Embedding Toolbox.

Welcome to the download page for the Embedding Toolbox.  The graph algorithm is adapted from one introduced in an article by Krissinel and Henrick(see abstract here). Changes were made to take advantage of the Levi graphs of projective planes and partial planes in an effort to speed the algorithm.  Additionally the search is limited to finding an isomorphic subgraph rather than a subgraph common to both parts.  An explanation of the algorithm is available here.


Plane Libraries (Download here)-updated Oct. 4, 2010


Name:planefiles
 Format of files:
Description:Stores the projective planes used by the programs

These files were created using the plane files of Eric Moorehouse and Gordon Royal. 		Planes are stored with each line of the file
representing a line of the plane and the
values on that line represent the points
 which are on that line


Name:partfiles
 Format of Files:
Description: Stores the library of partial planes.                                                                                                                      




            
Files list the number of
points then the number
of lines.  Then the lines
are listed in the form
number of points on the
line followed by the points on the line.


Name:quadfiles
 Format of files:
Description:Contains the files which have the lists of frames.  Frames are stored as the points of the frame. 

These files were created using nauty.
 Lists of the points of a frame




Program Library  (Download here)-updated April 7, 2011
 Name: sortframes
 Format of files:
Description: Contains a a program which will check a list of frames and see if those frames close to PG(2,2),PG(2,3),and Unreal10_3.  Output stored in a file in the folder report, which has a count of how many of each was found.  When found embeddings are stored is stored in the files fano, pg3files, and unrealfiles.  Frame files are read from the folder quadfiles, and planes are read from the folder planefiles
 Files written in C++ and their header files


Name:FIELDS
 Format of files:
Description:  Contains a program to generate fields.  As well as files that contain the data necessary to preform field mutliplication
 C++ program file, and files
representing field addition.
Let g be a primitive element then
These files are single arrays with
the ith entry representing (g^i)+1


Name:figueroaplanes
 Format of files:
Description:Contains the files needed to construct a Figueroa plane.  also contains the files needed to check if a specific
set of points forms a fano plane in a figueroa plane.
 Files in C++ and
their header files


Name:hughesplanes
 Format of files:
Description:Contains the files needed to construct a Hughes plane. Files in C++ and
their header files


Name:commonfiles
 Format of files:
Description: Contains files used by multiple programs, that are not specific to the Hughes or Figueroa planes.
 Files in C++ and
their header files


Name:findonepart
 Format of files:
Description:Contains the files used to find a single partial plane in a projective plane
Files in C++ and
their header files


Name:findallpart Format of files:
Description:Contains the files used to find a at most one partial plane per frame in a projective plane Files in C++ and
their header files


Name:points
 Format of files:
Description:Provides the lists of the points of the Hughes plane as ordered triples.  Files of the points of the Figueroa plane are stored here as type 1,2, and 3 points.
 the three numbers
on a line represent
the points of the plane


Name:refs
 Format of files:
Description:Contains lists which relate the numbers of the points and lines of the planes to the algebraic objects that those points represent.
 lists of numbers and the points associated with them


Name:lines
 Format of files:
Description:Provides the lists of the points of the Hughes plane as ordered triples.


Name:findframes
 Format of files:
Description:Contains programs to find the frames of a projective plane upto isomorphism
 Files in C++ and
their header files


Name:fano
 Format of files:
Description:Contains the output from sortframes
 Lists of embeddings, 1 embedding per line.
 To see which points associate with which
lines see the comments of sortframes


Name:unrealfiles
 Format of files:
Description:Contains output from sortframes
 Lists of embeddings, 1 embedding per line.
 To see which points associate with which
lines see the comments of sortframes


Name: report
 Format of files:
Description:Contains output from sortframes Files counting the number of frames that closed
to PG(2,2),PG(2,3) or neither, also contains the
number of frames which are contained in an unreal 10_3


Name:pg3files
 Format of files:
Description:Contains output from sortframes Lists of embeddings, 1 embedding per line.
 To see which points associate with which
lines see the comments of sortframes

Installation
To use the files, it will be necessary to install Nauty, which is available here.
After Nauty has been installed unzip the files move the file NAUTY to the same level as the folder commonfiles. The files are ready to be used.


Absolutely no guarantees or warranties are made concerning the suitability, correctness, or any other aspect of this program. Any use is at your own risk


This package was created by Bryan Petrak under the supervision of Dr. Gary Ebert and Dr. Felix Lazebnik.
The Project was /is supported by NSA grants H98230-08-1-0041 and H98230-09-1-0074