surfaces_arc_lifting_definition_node.cpp

Go to the documentation of this file.

/*
 * surfaces_arc_lifting_definition_node.cpp
 *
 *  Created on: Aug 3, 2020
 *      Author: betten
 */
 
 
 
 
 
#include "orbiter.h"
 
using namespace std;
 
namespace orbiter {
namespace layer5_applications {
namespace applications_in_algebraic_geometry {
namespace cubic_surfaces_and_arcs {
 
 
surfaces_arc_lifting_definition_node::surfaces_arc_lifting_definition_node()
{
    Lift = NULL;
 
    f = 0;
    orbit_idx = 0;
 
    SO = NULL;
    SOA = NULL;
 
    Flag_stab_gens = NULL;
    //longinteger_object Flag_stab_go;
 
    //int three_lines_idx[45 * 3];
    //long int three_lines[45 * 3];
    //seventytwo_cases Seventytwo[45 * 72];
 
    nb_coset_reps = 0;
    T = NULL;
    coset_reps = NULL;
 
    relative_order_table = NULL;
 
    f_has_F2 = FALSE;
    F2 = NULL;
    tally_F2 = NULL;
}
 
 
surfaces_arc_lifting_definition_node::~surfaces_arc_lifting_definition_node()
{
}
 
void surfaces_arc_lifting_definition_node::init_with_27_lines(surfaces_arc_lifting *Lift,
        int f, int orbit_idx, long int *Lines27, int *eqn20,
        int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::init_with_27_lines" << endl;
    }
 
    surfaces_arc_lifting_definition_node::Lift = Lift;
    surfaces_arc_lifting_definition_node::f = f;
    surfaces_arc_lifting_definition_node::orbit_idx = orbit_idx;
 
 
    SO = NEW_OBJECT(algebraic_geometry::surface_object);
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::init_with_27_lines before SO->init_with_27_lines" << endl;
    }
    SO->init_with_27_lines(Lift->Surf_A->Surf, Lines27, eqn20,
            FALSE /* f_find_double_six_and_rearrange_lines */,
            verbose_level - 2);
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::init_with_27_lines after SO->init_with_27_lines" << endl;
    }
 
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::init_with_27_lines done" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::tally_f2(
        int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::tally_f2" << endl;
    }
    F2 = NEW_int(45 * 72);
    for (i = 0; i < 45 * 72; i++) {
        F2[i] = Seventytwo[i].f2;
    }
    tally_F2 = NEW_OBJECT(data_structures::tally);
    tally_F2->init(F2, 45 * 72, FALSE, 0);
 
    f_has_F2 = TRUE;
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::tally_f2 done" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::report(int verbose_level)
{
    char fname_base[1000];
    orbiter_kernel_system::latex_interface L;
 
    sprintf(fname_base, "clebsch_maps_surface_%d", orbit_idx);
 
    char title[1000];
    char author[1000];
    string fname_report;
 
    fname_report.assign(fname_base);
    fname_report.append(".tex");
    snprintf(title, 1000, "Clebsch maps of surface %d", orbit_idx);
    strcpy(author, "");
 
    {
        ofstream fp(fname_report.c_str());
        L.head(fp,
            FALSE /* f_book */,
            TRUE /* f_title */,
            title, author,
            FALSE /*f_toc */,
            FALSE /* f_landscape */,
            FALSE /* f_12pt */,
            TRUE /*f_enlarged_page */,
            TRUE /* f_pagenumbers*/,
            NULL /* extra_praeamble */);
 
 
        report2(fp, verbose_level);
 
        L.foot(fp);
 
    }
    orbiter_kernel_system::file_io Fio;
 
    cout << "Written file " << fname_report << " of size " << Fio.file_size(fname_report.c_str()) << endl;
 
}
 
void surfaces_arc_lifting_definition_node::report2(ostream &ost, int verbose_level)
{
    report_Clebsch_maps(ost, verbose_level);
 
    if (SOA) {
        SOA->cheat_sheet_basic(ost, verbose_level);
    }
}
 
void surfaces_arc_lifting_definition_node::report_cosets(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets" << endl;
    }
    //ost << "\\begin{enumerate}" << endl;
    for (i = 0; i < nb_coset_reps; i++) {
 
        ost << endl << "\\bigskip" << endl << endl;
        //ost << "\\item" << endl;
        ost << "Aut coset " << i << " / " << nb_coset_reps << ": relative order is "
                << relative_order_table[i] << "\\\\" << endl;
        ost << "$$" << endl;
        Lift->A4->element_print_latex(coset_reps->ith(i), ost);
        ost << "$$" << endl;
    }
    //ost << "\\end{enumerate}" << endl;
 
