polyhedralComplex(Matrix,Matrix,Matrix,List) -- Constructing a polyhedral complex.

Synopsis

Function: polyhedralComplex
Usage:

PC = polyhedralComplex(V,R,N,L)
Inputs:
- V, a matrix, Matrix containing the vertices as columns
- R, a matrix, Matrix containing rays as columns (optional)
- N, a matrix, Matrix containing generators of the lineality space as columns (optional)
- L, a list, List containing lists with indices of the vertices of the maximal cells.
Outputs:
- PC, an instance of the type PolyhedralComplex,

Description

Basic constructor for polyhedral complices that takes a matrix containing the vertices of the polyhedral complex and a list of lists with the indices of the vertices and rays in the maximal cells. Both the rays and the lineality space are optional arguments. If two matrices are provided, then the second matrix is considered to contain rays. To input a lineality space, one must provide three matrices.

This constructor does not check well-definedness, see isWellDefined.

i1 : M = matrix {{0,1,2}}

o1 = | 0 1 2 |

              1       3
o1 : Matrix ZZ  <-- ZZ

i2 : L = {{0,1},{1,2}}

o2 = {{0, 1}, {1, 2}}

o2 : List

i3 : PC = polyhedralComplex(M,L)

o3 = PC

o3 : PolyhedralComplex

i4 : C = hypercube 2

o4 = C

o4 : Polyhedron

i5 : F = faces(1,C)

o5 = {({0, 2}, {}), ({1, 3}, {}), ({0, 1}, {}), ({2, 3}, {})}

o5 : List

i6 : V = vertices C

o6 = | -1 1  -1 1 |
     | -1 -1 1  1 |

              2       4
o6 : Matrix QQ  <-- QQ

i7 : L = linealitySpace C

o7 = 0

              2
o7 : Matrix QQ  <-- 0

i8 : PC = polyhedralComplex(V,L,F)

o8 = PC

o8 : PolyhedralComplex

i9 : vertices PC

o9 = | -1 1  -1 1 |
     | -1 -1 1  1 |

              2       4
o9 : Matrix QQ  <-- QQ

i10 : maxPolyhedra PC

o10 = {({0, 2}, {}), ({1, 3}, {}), ({0, 1}, {}), ({2, 3}, {})}

o10 : List

i11 : dim PC

o11 = 1

Ways to use this method: