hypermap Combinatorial oriented hypermaps
H=hypermap(sigma,alpha) creates a hypermap from two permutations
that satisfy <sigma,alpha> transitive
as an example of possible input we give a small hypermap from a
square-octagon tesselation of the plane (i.e. this is a hypergraph
embedded on the torus)
sigma=perm({[1 24 20],[2 14 9],[3 11 13],[4 18 23],[5 21 17],[6 7 10],[8 16 12],[15 19 22]});
alpha=perm({[1 2 3],[4 5 6],[7 8 9],[10 11 12],[13 14 15],[16 17 18],[19 20 21],[22,23,24]});
H=hypermap(sigma,alpha);
hypermap Properties:
sigma - the permutation representing vertices
alpha - the permutation representing edges
alphaInverseSigma - the permutation representing faces
n - the number of darts
hypermap Methods:
hypermap - constructs a hypermap from two permutations
genus - computes the genus of the hypermap
showVertices - prints the vertices of the hypermap to screen
showEdges - prints the edges of the hypermap to screen
showFaces - prints the faces of the hypermap to screen
dual - creates the combinatorial dual of the hypermap
boundaryFaceToDartModEdge - computes the matrix representing \partial_2
boundaryDartModEdgeToVertex - computes the matrix representing \partial_1
classicalBoundaryFaceToDart - computes the matrix representing \overline{d}_2
classicalBoundaryDartToVertexPlusEdge - computes the matrix representing \overline{d}_1