 
    //surfaces_arc_lifting_trace *T; // [nb_coset_reps]
    //vector_ge *coset_reps;
 
    //int *relative_order_table; // [nb_coset_reps]
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets done" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::report_cosets_detailed(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_detailed" << endl;
    }
 
    ost << "We consider the Clebsch map " << endl;
    ost << "$$" << endl;
    ost << "\\Phi_{\\ell_1,\\ell_2,\\pi}" << endl;
    ost << "$$" << endl;
    ost << "with defining lines $\\ell_1,\\ell_2$ and image tritangent plane $\\pi$.\\\\" << endl;
    ost << "The line $m_1$ is in $\\pi$ and $\\ell_i \\cap \\pi =P_i \\in m_1.$\\\\" << endl;
    ost << "The four transversals besides $m_1$ to $\\ell_1,\\ell_2$ are called $t_3,t_4,t_5,t_6$.\\\\" << endl;
    //ost << "The points $P_1,P_2$ are the points of intersection of $(\\ell_1,\\ell_2)$ with the tritangent plane.\\\\" << endl;
    ost << "The points $P_3,P_4,P_5,P_6$ are the points of intersection of $t_3,t_4,t_5,t_6$ with the tritangent plane.\\\\" << endl;
    ost << "Alpha1 * Alpha2 * Beta1 * Beta2 * Beta3 = AutCoset\\\\" << endl;
    ost << "Alpha1 takes the chosen tritangent plane to the tritangent plane from the defining flag orbit.\\\\" << endl;
    ost << "Alpha2 maps the 6-arc to the canonical representative.\\\\" << endl;
    ost << "Beta1 maps the two points $P_1$ and $P_2$ defined by the lines $(\\ell_1,\\ell_2)$ to the canonical pair.\\\\" << endl;
    ost << "Beta2 maps the partition defined by $\\{\\{P_3,P_4\\}, \\{P_5,P_6\\}\\}$ to the canonical partition.\\\\" << endl;
    ost << "Beta3 maps the image of the lines $(\\ell_1,\\ell_2)$ under Alpha1*Alpha2*Beta1*Beta2 to the canonical pair.\\\\" << endl;
    //ost << "\\begin{enumerate}" << endl;
    for (i = 0; i < nb_coset_reps; i++) {
 
        ost << endl << "\\bigskip" << endl << endl;
        //ost << "\\item" << endl;
        ost << "Aut coset " << i << " / " << nb_coset_reps << ": relative order is "
                << relative_order_table[i] << "\\\\" << endl;
 
        T[i]->report_product(ost, coset_reps->ith(i), verbose_level);
 
        T[i]->The_case.report_single_Clebsch_map(ost, verbose_level);
 
 
        //SO->print_lines(ost);
 
 
        T[i]->The_case.report_Clebsch_map_details(ost, SO, verbose_level);
 
        //T[i]->report_product(ost, coset_reps->ith(i), verbose_level);
 
    }
    //ost << "\\end{enumerate}" << endl;
 
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_detailed done" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::report_cosets_HDS(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int coset;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_HDS" << endl;
    }
 
    report_HDS_top(ost);
 
    for (coset = 0; coset < nb_coset_reps; coset++) {
 
        //ost << "Aut coset " << i << " / " << nb_coset_reps << ": relative order is "
        //      << relative_order_table[i] << "\\\\" << endl;
 
        //T[i]->The_case.report_single_Clebsch_map(ost, verbose_level);
 
 
 
        if ((coset % 24) == 0) {
            report_HDS_bottom(ost);
            report_HDS_top(ost);
        }
 
 
        T[coset]->The_case.report_Clebsch_map_aut_coset(ost, coset,
                relative_order_table[coset], verbose_level);
 
 
    }
 
    report_HDS_bottom(ost);
 
