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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* 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; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include "algebra/nabeliangroup.h"
#include "manifold/nlensspace.h"
#include "maths/numbertheory.h"
#include "triangulation/ntriangulation.h"
namespace regina {
void NLensSpace::reduce() {
if (p == 0) {
q = 1;
return;
} else if (p == 1) {
q = 0;
return;
}
// p > 1 and gcd(p,q) = 1.
// Reduce q to +/-q.
q = q % p;
if (2 * q > p)
q = p - q;
unsigned long inv = modularInverse(p, q);
if (2 * inv > p)
inv = p - inv;
if (inv < q)
q = inv;
}
NTriangulation* NLensSpace::construct() const {
NTriangulation* ans = new NTriangulation();
ans->insertLayeredLensSpace(p, q);
return ans;
}
NAbelianGroup* NLensSpace::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
if (p == 0)
ans->addRank();
else if (p > 1)
ans->addTorsionElement(p);
return ans;
}
std::ostream& NLensSpace::writeName(std::ostream& out) const {
if (p == 0)
out << "S2 x S1";
else if (p == 1)
out << "S3";
else if (p == 2 && q == 1)
out << "RP3";
else
out << "L(" << p << ',' << q << ')';
return out;
}
std::ostream& NLensSpace::writeTeXName(std::ostream& out) const {
if (p == 0)
out << "S^2 \\times S^1";
else if (p == 1)
out << "S^3";
else if (p == 2 && q == 1)
out << "\\mathbb{R}P^3";
else
out << "L(" << p << ',' << q << ')';
return out;
}
} // namespace regina
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