Function M

IntegerProgramming/binomial.cc:1138–1180

BOOLEAN M(const binomial& a, const binomial& b, const binomial& c)
// Returns TRUE iff lcm(head(a),head(c)) divides properly lcm(head(b),head(c)).
// This is checked by comparing the positive components of the exponent
// vectors.
{


#ifdef SUPPORT_DRIVEN_METHODS

  long b_or_c=b.head_support|c.head_support;

  if((a.head_support|b_or_c) != b_or_c)
    return FALSE;
  // The support of lcm(head(a),head(c)) equals the union of the head supports
  // of a and c. The above condition verifies if the support of
  // lcm(head(a),head(c)) is contained in the support of lcm(head(b),head(c))
  // by checking if head a involves a variable that is not involved in
  // head(b) or head(c).

#endif  // SUPPORT_DRIVEN_METHODS


  BOOLEAN properly=FALSE;

  for(short i=0;i<a._number_of_variables;i++)
  {
    Integer a_exponent=a.exponent_vector[i];
    Integer b_exponent=b.exponent_vector[i];
    Integer c_exponent=c.exponent_vector[i];
    Integer m1=MAXIMUM(a_exponent,c_exponent);
    Integer m2=MAXIMUM(b_exponent,c_exponent);

    if(m1>0)
    {
      if(m1>m2)
        return FALSE;
      if(m1<m2)
        properly=TRUE;
    }
  }

  return properly;
}