topcomNumTriangulations(Matrix) -- the number of triangulations of a point or vector configuration

Synopsis

• Function: topcomNumTriangulations

• Usage:

  topcomNumTriangulations A

  topcomNumTriangulations(A, Homogenize => true, Fine => true, RegularOnly => true)

• Inputs:
  • A, a matrix,
• Optional inputs:
  • Homogenize => a Boolean value, default value true
  • ConnectedToRegular => a Boolean value, default value true
  • Fine => a Boolean value, default value false
  • RegularOnly => a Boolean value, default value true
• Outputs:
  • an integer,

Description

i1 : A = transpose matrix {{0,3},{0,1},{-1,-1},{1,-1},{-4,-2},{4,-2}}

o1 = | 0 0 -1 1  -4 4  |
     | 3 1 -1 -1 -2 -2 |

              2       6
o1 : Matrix ZZ  <-- ZZ

i2 : topcomNumTriangulations A == 16

o2 = true

i3 : topcomNumTriangulations A == # topcomAllTriangulations A

o3 = true

i4 : topcomNumTriangulations(A, RegularOnly => false)

o4 = 18

i5 : assert(topcomNumTriangulations(A, RegularOnly => false) == 18)

i6 : assert(topcomNumTriangulations(A, RegularOnly => false) == # topcomAllTriangulations(A, RegularOnly => false))

See also

• topcomAllTriangulations(Matrix) -- generate all triangulations of a point or vector configuration