Polynom<MonomType>* BooleanInvolutiveBasis<MonomType>::NormalForm(const Triple<MonomType>* triple) const
{
/* As far as currentTriple can't be 0 (checked in QSET and TSET),
* no need to check for NULL pointer.
*/
const Triple<MonomType>* involutiveDivisor = 0;
Polynom<MonomType>* originalForm = 0;
Polynom<MonomType>* normalForm = new Polynom<MonomType>();
if (triple->GetVariable() == -1)
{
originalForm = new Polynom<MonomType>(*triple->GetPolynom());
}
else
{
originalForm = new Polynom<MonomType>(*triple->GetWeakAncestor()->GetPolynom());
(*originalForm) *= triple->GetVariable();
}
while (!originalForm->IsZero())
{
involutiveDivisor = IntermediateBasis.Find(originalForm->Lm());
while (involutiveDivisor)
{
originalForm->HeadReduction(*involutiveDivisor->GetPolynom());
if (!originalForm->IsZero())
{
involutiveDivisor = IntermediateBasis.Find(originalForm->Lm());
}
else
{
involutiveDivisor = 0;
}
}
if (!originalForm->IsZero())
{
(*normalForm) += originalForm->Lm();
originalForm->RidOfLm();
}
}
delete originalForm;
return normalForm;
}
void BooleanInvolutiveBasis<MonomType>::ReduceSet(bool toGroebner)
{
std::list<Polynom<MonomType>*> tmpPolySet;
GBasis.sort(PointerMoreComparator<Polynom<MonomType> >());
while (!GBasis.empty())
{
Polynom<MonomType>* currentPolynom = GBasis.front();
GBasis.pop_front();
currentPolynom = Reduce(currentPolynom, tmpPolySet, toGroebner);
if (currentPolynom && !currentPolynom->IsZero())
{
const MonomType& hLm = currentPolynom->Lm();
typename std::list<Polynom<MonomType>*>::iterator iteratorTmpPolySet = tmpPolySet.begin();
while (iteratorTmpPolySet != tmpPolySet.end())
{
if ((**iteratorTmpPolySet).Lm().IsDivisibleBy(hLm))
{
GBasis.push_back(*iteratorTmpPolySet);
iteratorTmpPolySet = tmpPolySet.erase(iteratorTmpPolySet);
}
else
{
++iteratorTmpPolySet;
}
}
tmpPolySet.push_back(currentPolynom);
}
}
unsigned tmpPolySetSize = static_cast<unsigned int>(tmpPolySet.size());
for (register unsigned i = 0; i < tmpPolySetSize; ++i)
{
Polynom<MonomType>* currentPolynom = tmpPolySet.front();
tmpPolySet.pop_front();
currentPolynom = Reduce(currentPolynom, tmpPolySet, toGroebner);
if (!currentPolynom || currentPolynom->IsZero())
{
tmpPolySetSize--;
}
else
{
tmpPolySet.push_back(currentPolynom);
}
}
GBasis = tmpPolySet;
}
void BooleanInvolutiveBasis<MonomType>::ConstructInvolutiveBasis()
{
typename TSet<MonomType>::Iterator tit(IntermediateBasis.Begin());
Polynom<MonomType>* newNormalForm = 0;
Triple<MonomType>* currentTriple = 0;
while (!ProlongationsSet.Empty())
{
currentTriple = ProlongationsSet.Get();
newNormalForm = NormalForm(currentTriple);
/* As far as currentTriple can't be 0 (checked in QSET and TSET),
* NormalForm can't return 0.
*/
std::set<typename MonomType::Integer> currentNmpSet;
const Triple<MonomType>* currentAncestor = 0;
if (!newNormalForm->IsZero() && newNormalForm->Lm() == currentTriple->GetPolynomLm())
{
currentNmpSet = currentTriple->GetNmp();
currentAncestor = currentTriple->GetAncestor();
if (currentAncestor == currentTriple)
{
currentAncestor = 0;
}
}
delete currentTriple;
if (!newNormalForm->IsZero())
{
std::list<Triple<MonomType>*> newProlongations;
tit = IntermediateBasis.Begin();
while (tit != IntermediateBasis.End())
{
if ((**tit).GetPolynomLm().IsTrueDivisibleBy(newNormalForm->Lm()))
{
ProlongationsSet.DeleteDescendants(*tit);
newProlongations.push_back(*tit);
tit = IntermediateBasis.Erase(tit);
}
else
{
++tit;
}
}
IntermediateBasis.PushBack(new Triple<MonomType>(newNormalForm, currentAncestor, currentNmpSet, 0, -1));
if (!newNormalForm->Degree())
{
return;
}
IntermediateBasis.CollectNonMultiProlongations(--IntermediateBasis.End(), newProlongations);
ProlongationsSet.Insert(newProlongations);
}
else
{
delete newNormalForm;
}
}
}