Local Euler-Maclaurin formula for polytopes

Details Local Euler-Maclaurin formula for polytopes Local Euler-Maclaurin formula for polytopes

2005-07-13

arxiv.org/abs/math/0507256v3

Mathematics

Combinatorics

Revised version (July 2006) has some changes of notation and references added

Scientific paper

We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a differential operator of infinite order D(C) on W with constant rational coefficients, which is unchanged when C is translated by an integral vector. Then for every convex rational polytope P in a rational euclidean space V and every polynomial function f (x) on V, the sum of the values of f(x) at the integral points of P is equal to the sum, for all faces F of P, of the integral over F of the function D(N(F)).f, where we denote by N(F) the normal cone to P along F.

Affiliated with

Also associated with

No associations

Rating

Local Euler-Maclaurin formula for polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local Euler-Maclaurin formula for polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local Euler-Maclaurin formula for polytopes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-295212