linSpace -- computes a basis of the lineality space

Usage:

LS = linSpace C

LS = linSpace F

LS = linSpace P
Inputs:
- C, a convex rational cone
- F, an instance of the type Fan
- P, a convex polyhedron
Outputs:
- LS, a matrix

Description

linSpace returns a basis of the lineality space of the input as the columns of the matrix LS. The lineality space of a Fan is the lineality space of any Cone of the Fan, since they all have the same lineality space.

i1 : M = matrix {{1,1,1},{0,1,0},{-1,1,-1},{-1,-1,-1},{0,-1,0},{1,-1,1}};

              6       3
o1 : Matrix ZZ  <-- ZZ

i2 : v = matrix {{2},{1},{2},{2},{1},{2}};

              6       1
o2 : Matrix ZZ  <-- ZZ

i3 : P = intersection(M,v)

o3 = {ambient dimension => 3           }
      dimension of lineality space => 1
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 6

o3 : Polyhedron

i4 : linSpace P

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

              3       1
o4 : Matrix ZZ  <-- ZZ

i5 : C = dualCone intersection M

o5 = {ambient dimension => 3           }
      dimension of lineality space => 2
      dimension of the cone => 2
      number of facets => 0
      number of rays => 0

o5 : Cone

i6 : linSpace C

o6 = | 0 1 |
     | 1 0 |
     | 0 1 |

              3       2
o6 : Matrix ZZ  <-- ZZ

Ways to use linSpace:

linSpace(Cone)
linSpace(Fan)
linSpace(Polyhedron)

For the programmer

The object linSpace is a method function.

The source of this document is in OldPolyhedra.m2:5360:0.