linealitySpace -- computes a basis of the lineality space

Synopsis

• Usage:

  LS = linealitySpace C

  LS = linealitySpace F

  LS = linealitySpace P

• Inputs:
  • PO, an instance of the type PolyhedralObject
• Outputs:
  • LS, a matrix

Description

linealitySpace 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.

Please see V- and H-representation on the conventions we use for cones and polyhedra.

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 = polyhedronFromHData(M,v)

o3 = P

o3 : Polyhedron

i4 : linealitySpace P

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

              3        1
o4 : Matrix QQ  <--- QQ

i5 : C = dualCone coneFromHData M

o5 = C

o5 : Cone

i6 : linealitySpace C

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

              3        2
o6 : Matrix ZZ  <--- ZZ