Cone ? Cone -- compares the Cones

Operator: ?
Usage:

b = C1 ? C2
Inputs:
- C1, a convex rational cone
- C2, a convex rational cone
Outputs:
- b, a Boolean value, > or < or =

Description

This induces an order on Cones. C1 is greater then C2 if its ambient dimension is greater, if this is equal then if its dimension is higher and if this is equal if it has the higher ordered rays and lineality space.

i1 : C1 = posHull matrix {{1,0},{0,1},{1,1}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 2
      number of facets => 2
      number of rays => 2

o1 : Cone

i2 : C2 = posHull matrix {{1,0,1},{0,1,0},{1,1,0}}

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o2 : Cone

i3 : C1 ? C2

o3 = <

o3 : Keyword

Ways to use this method:

Cone ? Cone -- compares the Cones

The source of this document is in OldPolyhedra.m2:7699:0.