isSmooth -- checks if a Cone or Fan is smooth

Synopsis

• Usage:

  b = isSmooth C

  b = isSmooth F

• Inputs:
  • C, a convex rational cone
• Outputs:
  • b, true if the Cone/Fan is smooth, false otherwise

Description

isSmooth checks for a Cone if the rays are a subset of a basis of the lattice. For a Fan it checks smoothness for every Cone.

i1 : C = posHull matrix {{1,2,3},{3,1,2},{2,3,1}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o1 : Cone

i2 : isSmooth C

o2 = false

i3 : F = hirzebruch 3

o3 = {ambient dimension => 2         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 2

o3 : Fan

i4 : isSmooth F

o4 = true