seventytwo_cases.cpp

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/*
 * seventytwo_cases.cpp
 *
 *  Created on: Aug 2, 2020
 *      Author: betten
 */
 
 
#include "foundations.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer1_foundations {
namespace algebraic_geometry {
 
 
seventytwo_cases::seventytwo_cases()
{
    Surf = NULL;
 
    f = 0;
 
    tritangent_plane_idx = 0;
        // the tritangent plane picked for the Clebsch map,
        // using the Schlaefli labeling, in [0,44].
 
 
    //int three_lines_idx[3];
        // the index into Lines[] of the
        // three lines in the chosen tritangent plane
        // This is computed from the Schlaefli labeling
        // using the eckardt point class.
 
    //long int three_lines[3];
 
    tritangent_plane_rk = 0;
 
    //int Basis_pi[16];
    //int Basis_pi_inv[17]; // in case it is semilinear
 
    line_idx = 0;
        // the index of the line chosen to be P1,P2 in three_lines[3]
 
    m1 = m2 = m3 = 0;
        // rearrangement of three_lines_idx[3]
        // m1 = line_idx is the line through P1 and P2.
        // m2 and m3 are the two other lines.
 
    l1 = l2 = 0;
 
    line_l1_l2_idx = 0;
 
    //int transversals[5];
 
    //long int half_double_six[6];
 
    half_double_six_index = 0;
 
    //long int P6[6];
        // the points of intersection of l1, l2, and of the 4 transversals
        // with the tritangent plane
 
    L1 = L2 = 0;
 
    //long int P6a[6];
        // the arc after the plane has been moved
 
    //long int P6_local[6];
    //long int P6_local_canonical[6];
 
    //long int P6_perm[6];
    //long int P6_perm_mapped[6];
    //long int pair[2];
    //int the_rest[4];
 
    orbit_not_on_conic_idx = 0;
    pair_orbit_idx = 0;
 
    partition_orbit_idx = 0;
    //int the_partition4[4];
 
    f2 = 0;
}
 
seventytwo_cases::~seventytwo_cases()
{
}
 
void seventytwo_cases::init(surface_domain *Surf, int f, int tritangent_plane_idx,
        int *three_lines_idx, long int *three_lines,
        int line_idx, int m1, int m2, int m3, int line_l1_l2_idx, int l1, int l2)
{
    seventytwo_cases::Surf = Surf;
    seventytwo_cases::f = f;
    seventytwo_cases::tritangent_plane_idx = tritangent_plane_idx;
    Int_vec_copy(three_lines_idx, seventytwo_cases::three_lines_idx, 3);
    Lint_vec_copy(three_lines, seventytwo_cases::three_lines, 3);
 
    tritangent_plane_rk = 0;
 
    seventytwo_cases::line_idx = line_idx;
    seventytwo_cases::m1 = m1;
    seventytwo_cases::m2 = m2;
    seventytwo_cases::m3 = m3;
    seventytwo_cases::line_l1_l2_idx = line_l1_l2_idx;
    seventytwo_cases::l1 = l1;
    seventytwo_cases::l2 = l2;
}
 
 
void seventytwo_cases::compute_arc(surface_object *SO, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "seventytwo_cases::compute_arc" << endl;
    }
    int i, j;
 
    // determine the 5 transversals of lines l1 and l2:
    int nb_t = 0;
    int nb;
    int f_taken[4];
 
    for (i = 0; i < 27; i++) {
        if (i == l1 || i == l2) {
            continue;
        }
        if (SO->SOP->Adj_ij(i, l1) && SO->SOP->Adj_ij(i, l2)) {
            transversals[nb_t++] = i;
        }
    }
    if (nb_t != 5) {
        cout << "seventytwo_cases::compute_arc nb_t != 5" << endl;
        exit(1);
    }
 
    // one of the transversals must be m1, find it:
    for (i = 0; i < 5; i++) {
        if (transversals[i] == m1) {
            break;
        }
    }
    if (i == 5) {
        cout << "seventytwo_cases::compute_arc could not find m1 in transversals[]" << endl;
        exit(1);
    }
 
