# linSpace -- computes a basis of the lineality space

## Synopsis

• Usage:
LS = linSpace C
LS = linSpace F
LS = linSpace P
• Inputs:
• F, an instance of the type Fan
• Outputs:
• LS,

## 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 .