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TOPCOM(7) TOPCOM(7)

NAME

TOPCOM - Triangulations Of Point Configurations and Oriented Matroids

COMMANDS

The following commands are provided. In Debian, each command is prefixed by "topcom-".

Displays the point and their symmetry generators in a more readable form.
Computes the chirotope of a point configuration.
Computes the dual of a chirotope.
Computes the circuits of a chirotope.
Dto. for point configurations (using a faster method).
Computes the cocircuits of a chirotope.
Dto. for point configurations (using a faster method).
Computes the facets of a set of cocircuits.
Computes the facets of a point configuration.
Computes a Gale transform of a point configuration.
Computes the circuits of a point configuration.
Computes the cocircuits of a point configuration.
Computes the facets of a point configuration.
Computes the number of flips of a point configurations and the seed triangulation.
Computes all flips of a point configurations and the seed triangulation.
Computes the placing triangulation of a chirotope given by the numbering of the elements.
Dto. for point configurations.
Computes a fine (i.e., using all vertices) triangulation by placing and pushing.
Dto. for point configurations.
Computes all triangulations of a chirotope that are connected by bistellar flips to the seed, which is a regular triangulation if no seed is given in the input file.
Dto. for point configurations.
Computes the number of all triangulations of a chirotope that are connected by bistellar flips to the seed, which is a regular triangulation if no seed is given in the input file.
Dto. for point configurations.
Computes all fine triangulations (the ones that use all the points sometimes called “full”) of a chirotope that are connected by bistellar flips to a fine seed triangulation.
Dto. for point configurations.
Computes the number of all fine triangulations of a chirotope that are connected by bistellar flips to a fine seed triangulation.
Dto. for point configurations.
Computes all triangulations of a chirotope.
Dto. for point configurations.
Computes the number of all triangulations of a chirotope.
Dto. for point configurations.
Computes all fine triangulations (sometimes called “full”) of a chirotope.
Dto. for point configurations.
Computes the number of all fine triangulations of a chirotope.
Dto. for point configurations.
Computes a triangulation of a chirotope with a minimum number of simplices.
Dto. for point configurations.
Computes the vertices and symmetry generators of the permutation polytope of the symmetric group of degree n, also known as the Birkhoff polytope.
Computes the vertices and symmetry generators of the permutation polytope of the alternating group of degree n, also known as the even Birkhoff polytope.
Computes the vertices and symmetry generators of the permutation polytope of the dihedral group of degree n.
Computes B_S n with an additional center point.
Computes B_A n with an additional center point.
Computes B_D n with an additional center point.
Computes the vertices and symmetry generators of a d-cube.
Computes the vertices and symmetry generators of the cyclic d-polytope with n vertices.
Computes the vertices and symmetry generators of the d-dimensional crosspolytope.
Computes the nm two-dimensional lattice points with non-negative coordinates at most (n−1,m−1) and their symmetry generators.
Computes the vertices and symmetry generators of the k-th hypersimplex in dimension d. A third parameter makes it the S-hypersimplex with coordinate sums equal to k or l.
Computes the point configuration, the symmetry, and the Santos triangulation (without flips).

OPTIONS

The following command line options are supported. Note that not all options are sensible for all clients.

OPTIONS CONCERNING INPUT/OUTPUT FROM FILES

read input from [filename] instead of stdin.

OPTIONS CONCERNING OUTPUT OF INFORMATION

Print a usage message.
Debug.
Verbose.
Output a height vector for every regular triangulation (implies --regular).
Output all flips in terms of IDs of adjacent triangulations. (Can be used to generate the flip graph.)
Write asymptote graphics commands into file (in rank-3 triangulations, points are drawn as well). The graphics contains a view of the point configuration (only in rank 3), the enumeration tree with a classification of enumeration nodes into solutions, non-canonical nodes, deadends, and early detected deadends, as well a statistics file showing a histogram of enumeration node types. The output file has to be processed by the computer graphics compiler asy (https://asymptote.sourceforge.io) using the asy-library Combinatorial_Geometry.asy and the LATEX-macroes in triangbook_macroes.sty inside share/asy/.

OPTIONS FOR CHECKING INPUT

Check seed triangulation.

