action_on_determinant.cpp

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// action_on_determinant.cpp
//
// Anton Betten
// January 16, 2009
 
#include "foundations/foundations.h"
#include "group_actions.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer3_group_actions {
namespace induced_actions {
 
 
action_on_determinant::action_on_determinant()
{
    null();
}
 
action_on_determinant::~action_on_determinant()
{
    free();
}
 
void action_on_determinant::null()
{
    M = NULL;
}
 
void action_on_determinant::free()
{
    
    null();
}
 
 
void action_on_determinant::init(actions::action &A,
        int f_projective, int m, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    ring_theory::longinteger_object go;
    number_theory::number_theory_domain NT;
    
    if (f_v) {
        cout << "action_on_determinant::init" << endl;
        cout << "f_projective=" << f_projective << endl;
        cout << "m=" << m << endl;
        }
    action_on_determinant::f_projective = f_projective;
    action_on_determinant::m = m;
    if (A.type_G != matrix_group_t) {
        cout << "action_on_determinant::init action "
                "not of matrix group type" << endl;
        exit(1);
        }
    M = A.G.matrix_grp;
    q = M->GFq->q;
    if (f_projective) {
        degree = NT.gcd_lint(m, q - 1);
        }
    else {
        degree = q - 1;
        }
    if (f_v) {
        cout << "degree=" << degree << endl;
        }
    
    if (f_v) {
        cout << "action_on_determinant::init field order is " << q << endl;
        }
}
 
long int action_on_determinant::compute_image(actions::action *A,
        int *Elt, long int i, int verbose_level)
{
    //verbose_level = 1;
    int f_v = (verbose_level >= 1);
    long int a, b, c, l = 0, j;
    
    if (f_v) {
        cout << "action_on_determinant::compute_image "
                "i = " << i << endl;
        }
    if (i < 0 || i >= degree) {
        cout << "action_on_determinant::compute_image "
                "i = " << i << " out of range" << endl;
        exit(1);
        }
    if (f_projective) {
        a = M->GFq->alpha_power(i);
        }
    else {
        a = i + 1;
        }
    b = M->GFq->Linear_algebra->matrix_determinant(Elt, M->n, 0);
    c = M->GFq->mult(a, b);
    if (f_projective) {
        l = M->GFq->log_alpha(c);
        j = l % degree;
        }
    else {
        j = c - 1;
        }
    if (f_v) {
        cout << "action_on_determinant::compute_image "
                "det = " << b << endl;
        cout << "action_on_determinant::compute_image "
                << a << " * " << b << " = " << c << endl;
        if (f_projective) {
            cout << "f_projective, a = " << a
                    << " l = " << l << " c = " << c << endl;
            }
        cout << "image of " << i << " is " << j << endl;
        }
    return j;
}
 
}}}