Provided by: topcom_1.1.2+ds-1.1build2_amd64 bug

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/.