w3q.cpp

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// w3q.cpp
// 
// Anton Betten
//
// started: March 4, 2011
// 
//
//
 
#include "foundations.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer1_foundations {
namespace geometry {
 
 
 
W3q::W3q()
{
    null();
}
 
W3q::~W3q()
{
    freeself();
}
 
void W3q::null()
{
    q = 0;
    nb_lines = 0;
    P3 = NULL;
    Q4 = NULL;
    F = NULL;
    Basis = NULL;
    Lines = NULL;
    Q4_rk = NULL;
    Line_idx = NULL;
}
 
void W3q::freeself()
{
    if (P3) {
        FREE_OBJECT(P3);
    }
    if (Q4) {
        FREE_OBJECT(Q4);
    }
    if (Basis) {
        FREE_int(Basis);
    }
    if (Lines) {
        FREE_int(Lines);
    }
    if (Q4_rk) {
        FREE_int(Q4_rk);
    }
    if (Line_idx) {
        FREE_int(Line_idx);
    }
    null();
}
 
void W3q::init(field_theory::finite_field *F, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int f_vv = FALSE; //(verbose_level >= 2);
    int f_vvv = FALSE; //(verbose_level >= 3);
    int h, rk;
 
    W3q::F = F;
    W3q::q = F->q;
 
    if (f_v) {
        cout << "W3q::init" << endl;
    }
    P3 = NEW_OBJECT(projective_space);
    Q4 = NEW_OBJECT(orthogonal_geometry::orthogonal);
    Basis = NEW_int(2 * 4);
    
    P3->projective_space_init(3, F,
        FALSE /* f_init_incidence_structure */, 
        verbose_level - 1  /*MINIMUM(verbose_level - 1, 3)*/);
    F = P3->F;
    Q4->init(0, 5, F, verbose_level - 1);
 
 
    if (f_v) {
        cout << "W3q::init before find_lines" << endl;
    }
    find_lines(verbose_level);
    if (f_v) {
        cout << "W3q::init after find_lines" << endl;
    }
 
 
    if (f_v) {
        print_lines();
    }
 
#if 0
    cout << "They are" << endl;
    int_vec_print(cout, Lines, nb_lines);
    cout << endl;
#endif
 
    if (nb_lines != Q4->nb_points) {
        cout << "W3q::init nb_lines != Q4->nb_points" << endl;
        exit(1);
    }
    Q4_rk = NEW_int(nb_lines);
    Line_idx = NEW_int(nb_lines);
 
 
    for (h = 0; h < nb_lines; h++) {
        P3->unrank_line(Basis, Lines[h]);
        if (f_vv) {
            cout << "Line " << h << " is " << Lines[h] << ":" << endl;
            Int_vec_print_integer_matrix_width(cout,
                    Basis, 2, 4, 4, F->log10_of_q);
            cout << endl;
        }
 
        isomorphism_Q4q(Basis, Basis + 4, v5);
 
        if (f_vvv) {
            cout << "v5=";
            Int_vec_print(cout, v5, 5);
            cout << endl;
        }
        
        rk = Q4->rank_point(v5, 1, 0);
 
        if (f_vvv) {
            cout << "orthogonal point rank " << rk << endl;
        }
        
        Q4_rk[h] = rk;
        Line_idx[rk] = h;
    }
    
 
}
 
void W3q::find_lines(int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int h, c;
 
    if (f_v) {
        cout << "W3q::find_lines" << endl;
    }
    Lines = NEW_int(P3->N_lines);
    nb_lines = 0;
    for (h = 0; h < P3->N_lines; h++) {
        P3->unrank_line(Basis, h);
        c = evaluate_symplectic_form(Basis, Basis + 4);
        //c = F->evaluate_symmetric_form(2, Basis, Basis + 4);
        if (c) {
            continue;
        }
        Lines[nb_lines++] = h;
    }
    cout << "We found " << nb_lines << " absolute lines" << endl;
    if (f_v) {
        cout << "W3q::find_lines done" << endl;
    }
}
 
void W3q::print_lines()
{
    int h;
 
    cout << "the lines are:" << endl;
    for (h = 0; h < nb_lines; h++) {
        cout << setw(4) << h << " : ";
        cout << setw(4) << Lines[h] << " : " << endl;
        P3->unrank_line(Basis, Lines[h]);
        Int_matrix_print(Basis, 2, 4);
        cout << endl;
    }
}
 
int W3q::evaluate_symplectic_form(int *x4, int *y4)
{
    return F->Linear_algebra->evaluate_symplectic_form(4, x4, y4);
 
    /*F->add4(
            F->mult(x4[0], y4[1]), 
            F->negate(F->mult(x4[1], y4[0])), 
            F->mult(x4[2], y4[3]), 
            F->negate(F->mult(x4[3], y4[2]))
        );*/
}
 
void W3q::isomorphism_Q4q(int *x4, int *y4, int *v)
{
    v[0] = F->Linear_algebra->Pluecker_12(x4, y4);
    v[1] = F->negate(F->Linear_algebra->Pluecker_13(x4, y4));
    v[2] = F->Linear_algebra->Pluecker_42(x4, y4);
    v[3] = F->negate(F->Linear_algebra->Pluecker_14(x4, y4));
    v[4] = F->Linear_algebra->Pluecker_23(x4, y4);
}
 
 
void W3q::print_by_lines()
{
    int h;
    cout << "The isomorphism is:" << endl;
    cout << "h : Lines[h] : Q4_rk[h] : Line_idx[h] : "
            "x : y : point in Q(4,q)" << endl;
    cout << "Where x and y are a basis for the line" << endl;
    for (h = 0; h < nb_lines; h++) {
        cout << setw(4) << h << " : ";
        cout << setw(4) << Lines[h] << " : ";
        cout << setw(4) << Q4_rk[h] << " : ";
        cout << setw(4) << Line_idx[h] << " : ";
        P3->unrank_line(Basis, Lines[h]);
        Int_vec_print(cout, Basis, 4);
        cout << " : ";
        Int_vec_print(cout, Basis + 4, 4);
        Q4->unrank_point(v5, 1, Q4_rk[h], 0);
        cout << " : ";
        Int_vec_print(cout, v5, 5);
        cout << endl;
    }
}
 
void W3q::print_by_points()
{
    int h;
    cout << "The isomorphism is:" << endl;
    cout << "h : Line_idx[h] : Lines[Line_idx[h]] "
            "x : y : point in Q(4,q)" << endl;
    cout << "Where x and y are a basis for the line" << endl;
    for (h = 0; h < nb_lines; h++) {
        cout << setw(4) << h << " : ";
        cout << setw(4) << Line_idx[h] << " : ";
        cout << setw(4) << Lines[Line_idx[h]] << " : ";
        P3->unrank_line(Basis, Lines[Line_idx[h]]);
        Int_vec_print(cout, Basis, 4);
        cout << " : ";
        Int_vec_print(cout, Basis + 4, 4);
        Q4->unrank_point(v5, 1, h, 0);
        cout << " : ";
        Int_vec_print(cout, v5, 5);
        cout << endl;
    }
}
 
int W3q::find_line(int line)
{
    int idx;
    data_structures::sorting Sorting;
 
    if (!Sorting.int_vec_search(Lines, nb_lines, line, idx)) {
        cout << "W3q::find_line could not find the line" << endl;
        exit(1);
    }
    return idx;
}
 
}}}