OPTIONS FOR REPORTING PROPERTIES OF DISCOVERED TRIANGULATIONS

Check triangulations for flip deficiency during flip-graph exploration.
Check every k-th triangulation for regularity and stop if a regular one is found during flip-graph exploration.

OPTIONS CONCERNING WHICH TRIANGULATIONS ARE OUTPUT (NO INFLUENCE ON FLIP-GRAPH EXPLORATION)

Only count symmetry classes, not the total number.
Count/output only triangulations with exactly k simplices.
Count/oputput only triangulations with at most k simplices.
Output unimodular triangulations only; while this does not reduce the effort of flip graph exploration, since unimodular triangulations are in general not connected by themselves, it does reduce the effort of extension graph exploration linke in points2nalltriangs.
Output non-regular triangulations only; note that this does not reduce the effort of flip-graph exploration, since non-regular triangulations are in general not connected by themselves.

OPTIONS CONCERNING WHICH TRIANGULATIONS ARE EXPLORED

Search for regular triangulations only (checked liftings are w.r.t. the last homogeneous coordinate, e.g., last coordinates all ones is fine); note that this may reduce the effort of exploration, since regular triangulations are connected by themselves.
Never flip-in a point that is unused in the seed triangulation.
Try to greedily minimize the number of vertices used while flipping; keep a global upper bound on the current minimal number of vertices and do not accept triangulations with more vertices.
Never change the cardinality of triangulations by flipping.

OPTIONS CONCERNING SYMMETRIES

Assume that the symmetries are affine, in particular, that they conserve regularity.
Assume that the symmetries are isometric, in particular, that they preserve volume.
Ignore the symmetries.

OPTIONS CONTROLLING THE INTERNALS OF THE CLIENTS

Save memory by using caching techniques.
Use GKZ vectors as a finger print in symmetry handling (only for points with isometric symmetries).
Use naive full traversal of all symmetries for symmetry handling.
Use Jordan-Joswig-Kastner switch tables for symmetry handling.
Use tables of classified symmetries for symmetry handling. Obsolete, since slower than the other options.
Use [n] symtables for preprocessing symmetries. Obsolete, since slower than the other options.
Preprocess the chirotope (default for points2[n]alltriangs).
Heuristically transform points (only relevant for (co)circuit enumeration).
Preprocess a representation of the symmetry group on simplex indices (only relevant for triangulation enumeration).
Sort simplices in preprocessed index table randomly (only for points with isometric symmetries).
Sort simplices in preprocessed index table by volume (only for points with isometric symmetries).
Use volumes to check extendability of partial triangulations (only for points with isometric symmetries).
Put more effort in the check of extendability of a partial triangulation.
Skip the check of extendability of a partial triangulation.
Check extendability prior to symmetry.
Preprocess the coordinate matrix of the points (slightly useful for (co-)circuit enumeration)
Set the chirotope cache to n elements.
Set the cache for local operations.
Use QSopt_ex for regularity checks (not thread-safe).
Use soplex for regularity checks (requires separate installation of soplex).

OPTIONS CONCERNING MULTI-THREADING

Use multiple threads for enumeration.
Control the interrupt of workers by size of the current workbuffer.
Use multiple threads only locally for symmetry checks.
Use [n] threads (if possible).
Let each thread process at least [n] nodes (to avoid multithreading overhead).
Let each thread process at most [n] nodes (to avoid thread starving).
Scale the default node budget by [n] percent (n integer)
(Currently unused.) Try to keep the work buffer above [n] nodes (to balance overhead and thread starving).
(Currently unused.) Try to keep the work buffer below [n] node (to balance overhead and thread starving).

OPTIONS FOR WARM STARTS FROM PREVIOUS CALCULATIONS

These options currently only work for an interrupted flip graph exploration.

Write intermediate results into a file.
Write intermediate results into file dumpfilename (default: TOPCOM.dump).
Dump the results of each kth BFS round
Dump into k different rotating files.
Read intermediate results from a file.
Read intermediate results from file dumpfilename (default: TOPCOM.dump.[rotationnumber]).

AUTHOR

This manpage was adapted from sections 4 and 5 of the TOPCOM Manual by Jörg Rambau. See https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM-Manual/.

29 March 2024 1.1.2