.\" Text automatically generated by txt2man
.TH TOPCOM 7 "29 March 2024" "1.1.2" ""
.SH NAME
\fBTOPCOM \fP- Triangulations Of Point Configurations and Oriented Matroids
.SH COMMANDS
The following commands are provided. In Debian, each command is prefixed by
"topcom-".
.TP
.B
points2prettyprint
Displays the point and their symmetry generators in a
more readable form.
.TP
.B
points2chiro
Computes the chirotope of a point configuration.
.TP
.B
chiro2dual
Computes the dual of a chirotope.
.TP
.B
chiro2circuits
Computes the circuits of a chirotope.
.TP
.B
points2circuits
Dto. for point configurations (using a faster method).
.TP
.B
chiro2cocircuits
Computes the cocircuits of a chirotope.
.TP
.B
points2cocircuits
Dto. for point configurations (using a faster method).
.TP
.B
cocircuits2facets
Computes the facets of a set of cocircuits.
.TP
.B
points2facets
Computes the facets of a point configuration.
.TP
.B
points2gale
Computes a Gale transform of a point configuration.
.TP
.B
chiro2circuits
Computes the circuits of a point configuration.
.TP
.B
chiro2cocircuits
Computes the cocircuits of a point configuration.
.TP
.B
points2facets
Computes the facets of a point configuration.
.TP
.B
points2nflips
Computes the number of flips of a point configurations
and the seed triangulation.
.TP
.B
points2flips
Computes all flips of a point configurations and the
seed triangulation.
.TP
.B
chiro2placingtriang
Computes the placing triangulation of a chirotope
given by the numbering of the elements.
.TP
.B
points2placingtriang
Dto. for point configurations.
.TP
.B
chiro2finetriang
Computes a fine (i.e., using all vertices)
triangulation by placing and pushing.
.TP
.B
points2finetriang
Dto. for point configurations.
.TP
.B
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.
.TP
.B
points2triangs
Dto. for point configurations.
.TP
.B
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.
.TP
.B
points2ntriangs
Dto. for point configurations.
.TP
.B
chiro2finetriangs
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.
.TP
.B
points2finetriangs
Dto. for point configurations.
.TP
.B
chiro2nfinetriangs
Computes the number of all fine triangulations of a
chirotope that are connected by bistellar flips to a
fine seed triangulation.
.TP
.B
points2nfinetriangs
Dto. for point configurations.
.TP
.B
chiro2alltriangs
Computes all triangulations of a chirotope.
.TP
.B
points2alltriangs
Dto. for point configurations.
.TP
.B
chiro2nalltriangs
Computes the number of all triangulations of a
chirotope.
.TP
.B
points2nalltriangs
Dto. for point configurations.
.TP
.B
chiro2allfinetriangs
Computes all fine triangulations (sometimes called
“full”) of a chirotope.
.TP
.B
points2allfinetriangs
Dto. for point configurations.
.TP
.B
chiro2nallfinetriangs
Computes the number of all fine triangulations of a
chirotope.
.TP
.B
points2nallfinetriangs
Dto. for point configurations.
.TP
.B
chiro2mintriang
Computes a triangulation of a chirotope with a
minimum number of simplices.
.TP
.B
points2mintriang
Dto. for point configurations.
.TP
.B
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.
.TP
.B
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.
.TP
.B
B_D n
Computes the vertices and symmetry generators of the
permutation polytope of the dihedral group of degree
n.
.TP
.B
B_S_center n
Computes B_S n with an additional center point.
.TP
.B
B_A_center n
Computes B_A n with an additional center point.
.TP
.B
B_D_center n
Computes B_D n with an additional center point.
.TP
.B
cube d
Computes the vertices and symmetry generators of a
d-cube.
.TP
.B
cyclic n d
Computes the vertices and symmetry generators of the
cyclic d-polytope with n vertices.
.TP
.B
cross d
Computes the vertices and symmetry generators of the
d-dimensional crosspolytope.
.TP
.B
lattice n m
Computes the nm two-dimensional lattice points with
non-negative coordinates at most (n−1,m−1) and their
symmetry generators.
.TP
.B
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.
.TP
.B
santos_triang
Computes the point configuration, the symmetry, and
the Santos triangulation (without flips).
.SH OPTIONS
The following command line options are supported. Note that not all options
are sensible for all clients.
.PP
OPTIONS CONCERNING INPUT/OUTPUT FROM FILES
.TP
.B
\fB-I\fP [filename]
read input from [filename] instead of stdin.
.PP
OPTIONS CONCERNING OUTPUT OF INFORMATION
.TP
.B
\fB-h\fP or \fB--help\fP
Print a usage message.
.TP
.B
\fB-d\fP
Debug.
.TP
.B
\fB-v\fP
Verbose.
.TP
.B
\fB--heights\fP
Output a height vector for every regular
triangulation (implies \fB--regular\fP).
.TP
.B
\fB--flips\fP
Output all flips in terms of IDs of adjacent
triangulations. (Can be used to generate the flip
graph.)
.TP
.B
\fB--asy\fP
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/.
.PP
OPTIONS FOR CHECKING INPUT
.TP
.B
\fB--checktriang\fP
Check seed triangulation.
.PP
OPTIONS FOR REPORTING PROPERTIES OF DISCOVERED TRIANGULATIONS
.TP
.B
\fB--flipdeficiency\fP
Check triangulations for flip deficiency during
flip-graph exploration.
.TP
.B
\fB--findregular\fP [k]
Check every k-th triangulation for regularity and
stop if a regular one is found during flip-graph
exploration.
.PP
OPTIONS CONCERNING WHICH TRIANGULATIONS ARE OUTPUT (NO INFLUENCE ON
FLIP-GRAPH EXPLORATION)
.TP
.B
\fB--noorbitcount\fP
Only count symmetry classes, not the total number.
