smoothSubfan -- computes the subfan of all smooth cones

Synopsis

• Usage:

  F1 = smoothSubfan F

• Inputs:
  • F, an instance of the type Fan
• Outputs:
  • F1, an instance of the type Fan

Description

For a given Fan F the function computes the subfan F1 of all smooth cones.

Let's consider the fan consisting of the following three dimensional cone and all of its faces:

i1 : C = coneFromVData  matrix {{1,-1,0},{1,1,0},{1,1,1}}

o1 = C

o1 : Cone

i2 : F = fan C

o2 = F

o2 : Fan

This cone is not smooth, therefore also the fan is not. But if we remove the interior and one of the two dimensional faces the resulting subfan is smooth.

i3 : F1 = smoothSubfan F

o3 = F1

o3 : Fan

i4 : raysF1 = rays F1

o4 = | 0 -1 1 |
     | 0 1  1 |
     | 1 1  1 |

              3        3
o4 : Matrix ZZ  <--- ZZ

i5 : apply(maxCones F1, mc -> raysF1_mc)

o5 = {| 0 -1 |, | 0 1 |}
      | 0 1  |  | 0 1 |
      | 1 1  |  | 1 1 |

o5 : List