  The action of a torus on a graded module over a polynomial ring extends to
the entire minimal free resolution of the module. We explain how to determine
the action of the torus on the free modules in the resolution, when the
resolution can be calculated explicitly. The problem is reduced to analyzing
how the weights of a torus propagate along an equivariant map of free modules.
The results obtained are used to design algorithms which have been implemented
in the software system Macaulay2.
