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// thilbert.cc: test of Hilbert symbol functions
//////////////////////////////////////////////////////////////////////////
//
// 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/marith.h>
#include <eclib/quadratic.h>
#include <eclib/conic.h>
#include <eclib/hilbert.h>
//#define AUTO
int main()
{
bigint a,b,p,x0,y0,z0; int resp, res, checkres;
bigint zero, one; zero=0; one=1;
#ifdef AUTO
long la,lb,abmax;
cout<<"Enter max for a,b: "; cin>>abmax;
for(la=-abmax; la<=abmax; la++)
for(lb=-abmax; lb<=abmax; lb++)
{
a=la; b=lb;
if(a*b==0) continue;
#else
while(1) {
cout<<"Enter nonzero a and b: "; cin>>a>>b;
if(a*b==zero) break;
#endif
res=checkres=0;
cout<<"("<<a<<","<<b<<")_p\n";
resp = local_hilbert(a,b,0);
cout<<0<<"\t"<<resp<<endl;
res = res|resp;
checkres = checkres^resp;
resp = local_hilbert(a,b,2);
cout<<2<<"\t"<<resp<<endl;
res = res|resp;
checkres = checkres^resp;
vector<bigint> plist = vector_union(pdivs(a),pdivs(b));
for (vector<bigint>::iterator pr = plist.begin(); pr!=plist.end(); pr++)
{
p=*pr; if(p==2) continue;
resp=local_hilbert(a,b,p);
cout << p << "\t" << resp << endl;
res = res|resp;
checkres = checkres^resp;
}
cout<<"\nGlobal symbol = " << res << endl;
cout<<"Check (should be 0) = " << checkres << endl;
int gres = global_hilbert(a,b,plist,p);
if(res==gres)
cout<<"--agrees with single call to global_hilbert()\n";
else
cout<<"--DISAGREES with single call to global_hilbert()\n";
quadratic q(a,zero,b);
int oldres = !solve_conic(q,one,x0,y0,z0,4);
if(oldres==res)
{
cout<<"--agrees with solve_conic()\n";
}
else cout<<"--DISAGREES with solve_conic()\n";
}
cout<<endl;
}
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