[h] /* node */,
                6 /* level */, ol);
        D.add_in_place(Ol, ol);
        
        
        ost << "$" << h << " / " << nb_arcs_not_on_conic
                << "$ Arc $" << Not_on_conic_idx[h] << "$ $" << endl;
        R->print_set_tex(ost);
        ost << "$ orbit length $";
        ol.print_not_scientific(ost);
        ost << "$\\\\" << endl;
 
        FREE_OBJECT(R);
    }
    ost << "The overall number of 6-arcs not on a conic "
            "in $\\PG(2," << PA->F->q << ")$ is: " << Ol << "\\\\" << endl;
}
 
void six_arcs_not_on_a_conic::report_specific_arc_basic(ostream &ost, int arc_idx)
{
    data_structures_groups::set_and_stabilizer *The_arc;
    ring_theory::longinteger_object go;
 
    The_arc = Gen->gen->get_set_and_stabilizer(
            6 /* level */,
            Not_on_conic_idx[arc_idx],
            0 /* verbose_level */);
 
    The_arc->Strong_gens->group_order(go);
 
    ost << "Arc " << arc_idx << " / " << nb_arcs_not_on_conic << " is: ";
    ost << "$$" << endl;
    //int_vec_print(fp, Arc6, 6);
    //ost << "\{";
    The_arc->print_set_tex(ost);
    //ost << "\}_{" << go << "}";
    ost << "$$" << endl;
 
    //P2->F->display_table_of_projective_points(ost, The_arc->data, 6, 3);
 
 
    //ost << "The arc-stabilizer is the following group:\\\\" << endl;
    //The_arc->Strong_gens->print_generators_tex(ost);
 
    FREE_OBJECT(The_arc);
 
 
}
 
void six_arcs_not_on_a_conic::report_specific_arc(ostream &ost, int arc_idx)
{
    data_structures_groups::set_and_stabilizer *The_arc;
    ring_theory::longinteger_object go;
 
    The_arc = Gen->gen->get_set_and_stabilizer(
            6 /* level */,
            Not_on_conic_idx[arc_idx],
            0 /* verbose_level */);
 
    The_arc->Strong_gens->group_order(go);
 
    ost << "Arc " << arc_idx << " / " << nb_arcs_not_on_conic << " is: ";
    ost << "$$" << endl;
    //int_vec_print(fp, Arc6, 6);
    //ost << "\{";
    The_arc->print_set_tex(ost);
    //ost << "\}_{" << go << "}";
    ost << "$$" << endl;
 
    PA->F->display_table_of_projective_points(ost, The_arc->data, 6, 3);
 
 
    //ost << "The arc-stabilizer is the following group:\\\\" << endl;
    //The_arc->Strong_gens->print_generators_tex(ost);
 
    FREE_OBJECT(The_arc);
 
 
}
 
 
}}}}