 
    // remove m1 from the list of transversals to form transversals4[4]:
    for (j = 0; j < i; j++) {
        transversals4[j] = transversals[j];
    }
    for (j = i + 1; j < 5; j++) {
        transversals4[j - 1] = transversals[j];
    }
    if (f_v) {
        cout << "seventytwo_cases::compute_arc the four transversals are: ";
        Lint_vec_print(cout, transversals4, 4);
        cout << endl;
    }
 
 
    if (f_v) {
        cout << "seventytwo_cases::compute_arc before compute_half_double_six" << endl;
    }
    compute_half_double_six(SO, verbose_level);
    if (f_v) {
        cout << "seventytwo_cases::compute_arc after compute_half_double_six" << endl;
    }
 
 
 
 
    P6[0] = SO->Surf->P->intersection_of_two_lines(SO->Lines[l1], SO->Lines[m1]);
    P6[1] = SO->Surf->P->intersection_of_two_lines(SO->Lines[l2], SO->Lines[m1]);
    nb_t = 4;
    nb = 2;
    for (i = 0; i < nb_t; i++) {
        f_taken[i] = FALSE;
    }
    for (i = 0; i < nb_t; i++) {
        if (f_taken[i]) {
            continue;
        }
        if (SO->SOP->Adj_ij(transversals4[i], m2)) {
            P6[nb++] = SO->Surf->P->intersection_of_two_lines(
                    SO->Lines[transversals4[i]], SO->Lines[m2]);
            f_taken[i] = TRUE;
        }
    }
    if (nb != 4) {
        cout << "seventytwo_cases::compute_arc after intersecting with m2, nb != 4" << endl;
        exit(1);
    }
    for (i = 0; i < nb_t; i++) {
        if (f_taken[i]) {
            continue;
        }
        if (SO->SOP->Adj_ij(transversals4[i], m3)) {
            P6[nb++] = SO->Surf->P->intersection_of_two_lines(
                    SO->Lines[transversals4[i]], SO->Lines[m3]);
            f_taken[i] = TRUE;
        }
    }
    if (nb != 6) {
        cout << "seventytwo_cases::compute_arc after intersecting with m3, nb != 6" << endl;
        exit(1);
    }
    if (f_v) {
        cout << "seventytwo_cases::compute_arc P6=";
        Lint_vec_print(cout, P6, 6);
        cout << endl;
    }
 
    if (f_v) {
        cout << "seventytwo_cases::compute_arc done" << endl;
    }
}
 
void seventytwo_cases::compute_partition(int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i;
 
    if (f_v) {
        cout << "seventytwo_cases::compute_partition" << endl;
    }
    for (i = 0; i < 4; i++) {
        the_rest[i] = P6_perm_mapped[2 + i];
    }
    for (i = 0; i < 4; i++) {
        the_partition4[i] = the_rest[i];
        if (the_rest[i] > P6_perm_mapped[0]) {
            the_partition4[i]--;
        }
        if (the_rest[i] > P6_perm_mapped[1]) {
            the_partition4[i]--;
        }
    }
    for (i = 0; i < 4; i++) {
        if (the_partition4[i] < 0) {
            cout << "seventytwo_cases::compute_partition the_partition4[i] < 0" << endl;
            exit(1);
        }
        if (the_partition4[i] >= 4) {
            cout << "seventytwo_cases::compute_partition the_partition4[i] >= 4" << endl;
            exit(1);
        }
    }
    if (f_v) {
        cout << "seventytwo_cases::compute_partition done" << endl;
    }
}
 
void seventytwo_cases::compute_half_double_six(surface_object *SO, int verbose_level)
// needs transversals4[]
{
    int f_v = (verbose_level >= 1);
    int i;
 
    if (f_v) {
        cout << "seventytwo_cases::compute_half_double_six" << endl;
    }
 
