  This paper presents an algorithm to maximize the volume of an affine slice
through a given semialgebraic set. This slice-volume task is formulated as an
infinite-dimensional linear program in continuous functions, inspired by prior
work in volume computation of semialgebraic sets. A convergent sequence of
upper-bounds to the maximal slice volume are computed using the
moment-Sum-of-Squares hierarchy of semidefinite programs in increasing size.
The computational complexity of this scheme can be reduced by utilizing
topological structure (in dimensions 2, 3, 4, 8) and symmetry. This numerical
convergence can be accelerated through the introduction of redundant
Stokes-based constraints. Demonstrations of slice-volume calculation are
performed on example sets.
