bareiss_det()

ring_elem DetComputation::bareiss_det ( )

private

Definition at line 345 of file det.cpp.

{
  // Computes the determinant of the p by p matrix D. (dense form).
  int sign = 1;
  size_t pivot_col;
 
  ring_elem pivot = R->from_long(0);
  ring_elem lastpivot = R->from_long(0);
 
  for (size_t r = p - 1; r >= 1; --r)
    {
      R->remove(lastpivot);
      lastpivot = pivot;
      if (!get_pivot(D, r, pivot, pivot_col))  // sets pivot_col and pivot
        {
          // Remove the rest of D.
          for (size_t i = 0; i <= r; i++)
            for (size_t j = 0; j <= r; j++) R->remove(D[i][j]);
          R->remove(lastpivot);
          return R->from_long(0);
        }
      for (size_t i = 0; i < r; i++) gauss(D, i, r, pivot_col, lastpivot);
 
      if (((r + pivot_col) % 2) == 1)
        sign = -sign;  // MES: do I need to rethink this logic?
 
      for (size_t c = 0; c <= r; c++)
        if (c != pivot_col)
          R->remove(D[r][c]);
        else
          D[r][c] = ZERO_RINGELEM;
    }
 
  R->remove(pivot);
  R->remove(lastpivot);
  ring_elem r = D[0][0];
  D[0][0] = ZERO_RINGELEM;
 
  if (sign < 0) R->negate_to(r);
 
  return r;
}

References D, gauss(), get_pivot(), p, R, and ZERO_RINGELEM.

Referenced by step().