    half_double_six[0] = SO->Surf->Schlaefli->third_line_in_tritangent_plane(m1, l1, verbose_level);
    half_double_six[1] = SO->Surf->Schlaefli->third_line_in_tritangent_plane(m1, l2, verbose_level);
    for (i = 0; i < 4; i++) {
        half_double_six[2 + i] = transversals4[i];
    }
    half_double_six_index = SO->Surf->Schlaefli->find_half_double_six(half_double_six);
    if (f_v) {
        cout << "seventytwo_cases::compute_half_double_six done" << endl;
    }
}
 
void seventytwo_cases::print()
{
    cout << "line_idx=" << line_idx << " "
            "m=(" << m1 << "," << m2 << "," << m3 << ") "
                    "l1=" << l1 << " l2=" << l2 << endl;
}
 
void seventytwo_cases::report_seventytwo_maps_line(ostream &ost)
{
    int c;
 
    c = line_idx * 24 + line_l1_l2_idx;
    ost << c << " & ";
    ost << line_idx << " & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[m1]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[m2]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[m3] << ") & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[l1]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[l2] << ") & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[transversals4[0]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[1]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[2]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[3]]
        << ") & ";
    ost << half_double_six_index << " & ";
    ost << orbit_not_on_conic_idx << " & ";
    ost << pair_orbit_idx << " & ";
    ost << partition_orbit_idx << " & ";
    ost << f2; // << " & ";
    ost << "\\\\";
}
 
void seventytwo_cases::report_seventytwo_maps_top(ostream &ost)
{
    int t = tritangent_plane_idx;
 
    ost << "{\\renewcommand{\\arraystretch}{1.5}" << endl;
    ost << "$$" << endl;
    ost << "\\begin{array}{|c|c|c|c|c|c|c|c|c|c|}" << endl;
    ost << "\\hline" << endl;
    ost << "\\multicolumn{10}{|c|}{\\mbox{Tritangent Plane}\\; \\pi_{" << t << "} = \\pi_{" << Surf->Schlaefli->Eckard_point_label_tex[t] << "} \\; \\mbox{Part "<< line_idx << "}}\\\\" << endl;
    ost << "\\hline" << endl;
    ost << "\\mbox{Clebsch} & m_1-\\mbox{Case} & (m_1,m_2,m_3) & (\\ell_1',\\ell_2') & (t_3',t_4',t_5',t_6') & HDS & \\mbox{Arc} & \\mbox{Pair} & \\mbox{Part} &  \\mbox{Flag-Orb}  \\\\" << endl;
    ost << "\\hline" << endl;
}
 
void seventytwo_cases::report_seventytwo_maps_bottom(ostream &ost)
{
    ost << "\\hline" << endl;
    ost << "\\end{array}" << endl;
    ost << "$$}" << endl;
    ost << "\\bigskip" << endl;
}
 
void seventytwo_cases::report_single_Clebsch_map(ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_single_Clebsch_map" << endl;
    }
 
    report_seventytwo_maps_top(ost);
    report_seventytwo_maps_line(ost);
    report_seventytwo_maps_bottom(ost);
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_single_Clebsch_map done" << endl;
    }
}
 
void seventytwo_cases::report_Clebsch_map_details(ostream &ost, surface_object *SO, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int *H;
    int i;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_map_details" << endl;
    }
 
    ost << "\\bigskip" << endl << endl;
 
    ost << "$\\ell_1=" << Surf->Schlaefli->Labels->Line_label_tex[l1] << " = " << SO->Lines[l1] << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[l1]);
    ost << "$\\\\" << endl;
 
    ost << "$\\ell_2=" << Surf->Schlaefli->Labels->Line_label_tex[l2] << " = " << SO->Lines[l2] << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[l2]);
    ost << "$\\\\" << endl;
 
