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;
}
// put the words to the set
MalcevSet::MalcevSet(const VectorOf<Word>& v, const NGCollector& nc)
: isBasis(false), isNormal(dontknow), theCollector(nc)
{
for(int i = 0; i < v.length(); i++)
addWord( v.val(i) );
}