  This paper describes a method for the automatic evaluation of the Links-Gould
two-variable polynomial link invariant (LG) for any link, given only a braid
presentation. This method is currently feasible for the evaluation of LG for
links for which we have a braid presentation of string index at most 5. Data
are presented for the invariant, for all prime knots of up to 10 crossings and
various other links. LG distinguishes between these links, and also detects the
chirality of those that are chiral. In this sense, it is more sensitive than
the well-known two-variable HOMFLY and Kauffman polynomials. When applied to
examples which defeat the HOMFLY invariant, interestingly, LG `almost' fails.
The automatic method is in fact applicable to the evaluation of any such state
sum invariant for which an appropriate R matrix and cap and cup matrices have
been determined.
