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Polyhedra :: ehrhart

ehrhart -- calculates the Ehrhart polynomial of a polytope

Synopsis

Description

ehrhart can only be applied to polytopes, i.e. compact polyhedra. To calculate the Ehrhart polynomial, the number of lattice points in the first n dilations of the polytope are calculated, where n is the dimension of the polytope. A system of linear equations is then solved to find the polynomial.

i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}}

o1 = P

o1 : Polyhedron
i2 : ehrhart P

     1 3    2   3
o2 = -x  + x  + -x + 1
     2          2

o2 : QQ[x]

Ways to use ehrhart :