Function relations

IntegerProgramming/LLL.cc:207–433

short relations(BigInt **b, const short& number_of_vectors,
                const short& vector_dimension, BigInt**& H)
{

// first check arguments

  if(number_of_vectors<0)
  {
    cerr<<"\nWARNING: short relations(BigInt**, const short&, const short&, "
      "BigInt**):\nargument number_of_vectors out of range"<<endl;
    return -1;
  }

  if(vector_dimension<=0)
  {
    cerr<<"\nWARNING: short relations(BigInt**, const short&, const short&, "
      "BigInt**):\nargument vector_dimension out of range"<<endl;
    return -1;
  }


// consider special case

  if(number_of_vectors==1)
    // Only one vector which has no relations if it is not zero,
    // else relation 1.
  {
    short r=1;    // Suppose the only column of the matrix is zero.

    for(short m=0;m<vector_dimension;m++)
      if(b[0][m]!=BigInt(0))
        // nonzero entry detected
        r=0;

    if(r==1)
    {
      H=new BigIntP[1];
      H[0]=new BigInt[1];
      H[0][0]=1;
      // This is the lattice basis of the relations...
    }

    return r;
  }


// memory allocation

// The names are chosen (as far as possible) according to Cohen's book.
// However, for technical reasons, the indices do not run from 1 to
// (e.g.) number_of_vectors, but from 0 to number_of_vectors-1.
// Therefore all indices are shifted by -1 in comparison with this book,
// except from the indices of the array d which has size
// number_of_vectors+1.

  H=new BigIntP[number_of_vectors];
  for(short n=0;n<number_of_vectors;n++)
    H[n]=new BigInt[number_of_vectors];