Provided by: topcom_1.1.2+ds-1.1build2_amd64

**NAME**

TOPCOM- Triangulations Of Point Configurations and Oriented Matroids

**COMMANDS**

The following commands are provided. In Debian, each command is prefixed by "topcom-".points2prettyprintDisplays the point and their symmetry generators in a more readable form.points2chiroComputes the chirotope of a point configuration.chiro2dualComputes the dual of a chirotope.chiro2circuitsComputes the circuits of a chirotope.points2circuitsDto. for point configurations (using a faster method).chiro2cocircuitsComputes the cocircuits of a chirotope.points2cocircuitsDto. for point configurations (using a faster method).cocircuits2facetsComputes the facets of a set of cocircuits.points2facetsComputes the facets of a point configuration.points2galeComputes a Gale transform of a point configuration.chiro2circuitsComputes the circuits of a point configuration.chiro2cocircuitsComputes the cocircuits of a point configuration.points2facetsComputes the facets of a point configuration.points2nflipsComputes the number of flips of a point configurations and the seed triangulation.points2flipsComputes all flips of a point configurations and the seed triangulation.chiro2placingtriangComputes the placing triangulation of a chirotope given by the numbering of the elements.points2placingtriangDto. for point configurations.chiro2finetriangComputes a fine (i.e., using all vertices) triangulation by placing and pushing.points2finetriangDto. for point configurations.chiro2triangsComputes 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.points2triangsDto. for point configurations.chiro2ntriangsComputes 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.points2ntriangsDto. for point configurations.chiro2finetriangsComputes 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.points2finetriangsDto. for point configurations.chiro2nfinetriangsComputes the number of all fine triangulations of a chirotope that are connected by bistellar flips to a fine seed triangulation.points2nfinetriangsDto. for point configurations.chiro2alltriangsComputes all triangulations of a chirotope.points2alltriangsDto. for point configurations.chiro2nalltriangsComputes the number of all triangulations of a chirotope.points2nalltriangsDto. for point configurations.chiro2allfinetriangsComputes all fine triangulations (sometimes called “full”) of a chirotope.points2allfinetriangsDto. for point configurations.chiro2nallfinetriangsComputes the number of all fine triangulations of a chirotope.points2nallfinetriangsDto. for point configurations.chiro2mintriangComputes a triangulation of a chirotope with a minimum number of simplices.points2mintriangDto. for point configurations.B_SnComputes the vertices and symmetry generators of the permutation polytope of the symmetric group of degree n, also known as the Birkhoff polytope.B_AnComputes the vertices and symmetry generators of the permutation polytope of the alternating group of degree n, also known as the even Birkhoff polytope.B_DnComputes the vertices and symmetry generators of the permutation polytope of the dihedral group of degree n.B_S_centernComputes B_S n with an additional center point.B_A_centernComputes B_A n with an additional center point.B_D_centernComputes B_D n with an additional center point.cubedComputes the vertices and symmetry generators of a d-cube.cyclicndComputes the vertices and symmetry generators of the cyclic d-polytope with n vertices.crossdComputes the vertices and symmetry generators of the d-dimensional crosspolytope.latticenmComputes the nm two-dimensional lattice points with non-negative coordinates at most (n−1,m−1) and their symmetry generators.hypersimplexdk[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_triangComputes 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-hor--helpPrint a usage message.-dDebug.-vVerbose.--heightsOutput a height vector for every regular triangulation (implies--regular).--flipsOutput all flips in terms of IDs of adjacent triangulations. (Can be used to generate the flip graph.)--asyWrite 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--checktriangCheck seed triangulation. OPTIONS FOR REPORTING PROPERTIES OF DISCOVERED TRIANGULATIONS--flipdeficiencyCheck 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)--noorbitcountOnly 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.--unimodularOutput 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.--nonregularOutput 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--regularSearch 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.--noinsertionNever flip-in a point that is unused in the seed triangulation.--reducepointsTry 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.--keepcardNever change the cardinality of triangulations by flipping. OPTIONS CONCERNING SYMMETRIES--affinesymmetriesAssume that the symmetries are affine, in particular, that they conserve regularity.--isometricsymmetriesAssume that the symmetries are isometric, in particular, that they preserve volume.--nosymmetriesIgnore the symmetries. OPTIONS CONTROLLING THE INTERNALS OF THE CLIENTS--memoptSave memory by using caching techniques.--usegkzUse GKZ vectors as a finger print in symmetry handling (only for points with isometric symmetries).--usenaivesymmetriesUse naive full traversal of all symmetries for symmetry handling.--useswitchtablesUse Jordan-Joswig-Kastner switch tables for symmetry handling.--usesymmetrytablesUse 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.--preprocesschiroPreprocess the chirotope (default for points2[n]alltriangs).--preprocesspointsHeuristically transform points (only relevant for (co)circuit enumeration).--simpidxsymmetriesPreprocess a representation of the symmetry group on simplex indices (only relevant for triangulation enumeration).--userandomorderSort simplices in preprocessed index table randomly (only for points with isometric symmetries).--usevolumeorderSort simplices in preprocessed index table by volume (only for points with isometric symmetries).--usevolumesUse volumes to check extendability of partial triangulations (only for points with isometric symmetries).--fullextensioncheckPut more effort in the check of extendability of a partial triangulation.--noextensioncheckSkip the check of extendability of a partial triangulation.--extensioncheckfirstCheck extendability prior to symmetry.--preprocesspointsPreprocess 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_exUse QSopt_ex for regularity checks (not thread-safe).--soplexUse soplex for regularity checks (requires separate installation of soplex). OPTIONS CONCERNING MULTI-THREADING--parallelenumerationUse multiple threads for enumeration.--workbuffercontrolControl the interrupt of workers by size of the current workbuffer.--parallelsymmetriesUse 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.--dumpWrite 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.--readRead 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/.