// complete algorithm to compute a Groebner basis F
void gb( IntermediateBasis &F, int n) {
int nextIndex = F.size();
rearrangeBasis(F, -1);
interreduction(F);
Pairs B = makeList(F, n);
//unsigned int countAddPoly = 0;
//unsigned int numSPoly= 0;
int interreductionCounter = 0;
while (!B.empty()) {
Pair pair = *(B.begin());
B.erase(B.begin());
if (isGoodPair(pair,F,B,n)) {
//numSPoly++;
BRP S = sPolynomial(pair,F,n);
reduce(S,F);
if ( ! S.isZero() ) {
//countAddPoly++;
F[nextIndex] = S;
if(interreductionCounter == 5) {
interreductionCounter = 0;
interreduction(F);
B = makeList(F, n);
} else {
interreductionCounter++;
Pairs newList = makeNewPairs(nextIndex, F, n);
B.insert(newList.begin(), newList.end());
}
nextIndex++;
}
}
}
interreduction(F);
//cout << "we computed " << numSPoly << " S Polynomials and added " << countAddPoly << " of them to the intermediate basis." << endl;
}
// generate list of index pairs for a new index and an intermediate basis
Pairs makeNewPairs(int newIndex, const IntermediateBasis &F, int n) {
Pairs B;
Pairs::iterator position = B.begin();
for(int i=-n; i<0; i++) {
Pair pair = Pair(i, newIndex, F);
position = B.insert(position, pair);
}
IntermediateBasis::const_iterator end = F.end();
end--;
for(IntermediateBasis::const_iterator iter = F.begin(); iter != end; ++iter) {
int j = iter->first;
Pair pair = Pair(newIndex, j, F);
if (pair.good) {
position = B.insert(position, pair);
}
}
return B;
}
// generate list of index pairs for given intermediate basis
// first insert all pairs with FPs, then insert pairs of all other polynomials
// the list of indeces was ordered by increasingly
Pairs makeList(const IntermediateBasis &F, int n) {
Pairs B;
Pairs::iterator position = B.begin();
IntermediateBasis::const_iterator end = F.end();
for(IntermediateBasis::const_iterator iter = F.begin(); iter != end; ++iter) {
int j = iter->first;
for(int i=-n; i<0; i++) {
Pair pair = Pair(i, j, F);
position = B.insert(position, pair);
}
for(int i=0; i<j; i++) {
Pair pair = Pair(i, j, F);
if (pair.good) {
position = B.insert(position, pair);
}
}
}
return B;
}