  We detail the automatic construction of R matrices corresponding to (the
tensor products of) the (0|\alpha) families of highest-weight representations
of the quantum superalgebras U_q[gl(m|n)]. These representations are
irreducible, contain a free complex parameter \alpha, and are 2^{mn}
dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a
total of 2^{4mn} components, each of which is in general an algebraic
expression in the two complex variables q and \alpha.
  Although the constructions are straightforward, we describe them in full
here, to fill a perceived gap in the literature. As the algorithms are
generally impracticable for manual calculation, we have implemented the entire
process in Mathematica; illustrating our results with U_q[gl(3|1)].
