pp1ProductFan -- the fan of n products of PP^1

Synopsis

• Usage:

  F = pp1ProductFan n

• Inputs:
  • n, an integer, strictly positive
• Outputs:
  • F, an instance of the type Fan

Description

Generates the fan of the product of $n$ projective one-spaces. This is the same as the normal fan of the $n$ dimensional hypercube.

i1 : F = pp1ProductFan 2

o1 = {ambient dimension => 2         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 2

o1 : Fan

i2 : apply(maxCones F, rays)

o2 = {| -1 0  |, | 1 0  |, | 1 0 |, | -1 0 |}
      | 0  -1 |  | 0 -1 |  | 0 1 |  | 0  1 |

o2 : List

See also

• Fan -- the class of all fans
• hirzebruchFan -- the fan of the n-th Hirzebruch surface
• projectiveSpaceFan -- the fan of projective n space