# 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, ,
• Optional inputs:
• Homogenize => , default value true
• ConnectedToRegular => , default value true
• Fine => , default value false
• RegularOnly => , default value true
• Outputs:

## Description

This function is identical in function to topcomAllTriangulations(Matrix) (including optional arguments), but instead just counts the number, rather than enumerate them.

For example, to use the same example as in topcomAllTriangulations(Matrix):

 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

Similarly, one can count the number of triangulations with different properties using the optional arguments.

 i4 : topcomNumTriangulations(A, RegularOnly => false) o4 = 18 i5 : assert(topcomNumTriangulations(A, RegularOnly => false) == 18) i6 : assert(topcomNumTriangulations(A, RegularOnly => false) == # topcomAllTriangulations(A, RegularOnly => false))