cyclotomic_sets.cpp

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/*
 * cyclotomic_sets.cpp
 *
 *  Created on: Sep 30, 2021
 *      Author: betten
 */
 
 
 
#include "foundations.h"
 
using namespace std;
 
namespace orbiter {
namespace layer1_foundations {
namespace number_theory {
 
 
cyclotomic_sets::cyclotomic_sets()
{
    n = 0;
    q = 0;
    m = 0;
    qm = 0;
    Index = NULL;
    S = NULL;
}
 
cyclotomic_sets::~cyclotomic_sets()
{
    if (Index) {
        FREE_int(Index);
    }
    if (S) {
        FREE_OBJECT(S);
    }
}
 
void cyclotomic_sets::init(field_theory::finite_field *F, int n, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "cyclotomic_sets::init, n=" << n << endl;
    }
    cyclotomic_sets::n = n;
    cyclotomic_sets::q = F->q;
    //longinteger_object Qm1, Idx;
    //longinteger_domain D;
    number_theory_domain NT;
 
    m = NT.order_mod_p(q, n);
    if (f_v) {
        cout << "cyclotomic_sets::init order of q mod n is m=" << m << endl;
    }
 
    qm = NT.i_power_j(q, m);
    if (f_v) {
        cout << "cyclotomic_sets::init qm = " << qm << endl;
    }
 
    //D.create_qnm1(Qm1, q, m);
 
    //D.integral_division_by_int(Qm1, n, Idx, r);
 
    int i;
    int *f_taken;
    int *transversal;
    long int *set;
    int sz;
    int tl;
 
    Index = NEW_int(n);
    f_taken = NEW_int(n);
    transversal = NEW_int(n);
    for (i = 0; i < n; i++) {
        f_taken[i] = FALSE;
    }
 
 
    S = NEW_OBJECT(data_structures::set_of_sets);
 
    if (f_v) {
        cout << "cyclotomic_sets::init before S->init_simple" << endl;
    }
 
    S->init_simple(n /* underlying_set_size */,
            n /* nb_sets */, 0 /* verbose_level */);
 
    if (f_v) {
        cout << "cyclotomic_sets::init after S->init_simple" << endl;
    }
 
    tl = 0;
 
    for (i = 0; i < n; i++) {
        if (f_taken[i]) {
            cout << q << "-cyclotomic coset of "
                    << i << " already taken" << endl;
            continue;
        }
        transversal[tl] = i;
        f_taken[i] = TRUE;
        set = NEW_lint(n);
        set[0] = i;
        sz = 1;
        Index[i] = tl;
        if (f_v) {
            cout << q << "-cyclotomic coset of "
                    << i << " : " << i;
        }
        while (TRUE) {
            i = (q * i) % n;
            if (f_taken[i]) {
                break;
            }
            f_taken[i] = TRUE;
            set[sz++] = i;
            Index[i] = tl;
        }
        S->Sets[tl] = set;
        S->Set_size[tl] = sz;
        tl++;
        if (f_v) {
            cout << " has size = " << sz << endl;
        }
    }
    S->nb_sets = tl;
 
    if (f_v) {
        cout << "cyclotomic_sets::init cyclotomic sets are:" << endl;
        S->print_table();
        cout << "cyclotomic_sets::init Index:" << endl;
        Int_vec_print(cout, Index, n);
        cout << endl;
    }
 
 
 
    if (f_v) {
        cout << "cyclotomic_sets::init done" << endl;
    }
}
 
void cyclotomic_sets::print()
{
    S->print_table();
}
 
void cyclotomic_sets::print_latex(std::ostream &ost)
{
    S->print_table_latex_simple(ost);
}
 
void cyclotomic_sets::print_latex_with_selection(std::ostream &ost, int *Selection, int nb_sel)
{
    S->print_table_latex_simple_with_selection(ost, Selection, nb_sel);
}
 
 
}}}