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// FILE MHCOUNT.CC: Program to list/count Manin-Heilbronn matrices
//////////////////////////////////////////////////////////////////////////
//
// 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/arith.h>
void outmat(int n, long a, long b, long c, long d)
{
cout<<"mats["<<n<<"]=mat22("<<a<<","<<b<<","<<c<<","<<d<<");\n";
}
int main(void)
{
int seemats=0; int np=10;
cout << "See the matrices? "; cin>>seemats;
cout << "How many primes? "; cin >> np;
for(primevar pr(np); pr.ok(); pr++)
{
long p = (long)pr; if(p==2) continue;
long p2 = (p-1)/2;
int nmats=0;
cout << "p = " << p << ";\t";
if(seemats) cout << "\n";
if(seemats) outmat(nmats,1,0,0,p);
nmats++;
if(seemats) outmat(nmats,p,0,0,1);
nmats++;
for(int s=1; s>-2; s-=2)
for(long r=1; r<=p2; r++)
{
// cout<<"r = " << s*r << ":" << endl;
long x1=p, x2=-s*r, y1=0, y2=1, a=-p, b=s*r, c, q, x3, y3;
if(seemats) outmat(nmats,x1,x2,y1,y2);
nmats++;
while(b!=0)
{
c=mod(a,b); q=(a-c)/b;
x3=q*x2-x1; y3=q*y2-y1;
a=-b; b=c; x1=x2; x2=x3; y1=y2; y2=y3;
if(seemats) outmat(nmats,x1,x2,y1,y2);
nmats++;
}
}
if(seemats)cout<<"\n";
cout << "nmats = " << nmats << ";" << endl;
}
}
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