sims3.cpp

Go to the documentation of this file.

// sims3.cpp
//
// Anton Betten
// November 22, 2016
 
#include "foundations/foundations.h"
#include "group_actions.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer3_group_actions {
namespace groups {
 
 
 
void sims::subgroup_make_characteristic_vector(
        sims *Sub, int *C, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int go, go_sub;
    long int i, j;
 
 
    if (f_v) {
        cout << "sims::subgroup_make_characteristic_vector" << endl;
        }
 
    go = group_order_lint();
    Int_vec_zero(C, go);
    go_sub = Sub->group_order_lint();
    for (i = 0; i < go_sub; i++) {
        Sub->element_unrank_lint(i, Elt1);
        j = element_rank_lint(Elt1);
        C[j] = TRUE;
        }
    if (f_v) {
        cout << "The characteristic vector of the "
                "subgroup of order " << go_sub << " is:" << endl;
        orbiter_kernel_system::Orbiter->Int_vec->print_as_table(cout, C, go, 25);
        }
    if (f_v) {
        cout << "sims::subgroup_make_characteristic_vector done" << endl;
        }
}
 
void sims::normalizer_based_on_characteristic_vector(int *C_sub, 
    int *Gen_idx, int nb_gens, int *N, long int &N_go, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int go;
    long int i, j, a;
    data_structures_groups::vector_ge *gens;
 
 
    if (f_v) {
        cout << "sims::normalizer_based_on_characteristic_vector" << endl;
        }
 
    gens = NEW_OBJECT(data_structures_groups::vector_ge);
    gens->init(A, verbose_level - 2);
    gens->allocate(nb_gens, verbose_level - 2);
    for (j = 0; j < nb_gens; j++) {
        a = Gen_idx[j];
        element_unrank_lint(a, gens->ith(j));
        }
 
    go = group_order_lint();
    Int_vec_zero(N, go);
 
    N_go = 0;
    for (i = 0; i < go; i++) {
        element_unrank_lint(i, Elt1);
        A->element_invert(Elt1, Elt2, 0);
        for (j = 0; j < nb_gens; j++) {
            A->element_mult(Elt2, gens->ith(j), Elt3, 0);
            A->element_mult(Elt3, Elt1, Elt4, 0);
            a = element_rank_lint(Elt4);
            if (!C_sub[a]) {
                break;
                }
            }
        if (j == nb_gens) {
            N[i]++;
            N_go++;
            }
        }
    FREE_OBJECT(gens);
    if (f_v) {
        cout << "sims::normalizer_based_on_characteristic_vector done" << endl;
        }
}
 
void sims::order_structure_relative_to_subgroup(int *C_sub, 
    int *Order, int *Residue, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int go;
    long int i, j, a;
 
 
    if (f_v) {
        cout << "sims::order_structure_relative_to_subgroup" << endl;
        }
 
 
    go = group_order_lint();
    for (i = 0; i < go; i++) {
        element_unrank_lint(i, Elt1);
        A->element_move(Elt1, Elt2, 0);
        for (j = 1; ; j++) {
            a = element_rank_lint(Elt2);
            if (C_sub[a]) {
                break;
                }
            A->element_mult(Elt2, Elt1, Elt3, 0);
            A->element_move(Elt3, Elt2, 0);
            }
        Order[i] = j;
        Residue[i] = a;
#if 0
        if ((j % 2) == 0) {
            cout << "element " << i << " has relative order " << j << endl;
            cout << "element:" << endl;
            A->element_print(Elt1, cout);
            }
#endif
        }
 
    if (f_v) {
        cout << "sims::order_structure_relative_to_subgroup done" << endl;
        }
}
 
}}}