Givaro
examples/FiniteField/GF128.C

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// ========================================================== //
// Copyright(c)'1994-2009 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Time-stamp: <12 Jun 15 18:38:55 Jean-Guillaume.Dumas@imag.fr>
// Thanks to Dieter Schuster
// ========================================================== //
#include <givaro/gfq.h>
#include <givaro/givtimer.h>
using namespace Givaro;
int main(int argc, char** argv)
{
GFqDom<int64_t> GF128(2, 7);
GF128.init(b, 5U);
GF128.init(c, 3);
GF128.write(std::cout, b) << std::endl;
GF128.write(std::cout, c) << std::endl;
Poly1Dom< GFqDom<int64_t>, Dense> Pol2(F2);
Poly1Dom< GFqDom<int64_t>, Dense>::Element P, Q, R;
Pol2.init(P,Degree(1));
F2.init(P[0],1);
F2.init(P[1],1);
GF128.init(f, P);
GF128.write(std::cout << "2-adic representation of 1+X is: ", f)
<< std::endl
<< " ... while its internal representation is: "
<< f << std::endl;
GF128.write(std::cout << "Indeed, we are in ") <<std::endl;
GF128.generator(gen);
GF128.write(std::cout <<
"In this field, the generator used is (in 2-adic): ", gen)
<< std::endl
<< " whose internal representation is "
<< gen << std::endl;
Poly1PadicDom< GFqDom<int64_t>, Dense > Padic2(Pol2);
//
std::cout << "Irreducible (in 2-adic): "
<< GF128.irreducible() << std::endl;
GF128.init(g, Padic2.radix( Q, Integer(5) ));
GF128.write(std::cout
<< "2-adic representation of 1+X^2 is: ", g)
<< std::endl;
GF128.init(h);
GF128.add(h, g, f);
GF128.write(std::cout
<< "2-adic representation of X+X^2 is: ", h)
<< std::endl;
GF128.mul(h, g, f);
GF128.write(std::cout
<< "2-adic representation of 1+X+X^2+X^3 is: ", h)
<< std::endl;
GF128.div(h, g, f);
GF128.write(std::cout
<< "2-adic representation of 1+X is: ", h)
<< std::endl;
GF128.init(j, Padic2.radix( Q, Integer(213) ));
GF128.write(std::cout
<< "2-adic representation of the moding out of X^7+X^6+X^4+X^2+1 by the irreducible is: ", j)
<< std::endl;
return 0;
}