testIso.c++

This example illustrates how to navigate a field lattice and how to use FAAST::Field::ArtinSchreierExtension(), FAAST::Field::toBivariate() and FAAST::Field::toUnivariate().

/*
    This file is part of the FAAST library.

    Copyright (c) 2009 Luca De Feo and Éric Schost.

    The most recent version of FAAST is available at http://www.lix.polytechnique.fr/~defeo/FAAST

    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License
    as published by the Free Software Foundation; either version 2
    of the License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; see file COPYING. If not, write to the Free Software
    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
*/
#include <faast.hpp>
#include <cstdlib>

using namespace std;
using namespace FAAST;

typedef Field<ZZ_p_Algebra>  gfp;
typedef FieldElement<ZZ_p_Algebra>  gfp_E;

int main(int argv, char* argc[]) {
    double cputime;
    int retval = 0;

    gfp::Infrastructure::BigInt p;
    long d, l;
    if (cin.peek() != EOF) {
      cin >> p; cin >> d; cin >> l;
    } else {
      p = 3; d = 2; l = 3;
    }

    cout << "Using " << gfp::Infrastructure::name << endl << endl;
    cputime = -NTL::GetTime();
    const gfp* K = &(gfp::createField(p,d));
    cputime += NTL::GetTime();
    cout << *K << " in " << cputime << endl;
#ifdef FAAST_TIMINGS
    cout << "Time spent building the irreducible polynomial : "
        << gfp::TIME.BUILDIRRED << endl;
#endif
    cout << endl;

    cout << "\tCreate\tCrStem\tPushDow\tLiftUp\tPrePseu\tPreLift" << endl;
    for (int i = 1 ; i <= l ; i++) {
        cout << i << "\t";
        gfp_E alpha;
        do {
            alpha = K->random();
        } while (alpha.trace() == 0);
        cputime = -NTL::GetTime();
        K = &(K->ArtinSchreierExtension(alpha));
        cputime += NTL::GetTime();
        cout << cputime << "\t";
#ifdef FAAST_TIMINGS
        cout << gfp::TIME.BUILDSTEM;
#endif
        cout << "\t";

        const gfp& L = K->stemField().subField();
        vector<gfp_E> v;
        gfp_E a = K->random(), b;
        cputime = -NTL::GetTime();
        L.toBivariate(a, v);
        cputime += NTL::GetTime();
        cout << cputime << "\t";

        cputime = -NTL::GetTime();
        K->toUnivariate(v, b);
        cputime += NTL::GetTime();
        cout << cputime << "\t";

        if (a != b) {
            cout << "ERROR : Results don't match" << endl;
            cout << a << endl;
            cout << b << endl;
            vector<gfp_E>::iterator it;
            for (it = v.begin() ; it != v.end() ; it++)
                cout << *it << " ";
            cout << endl;
            retval = 1;
        }

#ifdef FAAST_TIMINGS
        cout << gfp::TIME.PSEUDOTRACES << "\t";
        cout << gfp::TIME.LIFTUP;
#endif
        cout << endl;
    }
#ifdef FAAST_TIMINGS
    cout << endl << "Time spent inverting the matrix " <<
        gfp::TIME.ARTINMATRIX << endl;
#endif

    return retval;
}