findDivisor()

std::pair< bool, NCF4::PreRow > NCF4::findDivisor ( Word w )

private

Definition at line 710 of file NCF4.cpp.

{
  Word newword;
 
  // look in previous F4 matrix for Monom before checking mWordTable
 
  auto usePreviousSuffix = findPreviousReducerSuffix(word);
  if (usePreviousSuffix.first)
    {
      // here, we use a multiple of a previously reduced row
      Word tmpWord;
      if (word.size() != 0)
        tmpWord.init(word.begin(), word.begin() + 1);
      return std::make_pair(true, PreRow {tmpWord,
                                          usePreviousSuffix.second,
                                          Word(),
                                          PreviousReducerPreRow});
    }
  auto usePreviousPrefix = findPreviousReducerPrefix(word);
  if (usePreviousPrefix.first)
    {
      // here, we use a multiple of a previously reduced row
      Word tmpWord;
      if (word.size() != 0)
        tmpWord.init(word.end()-1, word.end());
      return std::make_pair(true, PreRow {Word(),
                                          usePreviousPrefix.second,
                                          tmpWord,
                                          PreviousReducerPreRow});
    }
 
  // if we are here, then the Monom does not have a prefix/suffix
  // that was processed previously.
 
  // look in mWordTable for Monom
  std::pair<int,int> divisorInfo;
  
  // TODO: for certain inputs (e.g. Monoms that we *know* are of
  //       the form xm or mx for m a standard monomial and x a
  //       variable, one needs only to check prefixes or
  //       suffixes, not all subwords.  Not sure how to utilize that
  //       just yet.
 
  bool found = mWordTable.subword(word, divisorInfo);
  
  // if newword = x^a x^b x^c, with x^b in the word table, then:
  //  divisorInfo.first = index of the GB element with x^b as lead monomial.
  //  divisorInfo.second = position of the start of x^b in newword
  //   (that is, the length of x^a).
  if (not found)
    return std::make_pair(false, PreRow {Word(), 0, Word(), ReducerPreRow});
  // if found, then return this information to caller
  Word prefix = Word(word.begin(), word.begin() + divisorInfo.second);
  Word divisorWord = mWordTable[divisorInfo.first];
  Word suffix = Word(word.begin() + divisorInfo.second + divisorWord.size(),
                     word.end());
  return std::make_pair(true, PreRow {prefix, divisorInfo.first, suffix, ReducerPreRow});
}

References findPreviousReducerPrefix(), findPreviousReducerSuffix(), Word::init(), mWordTable, prefix(), PreviousReducerPreRow, ReducerPreRow, Word::size(), suffix(), and word.

Referenced by processWordInPreRow().