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// tilll.cc: test program for illl integer lll reduction
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib 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.
//
// eclib 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 eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
#include <eclib/mvector.h>
#include <eclib/mmatrix.h>
#include <eclib/illl.h>
int main()
{
int i, j, k, n;
cout<<"Enter size n: "; cin>>n;
vec_m* b = new vec_m[n+1];
b[0]=vec_m(n);
for(i=1; i<=n; i++)
{
b[0][i]=1; // these are the weights
b[i]=vec_m(n);
cout<<"Enter vector number "<<(i)<<": ";
cin>>b[i];
}
cout<<"Before reduction, vectors are:\n";
for(i=1; i<=n; i++) cout<<b[i]<<endl;
cout<<endl;
cout << "FIRST METHOD: JC'S implementation of integer LLL from HC's book\n";
lll_reduce(n,b);
cout<<"After reduction, vectors are:\n";
for(i=1; i<=n; i++) cout<<b[i]<<endl;
cout<<endl;
vec_m shortest=b[1];
bigint min_length=sdot(b,1,1);
for(i=1; i<=n; i++)
cout<<"Square length of vector "<<i<<" is "<<sdot(b,i,i)<<endl;
if(n==3) // then we know that any vector shorter than b[1] must be
// of the form a1*b[1]+a2*b[2]+a3*b[3] with all ai in {-1,0,1}
{
cout<<"Candidates for shortest vectors:\n";
int ok=1, better=0;
for(i=1; ok&&(i>-2); i--)
for(j=1; ok&&(j>-2); j--)
for(k=1; ok&&(k>-2); k--)
{
if((i==0)&&(j==0)&&(k==0)) {ok=0;break;}
vec_m v=i*b[1]+j*b[2]+k*b[3];
bigint norm = sqr(v[1])+sqr(v[2])+sqr(v[3]);
cout<<"("<<i<<","<<j<<","<<k<<"): "<<v<<", norm = "<<norm<<endl;
if(norm<min_length) {min_length=norm; shortest=v; better=1;}
}
cout<<"The shortest vector is "<<shortest
<<" with square length "<<min_length<<endl;
if(better)
cout<<"-- shorter than b[1]!"<<endl;
}
delete[] b;
}
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