Method reduce_head_by

IntegerProgramming/binomial.cc:814–899

int binomial::reduce_head_by(const binomial& b, const term_ordering& w)
{
  Integer reduction_number=head_reductions_by(b);
  if(reduction_number<=0)
    return 0;

  for(short i=0;i<_number_of_variables;i++)
    exponent_vector[i]-=(reduction_number * b.exponent_vector[i]);
  // multiple reduction
  // reduction corresponds to subtraction of vectors

  short sign=w.compare_to_zero(exponent_vector);


#ifdef NO_SUPPORT_DRIVEN_METHODS

  if(sign==0)
    // binomial reduced to zero
    return 2;

  for(short i=0;i<_number_of_variables;i++)
    exponent_vector[i]*=sign;

#endif  // NO_SUPPORT_DRIVEN_METHODS


#ifdef SUPPORT_DRIVEN_METHODS

  head_support=0;
  tail_support=0;

  if(sign==0)
    // binomial reduced to zero
    return 2;

  short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long);


  // recompute the support vectors

#ifdef SUPPORT_VARIABLES_FIRST

  for(short i=0;i<_number_of_variables;i++)
  {

    Integer& actual_entry=exponent_vector[i];
    // to avoid unnecessary pointer arithmetic

    actual_entry*=sign;

    if(i<size_of_support_vectors)
      if(actual_entry>0)
        head_support|=(1<<i);
      else
        if(actual_entry<0)
          tail_support|=(1<<i);
  }