.TP
.B
\fB--cardinality\fP [k]
Count/output only triangulations with exactly k
simplices.
.TP
.B
\fB--maxcardinality\fP [k]
Count/oputput only triangulations with at most k
simplices.
.TP
.B
\fB--unimodular\fP
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.
.TP
.B
\fB--nonregular\fP
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.
.PP
OPTIONS CONCERNING WHICH TRIANGULATIONS ARE EXPLORED
.TP
.B
\fB--regular\fP
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.
.TP
.B
\fB--noinsertion\fP
Never flip-in a point that is unused in the seed
triangulation.
.TP
.B
\fB--reducepoints\fP
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.
.TP
.B
\fB--keepcard\fP
Never change the cardinality of triangulations by
flipping.
.PP
OPTIONS CONCERNING SYMMETRIES
.TP
.B
\fB--affinesymmetries\fP
Assume that the symmetries are affine, in particular,
that they conserve regularity.
.TP
.B
\fB--isometricsymmetries\fP
Assume that the symmetries are isometric, in
particular, that they preserve volume.
.TP
.B
\fB--nosymmetries\fP
Ignore the symmetries.
.PP
OPTIONS CONTROLLING THE INTERNALS OF THE CLIENTS
.TP
.B
\fB--memopt\fP
Save memory by using caching techniques.
.TP
.B
\fB--usegkz\fP
Use GKZ vectors as a finger print in symmetry handling
(only for points with isometric symmetries).
.TP
.B
\fB--usenaivesymmetries\fP
Use naive full traversal of all symmetries for symmetry
handling.
.TP
.B
\fB--useswitchtables\fP
Use Jordan-Joswig-Kastner switch tables for symmetry
handling.
.TP
.B
\fB--usesymmetrytables\fP
Use tables of classified symmetries for symmetry
handling. Obsolete, since slower than the other options.
.TP
.B
\fB--symtables\fP [n]
Use [n] symtables for preprocessing symmetries.
Obsolete, since slower than the other options.
.TP
.B
\fB--preprocesschiro\fP
Preprocess the chirotope (default for
points2[n]alltriangs).
.TP
.B
\fB--preprocesspoints\fP
Heuristically transform points (only relevant for
(co)circuit enumeration).
.TP
.B
\fB--simpidxsymmetries\fP
Preprocess a representation of the symmetry group on
simplex indices (only relevant for triangulation
enumeration).
.TP
.B
\fB--userandomorder\fP
Sort simplices in preprocessed index table randomly
(only for points with isometric symmetries).
.TP
.B
\fB--usevolumeorder\fP
Sort simplices in preprocessed index table by volume
(only for points with isometric symmetries).
.TP
.B
\fB--usevolumes\fP
Use volumes to check extendability of partial
triangulations (only for points with isometric
symmetries).
.TP
.B
\fB--fullextensioncheck\fP
Put more effort in the check of extendability of a
partial triangulation.
.TP
.B
\fB--noextensioncheck\fP
Skip the check of extendability of a partial
triangulation.
.TP
.B
\fB--extensioncheckfirst\fP
Check extendability prior to symmetry.
.TP
.B
\fB--preprocesspoints\fP
Preprocess the coordinate matrix of the points
(slightly useful for (co-)circuit enumeration)
.TP
.B
\fB--chirocache\fP [n]
Set the chirotope cache to n elements.
.TP
.B
\fB--localcache\fP [n]
Set the cache for local operations.
.TP
.B
\fB--qsopt_ex\fP
Use QSopt_ex for regularity checks (not thread-safe).
.TP
.B
\fB--soplex\fP
Use soplex for regularity checks (requires separate
installation of soplex).
.PP
OPTIONS CONCERNING MULTI-THREADING
.TP
.B
\fB--parallelenumeration\fP
Use multiple threads for enumeration.
.TP
.B
\fB--workbuffercontrol\fP
Control the interrupt of workers by size of the current
workbuffer.
.TP
.B
\fB--parallelsymmetries\fP
Use multiple threads only locally for symmetry checks.
.TP
.B
\fB--threads\fP [n]
Use [n] threads (if possible).
.TP
.B
\fB--minnodebudget\fP [n]
Let each thread process at least [n] nodes (to avoid
multithreading overhead).
.TP
.B
\fB--maxnodebudget\fP [n]
Let each thread process at most [n] nodes (to avoid
thread starving).
.TP
.B
\fB--scalenodebudget\fP [n]
Scale the default node budget by [n] percent (n
integer)
.TP
.B
\fB--minworkbuffer\fP [n]
(Currently unused.) Try to keep the work buffer above
[n] nodes (to balance overhead and thread starving).
.TP
.B
\fB--maxworkbuffer\fP [n]
(Currently unused.) Try to keep the work buffer below
[n] node (to balance overhead and thread starving).
.PP
OPTIONS FOR WARM STARTS FROM PREVIOUS CALCULATIONS
.PP
These options currently only work for an interrupted flip graph exploration.
.TP
.B
\fB--dump\fP
Write intermediate results into a file.
.TP
.B
\fB--dumpfile\fP [dumpfilename]
Write intermediate results into file dumpfilename
(default: TOPCOM.dump).
.TP
.B
\fB--dumpfrequency\fP [k]
Dump the results of each kth BFS round
.TP
.B
\fB--dumprotations\fP [k]
Dump into k different rotating files.
.TP
.B
\fB--read\fP
Read intermediate results from a file.
.TP
.B
\fB--readfile\fP [readfilename]
Read intermediate results from file dumpfilename
(default: TOPCOM.dump.[rotationnumber]).
.SH 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/.