Edit detail for SandBox polymake revision 1 of 2

Here we demonstrate the PolyMake? wrappers Polytope and SimplicialComplex.

To use the Polytope domain we need to say

)lib STRCNV READFILE POLYTOPE

   StringConversions is now explicitly exposed in frame initial 
   StringConversions will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/STRCNV.NRLIB/STRCNV
   ReadFile is now explicitly exposed in frame initial 
   ReadFile will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/READFILE.NRLIB/READFILE
   Polytope is now explicitly exposed in frame initial 
   Polytope will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/POLYTOPE.NRLIB/POLYTOPE

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

c5 := cube 5

   >> System error:
   #<SB-SYS:FD-STREAM
  for "file /var/zope2/var/LatexWiki/POLYTOPE.NRLIB/POLYTOPE.fasl"
  {1005029651}>
is a fasl file compiled with SBCL 1.0.31, and can't be loaded into SBCL 1.0.47.

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 1 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

   There are 1 exposed and 0 unexposed library operations named simple 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op simple
      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 
      simple with argument type(s) 
                                Variable(c5)

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

Here are its vertices:

vertices c5

   There are 1 exposed and 0 unexposed library operations named 
      vertices having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op vertices
      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 
      vertices with argument type(s) 
                                Variable(c5)

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

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

r5 := randSphere(3, 6)

   >> System error:
   #<SB-SYS:FD-STREAM
  for "file /var/zope2/var/LatexWiki/POLYTOPE.NRLIB/POLYTOPE.fasl"
  {1005205331}>
is a fasl file compiled with SBCL 1.0.31, and can't be loaded into SBCL 1.0.47.

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

vertices r5

   There are 1 exposed and 0 unexposed library operations named 
      vertices having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op vertices
      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 
      vertices with argument type(s) 
                                Variable(r5)

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