maxCones(ToricVectorBundle) -- the list of maximal cones of the underlying fan

Synopsis

• Function: maxCones

• Usage:

  L = maxCones E

• Inputs:
  • E, an instance of the type ToricVectorBundle
• Outputs:
  • L, a list, of cones

Description

Returns the list of maximal cones of the underlying fan. These are the cones that generate the fan, i.e., are not a face of another. See Fan, maxCones and Cone.

i1 : E = tangentBundle pp1ProductFan 2

o1 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 2

o1 : ToricVectorBundleKlyachko

i2 : L = maxCones E

o2 = {Cone{...1...}, Cone{...1...}, Cone{...1...}, Cone{...1...}}

o2 : List

i3 : apply(L,rays)

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

o3 : List

i4 : E = tangentBundle(pp1ProductFan 2,"Type" => "Kaneyama")

o4 = {dimension of the variety => 2 }
      number of affine charts => 4
      rank of the vector bundle => 2

o4 : ToricVectorBundleKaneyama

i5 : L = maxCones E

o5 = {Cone{...1...}, Cone{...1...}, Cone{...1...}, Cone{...1...}}

o5 : List

i6 : apply(L,rays)

o6 = {| 1 0 |, | 1 0  |, | -1 0 |, | -1 0  |}
      | 0 1 |  | 0 -1 |  | 0  1 |  | 0  -1 |

o6 : List

See also

• Fan -- the class of all fans
• maxCones -- displays the generating Cones of a Fan
• Cone -- the class of all rational convex polyhedral cones
• charts -- the number of maximal affine charts
• fan(ToricVectorBundle) -- the underlying fan of a toric vector bundle
• rays(ToricVectorBundle) -- the rays of the underlying fan