TOPCOM

NAME

TOPCOM - Triangulations Of Point Configurations and Oriented Matroids

COMMANDS

The following commands are provided. In Debian, each command is prefixed by "topcom-".
points2prettyprint

Displays the point and their symmetry generators in a more readable form.

points2chiro

Computes the chirotope of a point configuration.

chiro2dual

Computes the dual of a chirotope.

chiro2circuits

Computes the circuits of a chirotope.

points2circuits

Dto. for point configurations (using a faster method).

chiro2cocircuits

Computes the cocircuits of a chirotope.

points2cocircuits

Dto. for point configurations (using a faster method).

cocircuits2facets

Computes the facets of a set of cocircuits.

points2facets

Computes the facets of a point configuration.

points2gale

Computes a Gale transform of a point configuration.

chiro2circuits

Computes the circuits of a point configuration.

chiro2cocircuits

Computes the cocircuits of a point configuration.

points2facets

Computes the facets of a point configuration.

points2nflips

Computes the number of flips of a point configurations and the seed triangulation.

points2flips

Computes all flips of a point configurations and the seed triangulation.

chiro2placingtriang

Computes the placing triangulation of a chirotope given by the numbering of the elements.

points2placingtriang

Dto. for point configurations.

chiro2finetriang

Computes a fine (i.e., using all vertices) triangulation by placing and pushing.

points2finetriang

Dto. for point configurations.

chiro2triangs

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.

points2triangs

Dto. for point configurations.

chiro2ntriangs

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.

points2ntriangs

Dto. for point configurations.

chiro2finetriangs

Computes all fine triangulations (the ones that use all the points sometimes called âfullâ) of a chirotope that are connected by bistellar flips to a fine seed triangulation.

points2finetriangs

Dto. for point configurations.

chiro2nfinetriangs

Computes the number of all fine triangulations of a chirotope that are connected by bistellar flips to a fine seed triangulation.

points2nfinetriangs

Dto. for point configurations.

chiro2alltriangs

Computes all triangulations of a chirotope.

points2alltriangs

Dto. for point configurations.

chiro2nalltriangs

Computes the number of all triangulations of a chirotope.

points2nalltriangs

Dto. for point configurations.

chiro2allfinetriangs

Computes all fine triangulations (sometimes called âfullâ) of a chirotope.

points2allfinetriangs

Dto. for point configurations.

chiro2nallfinetriangs

Computes the number of all fine triangulations of a chirotope.

points2nallfinetriangs

Dto. for point configurations.

chiro2mintriang

Computes a triangulation of a chirotope with a minimum number of simplices.

points2mintriang

Dto. for point configurations.

	B_S n		Computes the vertices and symmetry generators of the permutation polytope of the symmetric group of degree n, also known as the Birkhoff polytope.
	B_A n		Computes the vertices and symmetry generators of the permutation polytope of the alternating group of degree n, also known as the even Birkhoff polytope.
	B_D n		Computes the vertices and symmetry generators of the permutation polytope of the dihedral group of degree n.

B_S_center n

Computes B_S n with an additional center point.

B_A_center n

Computes B_A n with an additional center point.

B_D_center n

Computes B_D n with an additional center point.

cube d

Computes the vertices and symmetry generators of a d-cube.

cyclic n d

Computes the vertices and symmetry generators of the cyclic d-polytope with n vertices.

cross d

Computes the vertices and symmetry generators of the d-dimensional crosspolytope.

lattice n m

Computes the nm two-dimensional lattice points with non-negative coordinates at most (nâ1,mâ1) and their symmetry generators.

hypersimplex d k [l]

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.

santos_triang

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
-I [filename]

read input from [filename] instead of stdin.

OPTIONS CONCERNING OUTPUT OF INFORMATION
-h or --help

Print a usage message.

	-d		Debug.
	-v		Verbose.

--heights

Output a height vector for every regular triangulation (implies --regular).

--flips

Output all flips in terms of IDs of adjacent triangulations. (Can be used to generate the flip graph.)

