Algorithm and Software for Integration over a Convex Polyhedron

Software for exact integration of polynomials over polyhedra

“…4. Finally, we compare LattE integrale to other software tools and computational studies [16,38,39,3].…”

“…It is known that achieving such a decomposition is equivalent to the so-called Fourier-Motzkin elimination procedure [45] and as such it is of exponential complexity. The paper [39] gives an application to finding the probability a random-coefficient polynomial has one or two real roots in the interval [−1, 1]. To do this, they use their software to find the volume of a polytope.…”

“…M. Korenblit and E. Shmerling present a numerical integration algorithm in [39] which is based on a special decomposition of the integral into regions that have well-defined upper and lower limits of integration that, on an ordering of the variables, x 1 , x 2 , . .…”