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# 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:5360:0.