topcomFlips(Matrix,List) -- find the neighboring triangulations (bistellar flips) of a triangulation

Synopsis

Function: topcomFlips
Usage:

topcomFlips(A, tri)
Inputs:
- A, a matrix,
- tri, a list,
Optional inputs:
- Homogenize => a Boolean value, default value true
- RegularOnly => a Boolean value, default value true
Outputs:
- a list,

Description

i1 : A = transpose matrix {
         {-1, -1, -1, 0}, {-1, -1, 0, -1}, {-1, -1, 0, 0}, {-1, 0, -1, -1},
         {-1, 0, -1, 2}, {-1, 0, 0, -1}, {0, -1, 1, -1}, {1, 1, -1, 2},
         {1, 1, 1, -1}, {-1, 0, -1, 0}, {-1, 0, -1, 1}, {0, 0, -1, 1}, {0,0,0,0}}

o1 = | -1 -1 -1 -1 -1 -1 0  1  1  -1 -1 0  0 |
     | -1 -1 -1 0  0  0  -1 1  1  0  0  0  0 |
     | -1 0  0  -1 -1 0  1  -1 1  -1 -1 -1 0 |
     | 0  -1 0  -1 2  -1 -1 2  -1 0  1  1  0 |

              4        13
o1 : Matrix ZZ  <--- ZZ

i2 : tri1 = topcomRegularFineTriangulation A

o2 = {{0, 1, 2, 3, 6}, {1, 2, 3, 5, 6}, {0, 2, 3, 6, 9}, {2, 3, 5, 6, 9}, {0,
     ------------------------------------------------------------------------
     2, 6, 9, 10}, {2, 5, 6, 9, 10}, {0, 2, 4, 6, 10}, {2, 4, 5, 6, 10}, {0,
     ------------------------------------------------------------------------
     3, 6, 9, 11}, {3, 6, 7, 9, 11}, {6, 7, 9, 10, 11}, {4, 6, 7, 10, 11},
     ------------------------------------------------------------------------
     {0, 6, 9, 10, 11}, {0, 4, 6, 10, 11}, {3, 6, 7, 9, 12}, {6, 7, 9, 10,
     ------------------------------------------------------------------------
     12}, {4, 6, 7, 10, 12}, {4, 6, 7, 8, 12}, {3, 6, 7, 8, 12}, {3, 5, 7, 9,
     ------------------------------------------------------------------------
     12}, {5, 7, 9, 10, 12}, {4, 5, 7, 10, 12}, {4, 5, 7, 8, 12}, {3, 5, 7,
     ------------------------------------------------------------------------
     8, 12}, {3, 5, 6, 9, 12}, {5, 6, 9, 10, 12}, {4, 5, 6, 10, 12}, {4, 5,
     ------------------------------------------------------------------------
     6, 8, 12}, {3, 5, 6, 8, 12}}

o2 : List

i3 : topcomFlips(A, tri1)

o3 = {{{0, 5}, {2, 3}}, {{0, 7}, {11}}, {{1, 9}, {2, 3}}, {{2, 11}, {0, 4,
     ------------------------------------------------------------------------
     6}}, {{3, 10}, {9}}, {{4, 9}, {10}}, {{5, 6, 7}, {12}}, {{8, 9}, {3, 5,
     ------------------------------------------------------------------------
     7}}, {{8, 10}, {4, 5, 7}}, {{11, 12}, {6, 7, 9}}}

o3 : List

Ways to use this method: