Hi, Recalling (see ?nspin), in

    > npspin(coord, h, G, curinfo)

h is a Maple rank-2 tensor_type object of character [1,-1] (first index contravariant and second index covariant), representing the tetrad transformation "matrix". Using tensorial notation (to the left) and Maple matrix notation (to the right),

                   a
                  h   = h[compts][a,b]
                    b

where h entering the right-hand-side is the object created using the tensor[create] command, h[compts] is the matrix contents of that rank-2 tensor, and h satisfies (sum over the repeated indice c)

                    c    [  0,  1,  0,  0  ]
              h   h    = [  1,  0,  0,  0  ].
               ac  b     [  0,  0,  0, -1  ]
                         [  0,  0, -1,  0  ]

You can use the tetrad of null 4-vectors you mentioned [l, n, m, \bar{m}], satisfying

              a       a       a    _ _a
           l l  =  n n  =  m m  =  m m  = 0
            a       a       a       a

              a        _a
           l n  =  - m m  = 1
            a         a

to construct h with two covariant indices (so a Maple tensor of rank-2 with character [-1, -1]), via

                                   _
               h   = [ l , n , m , m  ]
                ab      b   b   b   b

and then use the metric tensor to rise the first indice and obtain the object entering the calling sequence of nspin. The formulas to compute the spin coefficients in terms of this tetrad of 4-vectors and the metrics are the standard ones; see for instance (5.5) page 167 of http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.cmp/1103840725 Although you already have the tetrad of 4-vectors, you may prefer to compute the spin coefficients directly from the connections using the tensor[convertNP] command. In turn other commands of the tensor package allow you to construct the connections from the metric tensor - see tensor[connexF]. Alternatively, the GRTensor package mentioned by Tom also has a command, nptetrad, which computes the null tetrad of 4-vectors from the the metric tensor - see http://grtensor.phy.queensu.ca/Griihelp/nptetrad.help. As far as I remember the GRTensor does not have a separate command to compute the spin coefficients. Edgardo S. Cheb-Terrab Research Fellow, Maplesoft