MATLAB File Help: hypermap View code for hypermap Default Topics
hypermap
 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
Class Details
Sealed false
Construct on load false
Constructor Summary
hypermap Construct hypermap 
Property Summary
alpha the permutation representing edges 
alphaInverseSigma the permutation representing faces 
n the number of darts 
sigma the permutation representing vertices 
Method Summary
  boundaryDartModEdgeToVertex compute the matrix representing \partial_1 assuming basis of W/i(E) 
  boundaryFaceToDartModEdge compute the matrix representing \partial_2 assuming basis of W/i(E) 
  classicalBoundaryDartToVertexPlusEdge compute the matrix representing \overline{d}_1 
  classicalBoundaryFaceToDart compute the matrix representing \overline{d}_2 
  dual create the combinatorial dual of the hypermap 
  genus compute genus of the hypermap 
  showEdges print the edges of the hypermap to screen 
  showFaces print the faces of the hypermap to screen 
  showVertices print the vertices of the hypermap to screen