Edit detail for SandBox polymake revision 2 of 2

Here we demonstrate the PolyMake wrappers Polytope and SimplicialComplex.

To use the Polytope domain we need to say

(1) -> )lib STRCNV READFILE POLYTOPE

   StringConversions is now explicitly exposed in frame initial 
   StringConversions will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/STRCNV.NRLIB/STRCNV
   ReadFile is now explicitly exposed in frame initial 
   ReadFile will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/READFILE.NRLIB/READFILE
   Polytope is now explicitly exposed in frame initial 
   Polytope will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/POLYTOPE.NRLIB/POLYTOPE

To create a cube of dimension 4 and look at its h-vector, we say

c5 := cube 5

(1)

h5 := hVector c5

   >> Error detected within library code:
   End of file

The idea is to factor the h-polynomial, for example:

factor reduce(+, [h5.(i+1) * t^i for i in 0..#h5-1])

   There are 2 exposed and 2 unexposed library operations named # 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op #
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named # 
      with argument type(s) 
                                Variable(h5)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Of course, the cube is simple:

simple c5

   >> Error detected within library code:
   End of file

Here are its vertices:

vertices c5

   >> Error detected within library code:
   End of file

Here is a random polytope with 6 vertices on the 3-dimensional sphere

r5 := randSphere(3, 6)

(2)

Now vertices spits out a matrix containing the coordinates of the vertices of the polytope:

vertices r5

   >> Error detected within library code:
   End of file