# 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

## Ways to use smoothSubfan :

• "smoothSubfan(Fan)"

## For the programmer

The object smoothSubfan is .