docs: def IJ(mu, N):
      """Return i, j, s for any given mu."""
      if mu == 0: return 1, 1, 1
  
      if mu not in range(0, N**2):
          raise ValueError('mu has an invalid value mu='+str(mu)+'.')
  
      if 1 <= mu <= N-1:
          return mu+1, mu+1, 1
      else:
          m = N-1
          M = N*(N-1)/2
          for jj in range(1, N):
              for ii in range(jj+1, N+1):
                  m += 1
                  if m == mu or m+M == mu:
                      if mu > N*(N+1)/2 - 1:
                          return ii, jj, -1
                      else:
                          return ii, jj, 1