sylow_structure.cpp

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/*
 * sylow_structure.cpp
 *
 *  Created on: Mar 24, 2019
 *      Author: betten
 */
 
 
 
 
#include "foundations/foundations.h"
#include "group_actions.h"
 
using namespace std;
 
 
namespace orbiter {
namespace layer3_group_actions {
namespace groups {
 
 
 
sylow_structure::sylow_structure()
{
    null();
}
 
sylow_structure::~sylow_structure()
{
    freeself();
}
 
void sylow_structure::null()
{
    primes = NULL;
    exponents = NULL;
    nb_primes = 0;
    S = NULL;
    Sub = NULL;
}
 
void sylow_structure::freeself()
{
    if (primes) {
        FREE_int(primes);
        }
    if (exponents) {
        FREE_int(exponents);
        }
    if (Sub) {
        FREE_OBJECTS(Sub);
        }
    null();
}
 
void sylow_structure::init(sims *S, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int idx;
 
    if (f_v) {
        cout << "sylow_structure::init" << endl;
    }
 
    ring_theory::longinteger_domain D;
    int i;
 
    sylow_structure::S = S;
    S->group_order(go);
 
    D.factor(go, nb_primes,
            primes, exponents,
            verbose_level);
 
    if (f_v) {
        cout << "sylow_structure::init group order = " << go << " = ";
        for (i = 0; i < nb_primes; i++) {
            cout << primes[i] << "^" << exponents[i];
            if (i < nb_primes - 1) {
                cout << " * ";
            }
        }
        cout << endl;
    }
 
    Sub = NEW_OBJECTS(subgroup, nb_primes);
 
    for (idx = 0; idx < nb_primes; idx++) {
        strong_generators *SG;
        sims *P;
 
        P = NEW_OBJECT(sims);
        SG = NEW_OBJECT(strong_generators);
        if (f_v) {
            cout << "sylow_structure::init "
                    "computing Sylow subgroup for prime "
                    << primes[idx] << ": " << endl;
        }
        S->sylow_subgroup(primes[idx], P, verbose_level);
        SG->init_from_sims(P, verbose_level);
        Sub[idx].init_from_sims(S, P, SG, verbose_level);
    }
 
    if (f_v) {
        cout << "sylow_structure::init done" << endl;
    }
}
 
void sylow_structure::report(ostream &ost)
{
    int idx;
 
    for (idx = 0; idx < nb_primes; idx++) {
        ost << "The " << primes[idx] << "-Sylow groups have order $"
                << primes[idx] << "^{" << exponents[idx] << "}$\\\\" << endl;
    }
    for (idx = 0; idx < nb_primes; idx++) {
        ost << "One " << primes[idx] << "-Sylow group has "
                "the following generators:\\\\" << endl;
        Sub[idx].report(ost);
    }
}
 
 
 
}}}