    SO->SOP->print_single_tritangent_plane(ost, tritangent_plane_idx);
 
    ost << "$m_1=" << Surf->Schlaefli->Labels->Line_label_tex[m1] << " = " << SO->Lines[m1] << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[m1]);
    ost << "$\\\\" << endl;
 
    ost << "$m_2=" << Surf->Schlaefli->Labels->Line_label_tex[m2] << " = " << SO->Lines[m2] << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[m2]);
    ost << "$\\\\" << endl;
 
    ost << "$m_3=" << Surf->Schlaefli->Labels->Line_label_tex[m3] << " = " << SO->Lines[m3] << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[m3]);
    ost << "$\\\\" << endl;
 
 
    ost << "\\bigskip" << endl << endl;
 
    ost << "The associated half double six " << half_double_six_index << " is: $";
    H = Surf->Schlaefli->Double_six + half_double_six_index * 6;
    for (i = 0; i < 6; i++) {
        ost << Surf->Schlaefli->Labels->Line_label_tex[H[i]];
        if (i < 6 - 1) {
            ost << ", ";
        }
    }
    ost << "$\\\\" << endl;
    for (i = 0; i < 6; i++) {
        ost << "$";
        ost << Surf->Schlaefli->Labels->Line_label_tex[H[i]];
        ost << " = " << SO->Lines[H[i]] << " = ";
        Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, SO->Lines[H[i]]);
        ost << "$\\\\" << endl;
    }
 
    //ost << "\\bigskip" << endl << endl;
 
    ost << "P6, P6 * Alpha1, P6 * Alpha1 local, P6 * Alpha1 * Alpha2:\\\\" << endl;
    ost << "{\\renewcommand*{\\arraystretch}{1.5}" << endl;
    ost << "$$" << endl;
    Surf->F->display_table_of_projective_points_easy(ost, P6, 6, 4);
    ost << "\\;" << endl;
    Surf->F->display_table_of_projective_points_easy(ost, P6a, 6, 4);
    ost << "\\;" << endl;
    Surf->F->display_table_of_projective_points_easy(ost, P6_local, 6, 3);
    ost << "\\;" << endl;
    Surf->F->display_table_of_projective_points_easy(ost, P6_local_canonical, 6, 3);
    ost << "$$}" << endl;
 
 
    //ost << "\\bigskip" << endl << endl;
 
    ost << "$\\ell_1\\tau=";
    ost << L1 << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, L1);
    ost << "$\\\\" << endl;
    ost << "$\\ell_2\\tau=";
    ost << L2 << " = ";
    Surf->P->Grass_lines->print_single_generator_matrix_tex(ost, L2);
    ost << "$\\\\" << endl;
 
    //ost << "\\bigskip" << endl << endl;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_map_details" << endl;
    }
}
 
void seventytwo_cases::report_Clebsch_map_aut_coset(ostream &ost, int coset, int relative_order, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int *H;
    int i;
    int ds;
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_map_aut_coset" << endl;
    }
    int c;
 
    ds = half_double_six_index >> 1;
    c = line_idx * 24 + line_l1_l2_idx;
    ost << coset << " & ";
    ost << c << " & ";
    //ost << line_idx << " & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[m1]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[m2]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[m3] << ") & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[l1]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[l2] << ") & ";
    ost << "(" << Surf->Schlaefli->Labels->Line_label_tex[transversals4[0]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[1]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[2]]
        << ", " << Surf->Schlaefli->Labels->Line_label_tex[transversals4[3]]
        << ") & ";
    ost << Surf->Schlaefli->Double_six_label_tex[ds] << " & ";
    H = Surf->Schlaefli->Double_six + half_double_six_index * 6;
    for (i = 0; i < 6; i++) {
        ost << Surf->Schlaefli->Labels->Line_label_tex[H[i]];
        if (i < 6 - 1) {
            ost << ", ";
        }
    }
    ost << " & " << relative_order;
    ost << "\\\\" << endl;
 
 
    //ost << half_double_six_index << " & ";
    //ost << orbit_not_on_conic_idx << " & ";
    //ost << pair_orbit_idx << " & ";
    //ost << partition_orbit_idx << " & ";
    //ost << f2; // << " & ";
 
    if (f_v) {
        cout << "surfaces_arc_lifting_definition_node::report_Clebsch_map_aut_coset done" << endl;
    }
}
 
 
 
 
}}}