trisetcmp(1) [debian man page]
TRISETCMP(1) The Regina Handbook TRISETCMP(1) NAME
trisetcmp - Compare triangulations between two Regina data files SYNOPSIS
trisetcmp [ -m | -n ] [ -s ] file1 file2 DESCRIPTION
Compares all triangulations in the first file against all triangulations in the second file, looking for pairs of triangulations that are combinatorially isomorphic. The two given files must be Regina data files. A full list of matches (or a full list of non-matches if -n is passed) is written to stan- dard output. A match occurs when some triangulation from file1 is combinatorially isomorphic to some triangulation from file2 (i.e., iden- tical up to a relabelling of tetrahedra and their vertices). This utility can also do subcomplex testing instead of full isomorphism testing. See the option -s for details. OPTIONS
-m (default) Output matches only. All isomorphic matches between triangulations in file1 and triangulations in file2 will be listed. -n Output non-matches only. All triangulations from file1 with no isomorphic match in file2 will be listed, and vice versa. If -s is passed then non-matches are tested in one direction only, not both; see below for details. -s Instead of testing triangulations for isomorphism, test whether one triangulation is isomorphic to a subcomplex of the other. In the default case of -m (output matches only), this program outputs all instances where a triangulation from file1 is isomorphic to a subcomplex of a triangulation from file2. In the case of -n (output non-matches only), this program outputs all triangulations from file1 that are not isomorphic to a subcom- plex of any triangulation from file2. INTERNATIONALISATION
If any packets contain international characters, Regina will attempt to convert these to your local character encoding as it writes them to the output. You can tell Regina what character encoding to use by setting standard locale-related environment variables, such as LANG, LC_CTYPE or LC_ALL. For example, if LANG is set to en_AU then output will be written in the Western European character set ISO-8859-1, and if LANG is set to en_AU.UTF-8 then output will be written in the universal character set UTF-8. Typically these environment variables will already be set for you when you install your GNU/Linux system, and Regina will just use the right character set out of the box. See your GNU/Linux system reference for further information on supporting different locales. MACOS X USERS
If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged Regina to the main Applications folder, you can run it as /Applications/Regina.app/Contents/MacOS/trisetcmp. WINDOWS USERS
The command-line utilities are installed beneath the Program Files directory; on some machines this directory is called Pro- gram Files (x86). You can start this utility by running c:Program FilesReginaRegina 4.93in risetcmp.exe. SEE ALSO
regina-gui. AUTHOR
This utility was written by Benjamin Burton <bab@debian.org>. Many people have been involved in the development of Regina; see the users' handbook for a full list of credits. 28 May 2012 TRISETCMP(1)
Check Out this Related Man Page
TRICENSUS(1) The Regina Handbook TRICENSUS(1) NAME
tricensus - Form a census of 3-manifold triangulations SYNOPSIS
tricensus [ -t, --tetrahedra=tetrahedra ] [ -b, --boundary | -i, --internal | -B, --bdryfaces=faces ] [ -o, --orientable | -n, --nonori- entable ] [ -f, --finite | -d, --ideal ] [ -m, --minimal | -M, --minprime | -N, --minprimep2 ] [ -s, --sigs= ] [ -p, --genpairs | -P, --usepairs ] output-file tricensus --help DESCRIPTION
Forms a census of all 3-manifold triangulations that satisfy some set of conditions. These conditions are specified using various command-line arguments. The only condition that you must provide is the number of tetrahedra, but there are many other options available. Each triangulation will be output precisely once up to combinatorial isomorphism. Invalid triangulations (i.e., triangulations with edges identified to themselves in reverse, or vertices whose links have boundary but are not discs) will not be output at all. As the census progresses, the state of progress will be written (slowly) to standard output. Once the census is complete, the full census will be saved to the given output file. You can use the options --genpairs and --usepairs to split a census into smaller pieces. See also tricensus-mpi, a more powerful tool that allows you to distribute a census across a high-performance computing cluster. Caution: A census with even a small number of tetrahedra can take an incredibly long time to run, and can chew up massive amounts of memory. It is recommended that you try very small censuses to begin with (such as 3 or 4 tetrahedra), and work upwards to establish the lim- its of your machine. For very large census runs, it is highly recommended that you use the --sigs option, which will keep the output file small and sig- nificantly reduce the memory footprint. OPTIONS
-t, --tetrahedra=tetrahedra Specifies the number of tetrahedra used to build the triangulations. -b, --boundary Only produce triangulations with at least one boundary face. -i, --internal Only produce triangulations with all faces internal (i.e., with no boundary faces). -B, --bdryfaces=faces Only produce triangulations with the precise number of boundary faces specified. -o, --orientable Only produce orientable triangulations. -n, --nonorientable Only produce non-orientable triangulations. -f, --finite Only produce finite triangulations (triangulations with no ideal vertices). -d, --ideal Only produce triangulations with at least one ideal vertex. There might or might not be internal vertices (whose links are spheres) as well. -m, --minimal Do not include triangulations that are obviously non-minimal. This option uses a series of fast tests that try to eliminate non-minimal triangulations, but that are not always conclusive. If Regina cannot quickly tell whether a triangulation is non-minimal, it will place the triangulation in the census regardless. -M, --minprime Do not include triangulations that are obviously non-minimal, non-prime and/or disc-reducible. This can significantly speed up the census and vastly reduce the final number of triangulations produced. As above, this option uses a series of fast tests that are not always conclusive. If Regina cannot quickly tell whether a triangu- lation is non-minimal, non-prime or disc-reducible, it will place the triangulation in the census regardless. -N, --minprimep2 Do not include triangulations that are obviously non-minimal, non-prime, P2-reducible and/or disc-reducible. This