Simplicial Complex Calculator ver 0.81

• How to compile.
  1. Untar the downloaded file and just type make, then you will have the binary scc.
• Usage.
  1. Prepare data files as described below.
  2. If you simply type
     % scc
     Usage will be output.
     For example, if you want to calculate the f-vector, you should type
     % scc fvector <datafile>
     
• Data file. For one simplicial complex, we prepare one data file. In the data file, we express the simplicial complex by a list of simplices. The vertices are numbered by integers. For example, a face with four vertices 1, 3, 4, 5 is expressed as follows.

  1 3 4 5
  

  An example of a simplicial complex is as follows.

  1 2 3 4
  5 6 7
  1 3 5 4
  7 8
  1 2
  

  By giving a list of simplices, the data file represent a simplicial complex generated by the simplices. For example, the list above represent a simplicial complex with faces:

  1 2 3 4 
  1 3 4 5 
  1 2 3 
  1 2 4 
  1 3 4 
  1 3 5 
  1 4 5 
  2 3 4 
  3 4 5 
  5 6 7 
  1 2 
  1 3 
  1 4 
  1 5 
  2 3 
  2 4 
  3 4 
  3 5 
  4 5 
  5 6 
  5 7 
  6 7 
  7 8 
  1 
  2 
  3 
  4 
  5 
  6 
  7 
  8 
  empty set
  

• Functions currently available:

  % ./scc 
  Usage:scc   [ or extra arguement]
  keyword:
      faces ........... show all faces
      facets .......... show all facets
      boundary ........ show the boundary facets
      pure_part ....... show the i-th pure part (scc pure_part  i
      union ........... union of two complexes (two input files needed)
      intersection .... intersection of two complexes (two input files needed)
      join ............ join of two complexes (two input files needed)
      fvector ......... show f-vector
      hvector ......... show h-vector
      Mseq_check ...... check if its h-vector is M-sequence
      purity .......... check if the complex is pure or not
      pseudomanifold .. check if the complex is a pseudomanifold
      dimension ....... show the dimension
      shellability .... check shellability
                        (search shelling by backtraking.)
      shellability_b .... check shellability
                         (use different algorithm: 
                          search reverse shelling by backtracking.
                                                  [ONLY FOR PURE CASE]) 
      shellability_c .... check shellability
                         (This is an improved version of shellability_b. 
                                                  [ONLY FOR PURE CASE]) 
      shellability_d .... check shellability
                         (This is an improved version of shellability_c. 
                                                  [ONLY FOR PURE CASE]) 
      shellability_e .... check shellability
                         (This is an improved version of shellability_d. 
                                                  [ONLY FOR PURE CASE]) 
      shellability_f .... check shellability
                         (This is an improved version of shellability_e. 
                          Recommended version.[ONLY FOR PURE CASE]) 
      barycentric_subdivision .... barycentric subdivision
      contractible_edges .... list contractible edges