volume of polyhedral set
area of polyhedral set
length of polyhedral set
(optional) non-negative integer, dimensionality of the set in which the volume should be computed; default is the dimension of polyset's coordinate space
The Volume command computes the volume of a polyhedral set in the generalized sense of a Lebesgue measure, defining a d-volume of a set in higher dimensions. For sets in 3, 2, and 1 dimensional spaces, this corresponds to the standard definitions of volume, area, and length, respectively.
The optional parameter d specifies which d-volume to compute for the set, where d is less than or equal to the number of polyset's coordinates. For sets of dimension greater than d, the sum of the volumes for the d-faces is computed.
The Area and Length commands are used to compute the 2-volume and 1-volume of polyset, respectively, and are equivalent to Volume(polyset, 2) and Volume(polyset, 1).
For the standard cube
c ≔ ExampleSets:-Cube⁡
the edges of the cube all have length 2
c_edges ≔ Edges⁡c:map⁡Length,c_edges
the cube has a volume of 8
and the total surface area of the cube is
The polyhedral set ps is a three-dimensional polytope in four-dimensional space.
ps ≔ PolyhedralSet⁡1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,x,y,z,u
Its four-dimensional volume is 0, but its three-dimensional volume is positive.
The PolyhedralSets[Volume], PolyhedralSets[Area] and PolyhedralSets[Length] commands were introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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