isPointed -- checks if a Cone or Fan is pointed

Usage:

b = isPointed C

b = isPointed F
Inputs:
- C, a convex rational cone
- F, an instance of the type Fan
Outputs:
- b, a Boolean value, true if the Cone or the Fan is pointed, false otherwise

Description

Tests if a Cone is pointed, i.e. the lineality space is 0. A Fan is pointed if one of its Cones is pointed. This is equivalent to all Cones being pointed.

i1 : C = intersection(matrix{{1,1,-1},{-1,-1,-1}})

o1 = {ambient dimension => 3           }
      dimension of lineality space => 1
      dimension of the cone => 3
      number of facets => 2
      number of rays => 2

o1 : Cone

i2 : isPointed C

o2 = false

i3 : C = intersection{C,(matrix{{1,-1,-1}},0)}

o3 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o3 : Cone

i4 : isPointed C

o4 = true

Ways to use isPointed:

isPointed(Cone)
isPointed(Fan)

For the programmer

The object isPointed is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:5720:0.