Software for exact integration of polynomials over polyhedra

Authors:
J. A. De Loera;B. Dutra;M. KöPpe;S. Moreinis;G. Pinto;J. Wu
Affiliations:
Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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Abstract

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 by some of the authors. We provide a new software implementation and 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.