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triangulation -- make a Triangulation object

Synopsis

• Usage:
triangulation(A, T)
• Inputs:
• A, ,
• T, a list, representing a triangulation of the columns of $A$ (each element in the list is a list of indices in the range $0, \ldots, n-1$, where $n$ is the number of columns of $A$)
• Optional inputs:
• Homogenize (missing documentation) => , default value true, if true, add a row of ones to think of this as a vector configuration in one higher dimension.
• Outputs:
• an instance of the type Triangulation (missing documentation) , A Triangulation (missing documentation) object. Very little computation is performed. The matrix and list representing a triangulation is packaged into an object to make clear that it is a triangulation

Description

 i1 : P = hypercube 3 o1 = P o1 : Polyhedron i2 : A = vertices P o2 = | -1 1 -1 1 -1 1 -1 1 | | -1 -1 1 1 -1 -1 1 1 | | -1 -1 -1 -1 1 1 1 1 | 3 8 o2 : Matrix QQ <-- QQ i3 : T = topcomRegularFineTriangulation A o3 = {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, ------------------------------------------------------------------------ {3, 5, 6, 7}} o3 : List i4 : tri = triangulation(A, T) o4 = triangulation {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}} o4 : Triangulation i5 : matrix tri o5 = | -1 1 -1 1 -1 1 -1 1 | | -1 -1 1 1 -1 -1 1 1 | | -1 -1 -1 -1 1 1 1 1 | | 1 1 1 1 1 1 1 1 | 4 8 o5 : Matrix QQ <-- QQ i6 : vectors tri o6 = {{-1, -1, -1, 1}, {1, -1, -1, 1}, {-1, 1, -1, 1}, {1, 1, -1, 1}, {-1, ------------------------------------------------------------------------ -1, 1, 1}, {1, -1, 1, 1}, {-1, 1, 1, 1}, {1, 1, 1, 1}} o6 : List i7 : max tri o7 = {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, ------------------------------------------------------------------------ {3, 5, 6, 7}} o7 : List i8 : isWellDefined tri o8 = true i9 : netList affineCircuits tri +------+------+ o9 = |{1, 2}|{0, 3}| +------+------+ |{3, 4}|{2, 5}| +------+------+ |{3, 4}|{1, 6}| +------+------+ |{5, 6}|{4, 7}| +------+------+ i10 : isFine tri o10 = true i11 : isStar tri o11 = false i12 : isRegularTriangulation tri o12 = true