  We introduce a new computable invariant for strong shift equivalence of
shifts of finite type. The invariant is based on an invariant introduced by
Trow, Boyle, and Marcus, but has the advantage of being readily computable.
  We summarize briefly a large-scale numerical experiment aimed at deciding
strong shift equivalence for shifts of finite type given by irreducible
$2\times 2$-matrices with entry sum less than 25, and give examples
illustrating to power of the new invariant, i.e., examples where the new
invariant can disprove strong shift equivalence whereas the other invariants
that we use can not.
