action_projective.cpp

Go to the documentation of this file.

/*
 * action_projective.cpp
 *
 *  Created on: Feb 18, 2019
 *      Author: betten
 */
 
 
 
#include "foundations/foundations.h"
#include "group_actions.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer3_group_actions {
namespace actions {
 
groups::strong_generators *action::set_stabilizer_in_projective_space(
        geometry::projective_space *P,
    long int *set, int set_size, //int &canonical_pt,
    int *canonical_set_or_NULL,
    int verbose_level)
// assuming we are in a linear action.
// added 2/28/2011, called from analyze.cpp
// November 17, 2014 moved here from TOP_LEVEL/extra.cpp
// December 31, 2014, moved here from projective_space.cpp
{
    int f_v = (verbose_level >= 1);
    geometry::object_with_canonical_form *OwCF;
    nauty_interface_with_group Nau;
 
    if (f_v) {
        cout << "action::set_stabilizer_in_projective_space" << endl;
        cout << "verbose_level = " << verbose_level << endl;
        cout << "set_size = " << set_size << endl;
    }
 
 
    OwCF = NEW_OBJECT(geometry::object_with_canonical_form);
 
    OwCF->init_point_set(set, set_size, verbose_level);
 
    OwCF->P = P;
 
    int nb_rows, nb_cols;
    data_structures::bitvector *Canonical_form = NULL;
 
    OwCF->encoding_size(
            nb_rows, nb_cols,
            verbose_level);
 
 
 
    groups::strong_generators *SG;
    data_structures::nauty_output *NO;
 
 
    NO = NEW_OBJECT(data_structures::nauty_output);
    NO->allocate(nb_rows + nb_cols, 0 /* verbose_level */);
 
    if (f_v) {
        cout << "action::set_stabilizer_in_projective_space before Nau.set_stabilizer_of_object" << endl;
    }
    SG = Nau.set_stabilizer_of_object(
            OwCF,
        this /* A_linear */,
        FALSE /* f_compute_canonical_form */, Canonical_form,
        NO,
        verbose_level - 2);
    if (f_v) {
        cout << "action::set_stabilizer_in_projective_space after Nau.set_stabilizer_of_object" << endl;
    }
 
    if (f_v) {
        cout << "canonical_form_nauty::quartic_curve "
                "go = " << *NO->Ago << endl;
 
        NO->print_stats();
 
 
    }
 
 
    FREE_OBJECT(NO);
 
 
    FREE_OBJECT(OwCF);
 
    return SG;
}
 
int action::reverse_engineer_semilinear_map(
        geometry::projective_space *P,
    int *Elt, int *Mtx, int &frobenius,
    int verbose_level)
// uses the function A->element_image_of
{
    int f_v = (verbose_level >= 1);
    int ret;
 
    if (f_v) {
        cout << "action::reverse_engineer_semilinear_map, before P->reverse_engineer_semilinear_map" << endl;
    }
    ret = P->reverse_engineer_semilinear_map(Elt, Mtx, frobenius, verbose_level);
    if (f_v) {
        cout << "action::reverse_engineer_semilinear_map, after P->reverse_engineer_semilinear_map" << endl;
    }
    if (f_v) {
        cout << "action::reverse_engineer_semilinear_map done" << endl;
    }
    return ret;
}
 
 
void action::report_fixed_objects_in_P3(ostream &ost,
        geometry::projective_space *P3,
    int *Elt,
    int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i, j, cnt;
    int v[4];
    field_theory::finite_field *F;
 
    if (f_v) {
        cout << "action::report_fixed_objects_in_P3" << endl;
    }
    //ost << "\\section{Fixed Objects}" << endl;
 
    F = P3->F;
 
    ost << "\\bigskip" << endl;
 
    ost << "The element" << endl;
    ost << "$$" << endl;
    element_print_latex(Elt, ost);
    ost << "$$" << endl;
    ost << "has the following fixed objects:\\\\" << endl;
 
 
    ost << "\\bigskip" << endl;
    //ost << "Fixed Points:\\" << endl;
 
    cnt = 0;
    for (i = 0; i < P3->N_points; i++) {
        j = element_image_of(i, Elt, 0 /* verbose_level */);
        if (j == i) {
            cnt++;
        }
    }
 
    ost << "There are " << cnt << " fixed points, they are: \\\\" << endl;
    for (i = 0; i < P3->N_points; i++) {
        j = element_image_of(i, Elt, 0 /* verbose_level */);
        F->PG_element_unrank_modified(v, 1, 4, i);
        if (j == i) {
            ost << i << " : ";
            Int_vec_print(ost, v, 4);
            ost << "\\\\" << endl;
            cnt++;
        }
    }
 
    ost << "\\bigskip" << endl;
    //ost << "Fixed Lines\\\\" << endl;
 
    {
        action *A2;
 
        A2 = induced_action_on_grassmannian(2, 0 /* verbose_level*/);
 
        cnt = 0;
        for (i = 0; i < A2->degree; i++) {
            j = A2->element_image_of(i, Elt, 0 /* verbose_level */);
            if (j == i) {
                cnt++;
            }
        }
 
        ost << "There are " << cnt << " fixed lines, they are: \\\\" << endl;
        cnt = 0;
        for (i = 0; i < A2->degree; i++) {
            j = A2->element_image_of(i, Elt, 0 /* verbose_level */);
            if (j == i) {
                ost << i << " : $";
                A2->G.AG->G->print_single_generator_matrix_tex(ost, i);
                ost << "$\\\\" << endl;
                cnt++;
            }
        }
 
        FREE_OBJECT(A2);
    }
 
    ost << "\\bigskip" << endl;
    //ost << "Fixed Planes\\\\" << endl;
 
    {
        action *A3;
 
        A3 = induced_action_on_grassmannian(3, 0 /* verbose_level*/);
 
        cnt = 0;
        for (i = 0; i < A3->degree; i++) {
            j = A3->element_image_of(i, Elt, 0 /* verbose_level */);
            if (j == i) {
                cnt++;
            }
        }
 
        ost << "There are " << cnt << " fixed planes, they are: \\\\" << endl;
        cnt = 0;
        for (i = 0; i < A3->degree; i++) {
            j = A3->element_image_of(i, Elt, 0 /* verbose_level */);
            if (j == i) {
                ost << i << " : $";
                A3->G.AG->G->print_single_generator_matrix_tex(ost, i);
                ost << "$\\\\" << endl;
                cnt++;
            }
        }
 
        FREE_OBJECT(A3);
    }
    if (f_v) {
        cout << "action::report_fixed_objects_in_P3 done" << endl;
    }
}
 
 
}}}