Calculations in the field of bifurcation with symmetry involve a number of stages.  The first step is to identify the isotropy subgroups for the group's action, which can be done using only the group and its representations. A second stage is to determine the number of invariants and equivariants. A third step is to explicitly construct equivariant vector fields and hence investigate the existence and stability of equilibria and periodic orbits. Most of these calculations are algorithmic and so can be carried out by computer programs. I will describe how this can be done using Gap and Maple and discuss the benefits of this approach.