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NormalToricVarieties :: fan(NormalToricVariety)

fan(NormalToricVariety) -- make the 'Polyhedra' fan associated to the normal toric variety

Synopsis

Description

This methods returns the Polyhedra fan associated to a normal toric variety. More precisely, this method takes the set of ray listed in max X, computes their positive hull as an object of class Cone and returns the fan generated by these cones.
i1 : PP3 = projectiveSpace 3;
i2 : F = fan PP3

o2 = {ambient dimension => 3         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 3

o2 : Fan
i3 : rays F

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

o3 : List
i4 : rays PP3

o4 = {{-1, -1, -1}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

o4 : List
i5 : FF2 = hirzebruchSurface 2;
i6 : F = fan FF2

o6 = {ambient dimension => 2         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 2

o6 : Fan
i7 : rays F

o7 = {| 0  |, | 1 |, | 0 |, | -1 |}
      | -1 |  | 0 |  | 1 |  | 2  |

o7 : List
i8 : rays FF2

o8 = {{1, 0}, {0, 1}, {-1, 2}, {0, -1}}

o8 : List

See also