  We consider the problem of fast zeta and M\"obius transforms in finite
posets, particularly in lattices. It has previously been shown that for a
certain family of lattices, zeta and M\"obius transforms can be computed in
$O(e)$ elementary arithmetic operations, where $e$ denotes the size of the
covering relation. We show that this family is exactly that of geometric
lattices. We also extend the algorithms so that they work in $e$ operations for
all semimodular lattices, including chains and divisor lattices. Finally, for
both transforms, we provide a more general algorithm that works in $e$
operations for all R-labelable posets and their non-graded generalization,
which we call U-labelable.
