Exemple #1
0
// 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;
}
Exemple #2
0
// 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;
}
Exemple #3
0
// 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;
}