Ubuntu Manpage: TOPCOM - Triangulations Of Point Configurations and Oriented Matroids

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
“full”) 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 “full”) 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 (n−1,m−1) 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/.