  We present several new algorithms for computing factorization invariant
values over affine semigroups. In particular, we give (i) the first known
algorithm to compute the delta set of any affine semigroup, (ii) an improved
method of computing the tame degree of an affine semigroup, and (iii) a dynamic
algorithm to compute catenary degrees of affine semigroup elements. Our
algorithms rely on theoretical results from combinatorial commutative algebra
involving Gr\"obner bases, Hilbert bases, and other standard techniques.
Implementation in the computer algebra system GAP is discussed.
