isStar -- test whether a triangulation is a star with respect to its last point

Usage:

isStar T

isStar(A, tri)
Inputs:
- T, an instance of the type Triangulation,
- A, a matrix,
- tri, a list,
Outputs:
- a Boolean value, whether every maximal simplex contains the last column index of the configuration

Description

A triangulation is a star (with respect to a distinguished point $p$) if every maximal simplex contains $p$ as a vertex. This function uses the convention that $p$ is the last column of the configuration: $T$ is a star iff every simplex of max T contains the index numColumns(matrix T) - 1.

This convention is common when triangulating a reflexive polytope with the origin placed last: a fine star triangulation refines the polytope into simplices all sharing the origin.

i1 : A = transpose matrix {{1,1},{-1,1},{-1,-1},{1,-1},{0,0}}

o1 = | 1 -1 -1 1  0 |
     | 1 1  -1 -1 0 |

              2       5
o1 : Matrix ZZ  <-- ZZ

i2 : T = regularFineTriangulation A

o2 = triangulation {{0, 1, 4}, {0, 3, 4}, {1, 2, 4}, {2, 3, 4}}

o2 : Triangulation

i3 : max T

o3 = {{0, 1, 4}, {0, 3, 4}, {1, 2, 4}, {2, 3, 4}}

o3 : List

i4 : isStar T

o4 = true

Caveat

This function does not check that tri is a valid triangulation or that the last column is genuinely interior; it only inspects the indices.

Ways to use isStar:

isStar(Matrix,List)
isStar(Triangulation)

For the programmer

The object isStar is a method function.

The source of this document is in Triangulations.m2:1775:0.

isStar -- test whether a triangulation is a star with respect to its last point

Description

Caveat

See also

Ways to use isStar:

For the programmer