action_on_spread_set.cpp

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// action_on_spread_set.cpp
//
// Anton Betten
// October 9, 2013
 
#include "foundations/foundations.h"
#include "group_actions.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer3_group_actions {
namespace induced_actions {
 
 
action_on_spread_set::action_on_spread_set()
{
    null();
}
 
action_on_spread_set::~action_on_spread_set()
{
    free();
}
 
void action_on_spread_set::null()
{
    mtx1 = NULL;
    mtx2 = NULL;
    Elt1 = NULL;
    Elt2 = NULL;
    subspace1 = NULL;
    subspace2 = NULL;
}
 
void action_on_spread_set::free()
{
    if (mtx1) {
        FREE_int(mtx1);
        }
    if (mtx2) {
        FREE_int(mtx2);
        }
    if (Elt1) {
        FREE_int(Elt1);
        }
    if (Elt2) {
        FREE_int(Elt2);
        }
    if (subspace1) {
        FREE_int(subspace1);
        }
    if (subspace2) {
        FREE_int(subspace2);
        }
    null();
}
 
void action_on_spread_set::init(
        actions::action *A_PGL_n_q,
        actions::action *A_PGL_k_q, groups::sims *G_PGL_k_q,
    int k, field_theory::finite_field *F, int verbose_level)
// we are acting on the elements of G_PGL_k_q, so the degree of the action 
// is the order of this group.
// A_PGL_k_q in only needed for make_element
{
    int f_v = (verbose_level >= 1);
    ring_theory::longinteger_object go;
    
    if (f_v) {
        cout << "action_on_spread_set::init" << endl;
        }
    action_on_spread_set::k = k;
    action_on_spread_set::F = F;
    action_on_spread_set::q = F->q;
    action_on_spread_set::A_PGL_n_q = A_PGL_n_q;
    action_on_spread_set::A_PGL_k_q = A_PGL_k_q;
    action_on_spread_set::G_PGL_k_q = G_PGL_k_q;
    n = 2 * k;
    k2 = k * k;
    low_level_point_size = k2;
 
    if (f_v) {
        cout << "action_on_spread_set::init" << endl;
        cout << "k=" << k << endl;
        cout << "n=" << n << endl;
        cout << "q=" << q << endl;
        cout << "low_level_point_size=" << low_level_point_size << endl;
        }
    
    G_PGL_k_q->group_order(go);
    degree = go.as_int();
    if (f_v) {
        cout << "action_on_spread_set::init the order of "
                "the group of matrices is " << degree << endl;
        }
 
    Elt1 = NEW_int(A_PGL_k_q->elt_size_in_int);
    Elt2 = NEW_int(A_PGL_k_q->elt_size_in_int);
    
 
    mtx1 = NEW_int(k * k);
    mtx2 = NEW_int(k * k);
    subspace1 = NEW_int(k * n);
    subspace2 = NEW_int(k * n);
    
    if (f_v) {
        cout << "degree = " << degree << endl;
        cout << "low_level_point_size = " << low_level_point_size << endl;
        }
    
    if (f_v) {
        cout << "action_on_spread_set::init done" << endl;
        }
}
 
void action_on_spread_set::report(std::ostream &ost, int verbose_level)
{
    ost << "Action on spread set has degree = " << degree << "\\\\" << endl;
    ost << "Low-level point size = " << low_level_point_size << "\\\\" << endl;
    ring_theory::longinteger_object go;
    G_PGL_k_q->group_order(go);
    ost << "PGL$(" << k << "," << q << ")$ has order " << go << "\\\\" << endl;
}
 
long int action_on_spread_set::compute_image_int(int *Elt,
        long int rk, int verbose_level)
{
    //verbose_level = 2;
    int f_v = (verbose_level >= 1);
    int f_vv = (verbose_level >= 2);
    long int i, rk2;
    
    if (f_v) {
        cout << "action_on_spread_set::compute_image_int "
                "rk = " << rk << endl;
        }
 
    unrank_point(rk, mtx1, verbose_level - 1);
    matrix_to_subspace(mtx1, subspace1, verbose_level);
 
    if (f_vv) {
        cout << "action_on_spread_set::compute_image_int "
                "after unrank_point" << endl;
        Int_vec_print_integer_matrix_width(cout,
                subspace1, k, n, n, F->log10_of_q);
        cout << "action_on_spread_set::compute_image_int "
                "group element:" << endl;
        Int_matrix_print(Elt, n, n);
        }
 
    for (i = 0; i < k; i++) {
        A_PGL_n_q->element_image_of_low_level(
            subspace1 + i * n, subspace2 + i * n, Elt, verbose_level - 1);
        }
 
    if (f_vv) {
        cout << "action_on_spread_set::compute_image_int "
                "after applying group element" << endl;
        Int_vec_print_integer_matrix_width(cout,
                subspace2, k, n, n, F->log10_of_q);
        }
 
    subspace_to_matrix(subspace2, mtx2, verbose_level - 1);
    rk2 = rank_point(mtx2, verbose_level - 1);
 
    if (f_v) {
        cout << "action_on_spread_set::compute_image_int "
                "image of " << rk << " is " << rk2 << endl;
        }
    return rk2;
}
 
void action_on_spread_set::matrix_to_subspace(
        int *mtx, int *subspace, int verbose_level)
{
    int i, j;
    
    Int_vec_zero(subspace, k * n);
    for (i = 0; i < k; i++) {
        subspace[i * n + i] = 1;
        for (j = 0; j < k; j++) {
            subspace[i * n + k + j] = mtx[i * k + j];
            }
        }
}
 
void action_on_spread_set::subspace_to_matrix(
        int *subspace, int *mtx, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i, j, r;
    
    if (f_v) {
        cout << "action_on_spread_set::subspace_to_matrix" << endl;
        }
    
    r = F->Linear_algebra->Gauss_easy(subspace, k, n);
    if (r != k) {
        cout << "action_on_spread_set::subspace_to_matrix "
                "r != k" << endl;
        exit(1);
        }
    if (f_v) {
        cout << "action_on_spread_set::subspace_to_matrix "
                "after Gauss_easy" << endl;
        }
    for (i = 0; i < k; i++) {
        for (j = 0; j < k; j++) {
            mtx[i * k + j] = subspace[i * n + k + j];
            }
        }
    if (f_v) {
        cout << "action_on_spread_set::subspace_to_matrix "
                "done" << endl;
        }
}
 
void action_on_spread_set::unrank_point(
        long int rk, int *mtx, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    
    if (f_v) {
        cout << "action_on_spread_set::unrank_point "
                "rk = " << rk << endl;
        }
    G_PGL_k_q->element_unrank_lint(rk, Elt1);
    Int_vec_copy(Elt1, mtx, k * k);
    if (f_v) {
        cout << "action_on_spread_set::unrank_point done" << endl;
        }
}
 
long int action_on_spread_set::rank_point(
        int *mtx, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    long int rk;
    
    if (f_v) {
        cout << "action_on_spread_set::rank_point" << endl;
        }
    A_PGL_k_q->make_element(Elt2, mtx, 0 /* verbose_level */);
 
    rk = G_PGL_k_q->element_rank_lint(Elt2);
    if (f_v) {
        cout << "action_on_spread_set::rank_point done, rk = " << rk << endl;
        }
    return rk;
}
 
void action_on_spread_set::compute_image_low_level(
        int *Elt, int *input, int *output, int verbose_level)
{
    //verbose_level = 2;
    int f_v = (verbose_level >= 1);
    int f_vv = (verbose_level >= 2);
    int i;
    
    if (f_v) {
        cout << "action_on_spread_set::compute_image_low_level" << endl;
        }
    if (f_vv) {
        cout << "action_on_spread_set::compute_image_low_level "
                "input=" << endl;
        Int_matrix_print(input, k, k);
        cout << "action_on_spread_set::compute_image_low_level "
                "matrix=" << endl;
        Int_matrix_print(Elt, n, n);
        }
 
    matrix_to_subspace(input, subspace1, verbose_level- 1);
 
 
    for (i = 0; i < k; i++) {
        A_PGL_n_q->element_image_of_low_level(
            subspace1 + i * n,
            subspace2 + i * n,
            Elt,
            verbose_level - 2);
        }
    if (f_vv) {
        cout << "action_on_spread_set::compute_image_low_level "
                "after mult=" << endl;
        Int_matrix_print(subspace2, k, n);
        }
 
    subspace_to_matrix(subspace2, output, verbose_level - 1);
 
    if (f_vv) {
        cout << "action_on_spread_set::compute_image_low_level "
                "output=" << endl;
        Int_matrix_print(output, k, k);
        }
 
    if (f_v) {
        cout << "action_on_spread_set::compute_image_low_level "
                "done" << endl;
        }
}
 
}}}