Given a zonotope (as an object of class Zonotope), this function computes the sum of the absolute values of the determinants of all the
exact_vol(P)
The exact volume of the input polytope, for zonotopes, simplices in V-representation and polytopes with known exact volume
A polytope
E. Gover and N. Krikorian, “Determinants and the Volumes of Parallelotopes and Zonotopes,” Linear Algebra and its Applications, 433(1), 28 - 40, 2010.
# compute the exact volume of a 5-dimensional zonotope defined by the Minkowski sum of 10 segments
Z = gen_rand_zonotope(2, 5)
vol = exact_vol(Z)
# compute the exact volume of a 2-d arbitrary simplex
V = matrix(c(2,3,-1,7,0,0),ncol = 2, nrow = 3, byrow = TRUE)
P = Vpolytope(V = V)
vol = exact_vol(P)
# compute the exact volume the 10-dimensional cross polytope
P = gen_cross(10,'V')
vol = exact_vol(P)
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