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OldPolyhedra :: cones

cones -- computes all cones of a fan of a certain dimension

Synopsis

Description

cones computes the List of all Cones in F of dimension d.

i1 : F = normalFan hypercube 3

o1 = {ambient dimension => 3         }
      number of generating cones => 8
      number of rays => 6
      top dimension of the cones => 3

o1 : Fan
i2 : L = cones(2,F)

o2 = {{ambient dimension => 3           }, {ambient dimension => 3         
       dimension of lineality space => 0    dimension of lineality space =>
       dimension of the cone => 2           dimension of the cone => 2     
       number of facets => 2                number of facets => 2          
       number of rays => 2                  number of rays => 2            
     ------------------------------------------------------------------------
      }, {ambient dimension => 3           }, {ambient dimension => 3      
     0    dimension of lineality space => 0    dimension of lineality space
          dimension of the cone => 2           dimension of the cone => 2  
          number of facets => 2                number of facets => 2       
          number of rays => 2                  number of rays => 2         
     ------------------------------------------------------------------------
         }, {ambient dimension => 3           },
     => 0    dimension of lineality space => 0  
             dimension of the cone => 2         
             number of facets => 2              
             number of rays => 2                
     ------------------------------------------------------------------------
     {ambient dimension => 3           }, {ambient dimension => 3         
      dimension of lineality space => 0    dimension of lineality space =>
      dimension of the cone => 2           dimension of the cone => 2     
      number of facets => 2                number of facets => 2          
      number of rays => 2                  number of rays => 2            
     ------------------------------------------------------------------------
      }, {ambient dimension => 3           }, {ambient dimension => 3      
     0    dimension of lineality space => 0    dimension of lineality space
          dimension of the cone => 2           dimension of the cone => 2  
          number of facets => 2                number of facets => 2       
          number of rays => 2                  number of rays => 2         
     ------------------------------------------------------------------------
         }, {ambient dimension => 3           },
     => 0    dimension of lineality space => 0  
             dimension of the cone => 2         
             number of facets => 2              
             number of rays => 2                
     ------------------------------------------------------------------------
     {ambient dimension => 3           }, {ambient dimension => 3         
      dimension of lineality space => 0    dimension of lineality space =>
      dimension of the cone => 2           dimension of the cone => 2
      number of facets => 2                number of facets => 2
      number of rays => 2                  number of rays => 2
     ------------------------------------------------------------------------
      }}
     0

o2 : List

To actually see the cones of the fan we can look at their rays, for example:

i3 : apply(L,rays)

o3 = {| 0  0 |, | -1 0 |, | -1 0  |, | 1 0 |, | 1 0  |, | 0 0 |, | 1 0 |, |
      | -1 0 |  | 0  0 |  | 0  -1 |  | 0 0 |  | 0 -1 |  | 1 0 |  | 0 1 |  |
      | 0  1 |  | 0  1 |  | 0  0  |  | 0 1 |  | 0 0  |  | 0 1 |  | 0 0 |  |
     ------------------------------------------------------------------------
     -1 0 |, | 0  0  |, | -1 0  |, | 0 0  |, | 1 0  |}
     0  1 |  | -1 0  |  | 0  0  |  | 1 0  |  | 0 0  |
     0  0 |  | 0  -1 |  | 0  -1 |  | 0 -1 |  | 0 -1 |

o3 : List

Ways to use cones :

For the programmer

The object cones is a method function.