Cluster Expansion
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[ Quick Start | Syntax definition | Examples ]

  Quick Start  
   
There is a test program written to demonstrate the abilities of the cluster package. This program called test-cluster allows you to define clusters and to investigate these clusters by a number of functions.
It also provides you with the possibility to generate all clusters of a given size defined on one of the default lattices.
 
 
  Syntax definition of the input file  
   
[ Clusters | Colored Clusters | Shared Functions | Lattice | Utilities ]

In the following the syntax of the input file of the test-cluster program is defined. The program is run with two arguments defining the name of the input and output file. If not specified, the default names are input and output.

Clusters
Syntax of expression
Semantics of expression
DefineCluster name
  [source, sink] ... [source, sink] %
Defines a cluster with the corresponding name by passing all edges. The end of the edge list is defined by the symbol %. In the following this cluster can be referenced by the given name.
GenerateClusters n
  destfilename psfilename
Generates all clusters with up to n edges which can be embedded in the previous defined lattice.
The result is saved in the file given by destfilename. A postscript file with the corresponding name is produced.

Colored Clusters
Syntax of expression
Semantics of expression
DefineColoredCluster name
  [source, sink] ... [source, sink] %
  DefineColors
  (vertex, color) ... (vertex, color)%
Defines a colored cluster with the corresponding name by first defining the underlying cluster as above.
Define the colors by passing a list of vertices paired with their color.The end of a list is defined by the symbol %. In the following this cluster can be referenced by the given name.
GenerateColoredClusters sourcefilename destfilename psfilename Generates all colored clusters which can be embedded in the previous defined lattice from those clusters specified in the file with the given sourcefilename.
The result is saved in the file given by destfilename. A postscript file with the corresponding name is produced.

Shared Functions
Syntax of expression
Semantics of expression
Dump name Displays the referenced cluster.
Postscript name Prints the referenced cluster in the postscript file. Per default this file is named cluster.ps.
Embeddings name Evaluates the number of embeddings of the referenced cluster in the actually defined lattice.
SizeOfAutG name Evaluates the size of the automorphism group of the referenced cluster.
SubCluster name Iterates all subclusters of the referenced cluster and displays them.
Edges name Iterates all edges of the referenced cluster and displays them.
Isomorphic name1 name2 Tests if the two referenced clusters are isomorphic.

Lattice
Syntax of expression
Semantics of expression
Lattice latticetype Defines the latticetype. Values for latticetype are linear, quadratic and triangle.
The default type is quadratic.
ColoredLattice coloredlatticetype <n> Defines a quadratic colored lattice. Possible values for coloredlatticetype are linear and bipartite.
If linear is chosen, n must be given. In this case the cluster is colored with n different colors.
If bipartite is chosen, no further argument is required.

Utilities
Syntax of expression
Semantics of expression
CompareClusterFiles filename1 filename2 Compares the clusters defined in file1 and file2.
// some comment Allows you to add some comments to your input file. Notice that comments are only allowed at the end of an expression statement, but not in between.
Exit Exit the program. Everything beyond this statement won't be interpreted.

Fat printed expressions are terminal symbols not to be changed. Normal printed expressions have to be specified in the input file by the user. Expression enclosed in <> - brackets are optional.
 
 
  Examples  
   
For an easy use some examples are given in the following.

Example 1

CompareClusterFiles eight.txt norbert.txt

Example 2

ColoredLattice linear 3
DefineColoredCluster MyCluster1
  [1,2] [2,3] [3,4] %
  DefineColors
  (1,1) (2,1) (3,2) (4,2) %
Dump MyCluster1

DefineColoredCluster MyCluster2
  [5,6] [6,7] [7,5] %
  DefineColors
  (5,3) (6,1) (7,1) %
Dump MyCluster2

Embeddings MyCluster1
Postscript MyCluster1   // draw a nice picture
Postscript MyCluster2
SubCluster MyCluster2   // display all subclusters

Example 3

ColoredLattice linear 3
GenerateColoredClusters five.txt cLin5.txt cLin5.ps

Example 4

ColoredLattice bipartite
GenerateColoredClusters eight.txt cBip8.txt cBip8.ps
Exit

 
 


Simon Trebst
Last modified: Fri May 14 15:36:47 MET DST 1999