  Computing the autotopism group of a partial Latin rectangle can be performed
in a variety of ways. This pilot study has two aims: (a) to compare these
methods experimentally, and (b) to identify the design goals one should have in
mind for developing practical software. To this end, we compare six families of
algorithms (two backtracking methods and four graph automorphism methods), with
and without the use of entry invariants, on two test suites. We consider two
entry invariants: one determined by the frequencies of row, column, and symbol
representatives, and one determined by $2 \times 2$ submatrices. We find: (a)
with very few entries, many symmetries often exist, and these should be
identified mathematically rather than computationally, (b) with an intermediate
number of entries, a quick-to-compute entry invariant was effective at reducing
the need for computation, (c) with an almost-full partial Latin rectangle, more
sophisticated entry invariants are needed, and (d) the performance for (full)
Latin squares is significantly poorer than other partial Latin rectangles of
comparable size, obstructed by the existence of Latin squares with large
(possibly transitive) autotopism groups.