can significantly speed up the census and vastly reduce the final number of triangulations produced, even more so than --min- prime. As above, this option uses a series of fast tests that are not always conclusive. If Regina cannot quickly tell whether a triangu- lation is non-minimal, non-prime, P2-reducible or disc-reducible, it will place the triangulation in the census regardless. -s, --sigs= Instead of writing a full Regina data file, just output a list of isomorphism signatures. The output file will be a plain text file. Each line will be a short string of letters, digits and punctuation that uniquely encodes a 3-manifold triangulation up to combinatorial isomorphism. You can import this text file from within Regina by selecting File->Import->Isomorphism Signature List from the menu. This option is highly recommended for large census enumerations. First, the output file will be considerably smaller. More impor- tantly, the memory footprint of tricensus will also be much smaller: triangulations can be written to the output file and forgotten immediately, instead of being kept in memory to construct a final Regina data file. -p, --genpairs Only generate face pairings, not triangulations. The outermost layer of the census code involves pairing off the faces of individual tetrahedra without determining the corresponding gluing permutations. For each face pairing that is produced, Regina will try many different sets of gluing permutations and gener- ated the corresponding triangulations. Face pairing generation consumes a very small fraction of the total census runtime, and effectively divides the census into multiple pieces. This option allows you to quickly generate a complete list of possible face pairings, so that you can feed subsets of this list to different machines to work on simultaneously. You can coordinate this manually, or you can use tricensus-mpi to coordinate it for you on a high-performance cluster. The list of all face pairings will be written to the given output file in text format (though you may omit the output file from the command line, in which case the face pairings will be written to standard output). If you are coordinating your sub-censuses manu- ally, you can use the option --usepairs to generate triangulations from a subset of these face pairings. Options for orientability, finiteness or minimality cannot be used with --genpairs; instead you should use them later with --use- pairs, or pass them to tricensus-mpi. This option does not come with progress reporting, though typically it runs fast enough that this does not matter. You can always track the state of progress by counting lines in the output file. -P, --usepairs Use only the given subset of face pairings to build the triangulations. Each face pairing that is processed must be in canonical form, i.e., must be a minimal representative of its isomorphism class. All face pairings generated using --genpairs are guaranteed to satisfy this condition. Face pairings should be supplied on standard input, one per line. They should be listed in the format produced by the option --gen- pairs. This option effectively lets you run a subset of a larger census. See --genpairs for further details on how to split a census into subsets that can run simultaneously on different machines, or tricensus-mpi which can coordinate this process using MPI on a high- performance cluster. Options for tetrahedra or boundary faces cannot be used with --usepairs; instead you should pass them earlier along with --genpairs when you split the original census into pieces. EXAMPLES
The following command forms a census of all 3-tetrahedron closed non-orientable triangulations and puts the results in the file results.rga. To ensure that triangulations are closed we use the options -i (no boundary faces) and -f (no ideal vertices). example$ tricensus -t 3 -nif results.rga Starting census generation... 0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 2:3 2:2 0:1 0:0 1:0 2:0 | 0:2 1:2 1:1 2:1 | 0:3 1:3 2:3 2:2 0:1 0:0 1:0 2:0 | 0:2 2:1 2:2 2:3 | 0:3 1:1 1:2 1:3 1:0 1:1 2:0 2:1 | 0:0 0:1 2:2 2:3 | 0:2 0:3 1:2 1:3 Finished. Total triangulations: 5 example$ The following command forms a census of 4-tetrahedron closed orientable triangulations, where the census creation is optimised for prime minimal triangulations. Although all prime minimal triangulations will be included, there may be some non-prime or non-minimal triangula- tions in the census also. example$ tricensus -t 4 -oifM results.rga Starting census generation... 0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ... 0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 3:0 | 1:2 2:2 2:1 3:1 | 1:3 ... ... 1:0 1:1 2:0 3:0 | 0:0 0:1 2:1 3:1 | 0:2 1:2 3:2 3:3 | 0:3 ... Finished. Total triangulations: 17 example$ The following command generates all face pairings for a 5-tetrahedron census in which all triangulations have precisely two boundary faces. The face pairings will be written to pairings.txt, whereupon they can be broken up and distributed for processing at a later date. example$ tricensus --genpairs -t 5 -B 2 pairings.txt Total face pairings: 118 example$ The face pairings generated in the previous example can then be fleshed out into a full census of all 3-manifold triangulations with five tetrahedra, precisely two boundary faces and no ideal vertices as follows. The number of tetrahedra and boundary faces were already speci- fied in the previous command, and cannot be supplied here. The face pairings will be read from pairings.txt, and the final census will be written to results.rga. example$ tricensus --usepairs -f results.rga < pairings.txt Trying face pairings... 0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ... 0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ... ... ... (running through all 118 face pairings) ... 1:0 2:0 3:0 4:0 | 0:0 2:1 3:1 4:1 | 0:1 1:1 3:2 4:2 | 0:2 ... Total triangulations: 5817 example$ MACOS X USERS
If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged Regina to the main Applications folder, you can run it as /Applications/Regina.app/Contents/MacOS/tricensus. WINDOWS USERS
The command-line utilities are installed beneath the Program Files directory; on some machines this directory is called Pro- gram Files (x86). You can start this utility by running c:Program FilesReginaRegina 4.93in ricensus.exe. SEE ALSO
sigcensus, tricensus-mpi, regina-gui. AUTHOR
This utility was written by Benjamin Burton <bab@debian.org>. Many people have been involved in the development of Regina; see the users' handbook for a full list of credits. 28 May 2012 TRICENSUS(1)