# linealitySpace -- computes a basis of the lineality space

## Synopsis

• Usage:
LS = linealitySpace C
LS = linealitySpace F
LS = linealitySpace P
• Inputs:
• Outputs:
• LS,

## 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

## Ways to use linealitySpace :

• "linealitySpace(PolyhedralObject)"

## For the programmer

The object linealitySpace is .