# isSmooth -- checks if a Cone or Fan is smooth

## Synopsis

• Usage:
b = isSmooth C
b = isSmooth F
• Inputs:
• Outputs:

## Description

isSmooth checks for a Cone if the rays are a subset of a basis of the lattice. For a Fan it checks smoothness for every Cone.

 i1 : C = posHull matrix {{1,2,3},{3,1,2},{2,3,1}} o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of the cone => 3 number of facets => 3 number of rays => 3 o1 : Cone i2 : isSmooth C o2 = false i3 : F = hirzebruch 3 o3 = {ambient dimension => 2 } number of generating cones => 4 number of rays => 4 top dimension of the cones => 2 o3 : Fan i4 : isSmooth F o4 = true

## Ways to use isSmooth :

• "isSmooth(Cone)"
• "isSmooth(Fan)"

## For the programmer

The object isSmooth is .