VectorOf<Word> SGOfFreeNilpotentGroupRep::normalClosureBasis() const {
//@ep I have found that the process is slower with the full basis,
// so I form it from the scratch.
MalcevSet newBasis(theGenerators, theParentGroup.collector());
newBasis.makeNormalClosure();
// The basis is found. Now we try to reduce it to make further
// processing easier.
VectorOf<Word> basis = newBasis.getCommutatorWords();
// First, we reduce words in terms of basic commutators.
// We could proceed without this step, but it helps
// to reduce the second one greatly.
FreeGroup F( theParentGroup.theHirschNumber() );
basis = F.nielsenBasis(basis);
// Convert words in terms of basic commutators to group
// generators.
for(int i = 0; i < basis.length(); i++) {
PolyWord pw = basis.val(i);
basis[i] = theParentGroup.commutators().wordForm().toWord(pw);
}
// Now reduce this vector
FreeGroup F1( theParentGroup.numberOfGenerators() );
basis = F1.nielsenBasis(basis);
return basis;
}
void Homology::findCompatibleBasisPair(int master, std::vector<int> dim)
{
if(!this->isHomologyComputed(dim)) this->findHomologyBasis(dim);
if(!this->isCohomologyComputed(dim)) this->findCohomologyBasis(dim);
for(unsigned int idim = 0 ; idim < dim.size(); idim++) {
int d = dim.at(idim);
if(d < 1 || d > 2) continue;
int n = this->betti(d);
if(n < 2) continue;
if((int)_chains[d].size() != n || (int)_cochains[d].size() != n) {
Msg::Warning("Cannot produce compatible %d-(co)homology bases.", d);
Msg::Debug("%d basis %d-chains and %d basis %d-cochains.",
(int)_chains[d].size(), d, (int)_cochains[d].size(), d);
continue;
}
fullMatrix<double> m(n,n);
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if(master==0) m(i,j) = incidence(*_cochains[d].at(i), *_chains[d].at(j));
else m(i,j) = incidence(*_chains[d].at(i), *_cochains[d].at(j));
}
}
int det = m.determinant();
if(abs(det) != 1 || !m.invertInPlace()) {
Msg::Warning("Cannot produce compatible %d-(co)homology bases.", d);
Msg::Debug("Incidence matrix: ");
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
Msg::Debug("(%d, %d) = %d", i, j, m(i,j));
continue;
}
std::vector<Chain<int>*> newBasis(n);
if(master==0) {
for(int i = 0; i < n; i++) {
newBasis.at(i) = new Chain<int>();
for(int j = 0; j < n; j++) {
*newBasis.at(i) += (int)m(i,j)*(*_cochains[d].at(j));
}
}
for(int i = 0; i < n; i++) {
newBasis.at(i)->setName(_cochains[d].at(i)->getName());
delete _cochains[d].at(i);
_cochains[d].at(i) = newBasis.at(i);
}
}
else {
for(int i = 0; i < n; i++) {
newBasis.at(i) = new Chain<int>();
for(int j = 0; j < n; j++) {
*newBasis.at(i) += (int)m(i,j)*(*_chains[d].at(j));
}
}
for(int i = 0; i < n; i++) {
newBasis.at(i)->setName(_chains[d].at(i)->getName());
delete _chains[d].at(i);
_chains[d].at(i) = newBasis.at(i);
}
}
}
}