Software for Exact Integration of Polynomials over Polyhedra
  We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software implementation and provide benchmark computations. The computation of integrals of polynomials over polyhedral regions has many applications; here we demonstrate our algorithmic tools solving a challenge from combinatorial voting theory. 
Jesus De Loera, Brandon Dutra, Matthias Koeppe, Stanislav Moreinis,   Gregory Pinto, Jianqiu Wu
math.MG