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

Synopsis

• Function: topcomFlips
• Usage:
topcomFlips(A, tri)
• Inputs:
• Optional inputs:
• Homogenize => , default value true
• RegularOnly => , default value true
• Outputs:

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