Description Usage Arguments Value References Examples

Given a zonotope (as an object of class Zonotope), this function computes the sum of the absolute values of the determinants of all the *d \times d* submatrices of the *m\times d* matrix *G* that contains row-wise the *m* *d*-dimensional segments that define the zonotope.
For an arbitrary simplex that is given in V-representation this function computes the absolute value of the determinant formed by the simplex's points assuming it is shifted to the origin.

1 | ```
exact_vol(P)
``` |

`P` |
A polytope |

The exact volume of the input polytope, for zonotopes, simplices in V-representation and polytopes with known exact volume

E. Gover and N. Krikorian,
“Determinants and the Volumes of Parallelotopes and Zonotopes,” *Linear Algebra and its Applications, 433(1), 28 - 40,* 2010.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# 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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