  The hyperelliptic Torelli group is the subgroup of the mapping class group
consisting of elements that act trivially on the homology of the surface and
that also commute with some fixed hyperelliptic involution. The authors and
Putman proved that this group is generated by Dehn twists about separating
curves fixed by the hyperelliptic involution. In this paper, we introduce an
algorithmic approach to factoring a wide class of elements of the hyperelliptic
Torelli group into such Dehn twists, and apply our methods to several basic
elements.
