  We use a well known problem in discrete and computational geometry
(partitions of measures by $k$-fans) as a motivation and as a point of
departure to illustrate many aspects, both theoretical and computational, of
the problem of calculating the obstructions for the existence of equivariant
maps. A variety of techniques are introduced and discussed with the emphasis on
concrete and explicit calculations. This eventually leads (Theorems 18 and 19)
to an almost exhaustive analysis of when such maps do or do not exist in the
particular case of interest.