--asy

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
--checktriang

Check seed triangulation.

OPTIONS FOR REPORTING PROPERTIES OF DISCOVERED TRIANGULATIONS
--flipdeficiency

Check triangulations for flip deficiency during flip-graph exploration.

--findregular [k]

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)
--noorbitcount

Only count symmetry classes, not the total number.

--cardinality [k]

Count/output only triangulations with exactly k simplices.

--maxcardinality [k]

Count/oputput only triangulations with at most k simplices.

--unimodular

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.

--nonregular

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
--regular

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.

--noinsertion

Never flip-in a point that is unused in the seed triangulation.

--reducepoints

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.

--keepcard

Never change the cardinality of triangulations by flipping.

OPTIONS CONCERNING SYMMETRIES
--affinesymmetries

Assume that the symmetries are affine, in particular, that they conserve regularity.

--isometricsymmetries

Assume that the symmetries are isometric, in particular, that they preserve volume.

--nosymmetries

Ignore the symmetries.

OPTIONS CONTROLLING THE INTERNALS OF THE CLIENTS
--memopt

Save memory by using caching techniques.

--usegkz

Use GKZ vectors as a finger print in symmetry handling (only for points with isometric symmetries).

--usenaivesymmetries

Use naive full traversal of all symmetries for symmetry handling.

--useswitchtables

Use Jordan-Joswig-Kastner switch tables for symmetry handling.

--usesymmetrytables

Use tables of classified symmetries for symmetry handling. Obsolete, since slower than the other options.

--symtables [n]

Use [n] symtables for preprocessing symmetries. Obsolete, since slower than the other options.

--preprocesschiro

Preprocess the chirotope (default for points2[n]alltriangs).

--preprocesspoints

Heuristically transform points (only relevant for (co)circuit enumeration).

--simpidxsymmetries

Preprocess a representation of the symmetry group on simplex indices (only relevant for triangulation enumeration).

--userandomorder

Sort simplices in preprocessed index table randomly (only for points with isometric symmetries).

--usevolumeorder

Sort simplices in preprocessed index table by volume (only for points with isometric symmetries).

--usevolumes

Use volumes to check extendability of partial triangulations (only for points with isometric symmetries).

--fullextensioncheck

Put more effort in the check of extendability of a partial triangulation.

--noextensioncheck

Skip the check of extendability of a partial triangulation.

--extensioncheckfirst

Check extendability prior to symmetry.

--preprocesspoints

Preprocess the coordinate matrix of the points (slightly useful for (co-)circuit enumeration)

--chirocache [n]

Set the chirotope cache to n elements.

--localcache [n]

Set the cache for local operations.

--qsopt_ex

Use QSopt_ex for regularity checks (not thread-safe).

--soplex

Use soplex for regularity checks (requires separate installation of soplex).

OPTIONS CONCERNING MULTI-THREADING
--parallelenumeration

Use multiple threads for enumeration.

--workbuffercontrol

Control the interrupt of workers by size of the current workbuffer.

--parallelsymmetries

Use multiple threads only locally for symmetry checks.

--threads [n]

Use [n] threads (if possible).

--minnodebudget [n]

Let each thread process at least [n] nodes (to avoid multithreading overhead).

--maxnodebudget [n]

Let each thread process at most [n] nodes (to avoid thread starving).

--scalenodebudget [n]

Scale the default node budget by [n] percent (n integer)

--minworkbuffer [n]

(Currently unused.) Try to keep the work buffer above [n] nodes (to balance overhead and thread starving).

--maxworkbuffer [n]

(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.
--dump

Write intermediate results into a file.

--dumpfile [dumpfilename]

Write intermediate results into file dumpfilename (default: TOPCOM.dump).

--dumpfrequency [k]

Dump the results of each kth BFS round

--dumprotations [k]

Dump into k different rotating files.

--read

Read intermediate results from a file.

--readfile [readfilename]

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/.