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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/nsfs.h"
#include "maths/nmatrixint.h"
#include "triangulation/ncomponent.h"
#include "triangulation/ntetrahedron.h"
#include "subcomplex/nlayeredchainpair.h"
namespace regina {
NLayeredChainPair* NLayeredChainPair::clone() const {
NLayeredChainPair* ans = new NLayeredChainPair();
if (chain[0])
ans->chain[0] = new NLayeredChain(*chain[0]);
if (chain[1])
ans->chain[1] = new NLayeredChain(*chain[1]);
return ans;
}
NLayeredChainPair* NLayeredChainPair::isLayeredChainPair(
const NComponent* comp) {
// Basic property check.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return 0;
unsigned long nTet = comp->getNumberOfTetrahedra();
if (nTet < 2)
return 0;
if (comp->getNumberOfVertices() != 1)
return 0;
// We have at least two tetrahedra and precisely 1 vertex.
// The component is closed and orientable (and connected, since it's
// a component).
// Start with tetrahedron 0. This must belong to *some* chain.
NTetrahedron* base = comp->getTetrahedron(0);
NLayeredChain* first;
NLayeredChain* second;
// Note that we only need check permutations in S3 since we can
// arbitrarily assign the role of one vertex in the tetrahedron.
NTetrahedron* firstBottom;
NTetrahedron* firstTop;
NTetrahedron* secondBottom;
NTetrahedron* secondTop;
NPerm firstBottomRoles, firstTopRoles, secondBottomRoles, secondTopRoles;
for (int p = 0; p < 6; p++) {
first = new NLayeredChain(base, allPermsS3[p]);
first->extendMaximal();
firstTop = first->getTop();
firstBottom = first->getBottom();
firstTopRoles = first->getTopVertexRoles();
firstBottomRoles = first->getBottomVertexRoles();
// Check to see if the first chain fills the entire component.
if (first->getIndex() == nTet) {
// The only success here will be if we have a chain pair of
// indices (n-1) and 1, which is in fact a layered loop.
NLayeredChain* longChain = new NLayeredChain(
firstBottom, firstBottomRoles);
if (longChain->extendBelow())
if (longChain->getBottom() == firstTop &&
longChain->getBottomVertexRoles() ==
firstTopRoles * NPerm(3, 2, 1, 0)) {
// We've got a layered loop!
NLayeredChainPair* ans = new NLayeredChainPair();
if (nTet == 2) {
// The new chain is already too long.
delete longChain;
longChain = new NLayeredChain(
firstBottom, firstBottomRoles);
}
// Extend longChain to (n-1) tetrahedra.
while (longChain->getIndex() + 1 < nTet)
longChain->extendBelow();
ans->chain[1] = longChain;
ans->chain[0] = new NLayeredChain(
firstBottom->getAdjacentTetrahedron(
firstBottomRoles[0]),
firstBottom->getAdjacentTetrahedronGluing(
firstBottomRoles[0]) * firstBottomRoles *
NPerm(0, 2, 1, 3));
delete first;
return ans;
}
delete longChain;
delete first;
continue;
}
// At this point we must have run into the second chain.
secondBottom = firstTop->getAdjacentTetrahedron(firstTopRoles[3]);
if (secondBottom == firstTop || secondBottom == firstBottom ||
secondBottom == 0) {
delete first;
continue;
}
second = new NLayeredChain(secondBottom,
firstTop->getAdjacentTetrahedronGluing(firstTopRoles[3]) *
firstTopRoles * NPerm(1, 3, 0, 2));
while (second->extendAbove())
;
if (second->getIndex() + first->getIndex() != nTet) {
delete first;
delete second;
continue;
}
secondTop = second->getTop();
secondTopRoles = second->getTopVertexRoles();
secondBottomRoles = second->getBottomVertexRoles();
// At this point we have two chains that together have the
// correct number of tetrahedra. All we need do is check the
// remaining three between-chain gluings.
if (secondTop == firstTop->getAdjacentTetrahedron(firstTopRoles[0]) &&
secondBottom == firstBottom->getAdjacentTetrahedron(
firstBottomRoles[2]) &&
secondTop == firstBottom->getAdjacentTetrahedron(
firstBottomRoles[1]) &&
secondTopRoles == firstTop->getAdjacentTetrahedronGluing(
firstTopRoles[0]) * firstTopRoles * NPerm(0, 2, 1, 3) &&
secondBottomRoles == firstBottom->getAdjacentTetrahedronGluing(
firstBottomRoles[2]) * firstBottomRoles *
NPerm(3, 1, 2, 0) &&
secondTopRoles == firstBottom->getAdjacentTetrahedronGluing(
firstBottomRoles[1]) * firstBottomRoles *
NPerm(2, 0, 3, 1)) {
// We found one!
NLayeredChainPair* ans = new NLayeredChainPair();
if (first->getIndex() > second->getIndex()) {
ans->chain[0] = second;
ans->chain[1] = first;
} else {
ans->chain[0] = first;
ans->chain[1] = second;
}
return ans;
} else {
delete first;
delete second;
}
}
// Nothing was found. Sigh.
return 0;
}
NManifold* NLayeredChainPair::getManifold() const {
NSFSpace* ans = new NSFSpace();
ans->insertFibre(2, -1);
ans->insertFibre(chain[0]->getIndex() + 1, 1);
ans->insertFibre(chain[1]->getIndex() + 1, 1);
ans->reduce();
return ans;
}
NAbelianGroup* NLayeredChainPair::getHomologyH1() const {
// The first homology group can be obtained from the matrix:
//
// [ 1 -1 1 ]
// [ n_1 1 1 ]
// [ 1 n_2 -1 ]
//
// This is established simply by examining the edges on the boundary
// of each layered chain.
NAbelianGroup* ans = new NAbelianGroup();
NMatrixInt mat(3, 3);
mat.initialise(1);
mat.entry(0, 1) = mat.entry(2, 2) = -1;
mat.entry(1, 0) = chain[0]->getIndex();
mat.entry(2, 1) = chain[1]->getIndex();
ans->addGroup(mat);
return ans;
}
} // namespace regina
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