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_HDS done" << endl;
    }
}
 
 
void surfaces_arc_lifting_definition_node::report_HDS_top(ostream &ost)
{
    int t = T[0]->The_case.tritangent_plane_idx;
 
    ost << "{\\renewcommand{\\arraystretch}{1.5}" << endl;
    ost << "$$" << endl;
    ost << "\\begin{array}{|c|c|c|c|c|c|c|c|}" << endl;
    ost << "\\hline" << endl;
    ost << "\\multicolumn{8}{|c|}{\\mbox{Tritangent Plane}\\; \\pi_{" << t
            << "} = \\pi_{" << Lift->Surf->Schlaefli->Eckard_point_label_tex[t] << "}}\\\\" << endl;
    ost << "\\hline" << endl;
    ost << "\\mbox{Coset} & \\mbox{Clebsch} & (m_1,m_2,m_3) & "
            "(\\ell_1',\\ell_2') & (t_3',t_4',t_5',t_6') & DS & HDS & \\mbox{r.o.}\\\\" << endl;
    ost << "\\hline" << endl;
}
 
void surfaces_arc_lifting_definition_node::report_HDS_bottom(ostream &ost)
{
    ost << "\\hline" << endl;
    ost << "\\end{array}" << endl;
    ost << "$$}" << endl;
    ost << "\\bigskip" << endl;
}
 
 
void surfaces_arc_lifting_definition_node::report_cosets_T3(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int coset;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_T3" << endl;
    }
 
    report_T3_top(ost);
 
    for (coset = 0; coset < nb_coset_reps; coset++) {
 
        //ost << "Aut coset " << i << " / " << nb_coset_reps << ": relative order is "
        //      << relative_order_table[i] << "\\\\" << endl;
 
        //T[i]->The_case.report_single_Clebsch_map(ost, verbose_level);
 
 
        if ((coset % 24) == 0) {
            report_T3_bottom(ost);
            report_T3_top(ost);
        }
 
        ost << coset << " & ";
        //Lift->Surf->F->display_table_of_projective_points2(ost, T[coset]->The_case.P6, 6, 4);
        ost << " & \\\\";
 
 
    }
 
    report_T3_bottom(ost);
 
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_cosets_T3 done" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::report_T3_top(ostream &ost)
{
    ost << "{\\renewcommand{\\arraystretch}{1.5}" << endl;
    ost << "$$" << endl;
    ost << "\\begin{array}{|c|c|c|}" << endl;
    ost << "\\hline" << endl;
    ost << "\\mbox{Coset} & \\mbox{Arc} & T_3 \\\\" << endl;
    ost << "\\hline" << endl;
}
 
void surfaces_arc_lifting_definition_node::report_T3_bottom(ostream &ost)
{
    ost << "\\hline" << endl;
    ost << "\\end{array}" << endl;
    ost << "$$}" << endl;
    ost << "\\bigskip" << endl;
}
 
 
 
void surfaces_arc_lifting_definition_node::report_tally_F2(ostream &ost, int verbose_level)
{
    if (f_has_F2) {
        ost << "Tally of flag orbits: ";
        tally_F2->print_file_tex(ost, FALSE /* f_backwards */);
        ost << "\\\\" << endl;
    }
}
 
void surfaces_arc_lifting_definition_node::report_Clebsch_maps(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_maps" << endl;
    }
 
    report_tally_F2(ost, verbose_level);
 
#if 1
    int plane_idx[] = {12, 30};
    int i;
 
    for (i = 0; i < sizeof(plane_idx) / sizeof(int); i++) {
 
        report_Clebsch_maps_for_one_tritangent_plane(ost,
                plane_idx[i], verbose_level);
    }
 
#else
    int t;
    for (t = 0; t < 45; t++) {
        ost << "\\clearpage" << endl;
        //ost << "Tritangent plane " << t << ": \\\\" << endl;
        report_Clebsch_maps_for_one_tritangent_plane(ost, t, verbose_level);
    }
#endif
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_maps done" << endl;
    }
}
 
 
void surfaces_arc_lifting_definition_node::report_Clebsch_maps_for_one_tritangent_plane(
        ostream &ost, int plane_idx, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i, j;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_maps_for_one_tritangent_plane" << endl;
    }
 
    for (i = 0; i < 3; i++) {
        Seventytwo[plane_idx * 72 + i * 24].report_seventytwo_maps_top(ost);
        for (j = 0; j < 24; j++) {
            Seventytwo[plane_idx * 72 + i * 24 + j].report_seventytwo_maps_line(ost);
        }
        Seventytwo[plane_idx * 72 + i * 24].report_seventytwo_maps_bottom(ost);
    }
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_maps_for_one_tritangent_plane done" << endl;
    }
}
 
 
 
 
}}}}