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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2009, 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 "subcomplex/nlayeredlensspace.h"
#include "triangulation/nedge.h"
#include "triangulation/ncomponent.h"
#include "triangulation/ntetrahedron.h"
namespace regina {
NLayeredLensSpace* NLayeredLensSpace::clone() const {
NLayeredLensSpace* ans = new NLayeredLensSpace();
ans->torus = torus->clone();
ans->mobiusBoundaryGroup = mobiusBoundaryGroup;
ans->p = p;
ans->q = q;
return ans;
}
NLayeredLensSpace* NLayeredLensSpace::isLayeredLensSpace(
const NComponent* comp) {
// Basic property check.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return 0;
if (comp->getNumberOfVertices() > 1)
return 0;
unsigned long nTet = comp->getNumberOfTetrahedra();
NLayeredSolidTorus* torus;
for (unsigned long i = 0; i < nTet; i++) {
torus = NLayeredSolidTorus::formsLayeredSolidTorusBase(
comp->getTetrahedron(i));
if (torus) {
// We have found a layered solid torus; either this makes the
// layered lens space or nothing makes the layered lens space.
NTetrahedron* tet = torus->getTopLevel();
int tf0 = torus->getTopFace(0);
int tf1 = torus->getTopFace(1);
if (tet->adjacentTetrahedron(tf0) != tet) {
delete torus;
return 0;
}
/* We already know the component is orientable; no need
to check orientation!
if (perm.sign() == 1) {
delete torus;
return 0;
}*/
// This is the real thing!
NLayeredLensSpace* ans = new NLayeredLensSpace();
ans->torus = torus;
NPerm perm = tet->adjacentGluing(tf0);
if (perm[tf1] == tf0) {
// Snapped shut.
ans->mobiusBoundaryGroup = torus->getTopEdgeGroup(
5 - NEdge::edgeNumber[tf0][tf1]);
} else {
// Twisted shut.
ans->mobiusBoundaryGroup = torus->getTopEdgeGroup(
NEdge::edgeNumber[perm[tf1]][tf0]);
}
// Work out p and q.
switch (ans->mobiusBoundaryGroup) {
// For layered solid torus (x < y < z):
case 0:
// L( x + 2y, y )
ans->p =
torus->getMeridinalCuts(1) + torus->getMeridinalCuts(2);
ans->q = torus->getMeridinalCuts(1);
break;
case 1:
// L( 2x + y, x )
ans->p =
torus->getMeridinalCuts(0) + torus->getMeridinalCuts(2);
ans->q = torus->getMeridinalCuts(0);
break;
case 2:
// L( y - x, x )
ans->p =
torus->getMeridinalCuts(1) - torus->getMeridinalCuts(0);
if (ans->p == 0)
ans->q = 1;
else
ans->q = torus->getMeridinalCuts(0) % ans->p;
break;
}
// Find the nicest possible value for q.
// Choices are +/- q, +/- 1/q.
if (ans->p > 0) {
if (2 * ans->q > ans->p)
ans->q = ans->p - ans->q;
if (ans->q > 0) {
unsigned long qAlt = modularInverse(ans->p, ans->q);
if (2 * qAlt > ans->p)
qAlt = ans->p - qAlt;
if (qAlt < ans->q)
ans->q = qAlt;
}
}
return ans;
}
}
return 0;
}
NManifold* NLayeredLensSpace::getManifold() const {
return new NLensSpace(p, q);
}
NAbelianGroup* NLayeredLensSpace::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
if (p == 0)
ans->addRank();
else if (p > 1)
ans->addTorsionElement(p);
return ans;
}
std::ostream& NLayeredLensSpace::writeName(std::ostream& out) const {
if (p == 3 && q == 1) {
out << "L(3,1)";
if (torus->getNumberOfTetrahedra() != 2)
return out;
else if (isSnapped())
return out << " (1)";
else
return out << " (2)";
} else
return out << "L(" << p << ',' << q << ')';
}
std::ostream& NLayeredLensSpace::writeTeXName(std::ostream& out) const {
if (p == 3 && q == 1) {
out << "L_{3,1}";
if (torus->getNumberOfTetrahedra() != 2)
return out;
else if (isSnapped())
return out << "^{(1)}";
else
return out << "^{(2)}";
} else
return out << "L_{" << p << ',' << q << '}';
}
} // namespace regina
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