Package TOPCOM

Triangulations Of Point Configurations and Oriented Matroids

http://www.rambau.wm.uni-bayreuth.de/TOPCOM/

TOPCOM is a package for computing Triangulations Of Point Configurations
and Oriented Matroids. It was very much inspired by the maple program
PUNTOS, which was written by Jesus de Loera. TOPCOM is entirely written
in C++, so there is a significant speed up compared to PUNTOS.

General Commands (Section 1)
B_A
Compute the group B_A_n. Output is written to stdout. The standard options described in TOPCOM(7) are available.
B_A_center
Compute the normalized group B_A_n. Output is written to stdout. The standard options described in TOPCOM(7) are available.
B_D
Compute the group B_D_n. Output is written to stdout. The standard options described in TOPCOM(7) are available.
checkregularity
Count the non-regular triangulations of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in...
chiro2allfinetriangs
Compute all fine triangulations of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
chiro2alltriangs
Compute all triangulations of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
chiro2circuits
Compute the circuits of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
chiro2cocircuits
Compute the cocircuits of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
chiro2dual
Compute the dual of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
chiro2finetriang
Compute a fine (i.e., using all vertices) triangulation of a chirotope by placing and pushing. Input is read from stdin; output is written to stdout. The...
chiro2finetriangs
Compute all fine triangulations of a chirotope that are connected by bistellar flips to a fine seed triangulation. Input is read from stdin; output is written...
chiro2mintriang
Compute the minimum triangulation of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
chiro2nallfinetriangs
Compute the number of fine triangulations of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
chiro2nalltriangs
Compute the number of triangulations of a chirotope. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
chiro2nfinetriangs
Compute the number of fine triangulations of a chirotope that are connected by bistellar flips to a fine seed triangulation. Input is read from stdin; output is...
chiro2ntriangs
Compute the number of triangulations of a chirotope that are connected by bistellar flips to the regular triangulations. Input is read from stdin; output is...
chiro2placingtriang
Compute the placing triangulation of a chirotope given by the numbering of the elements. Input is read from stdin; output is written to stdout. The standard...
chiro2triangs
Compute all triangulations of a chirotope that are connected by bistellar flips to the regular triangulations. Input is read from stdin; output is written to...
cocircuits2facets
Compute the facets of a set of cocircuits. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
points2allfinetriangs
Compute all fine triangulations of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
points2alltriangs
Compute all triangulations of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
points2chiro
Compute the chirotope of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are...
points2facets
Compute the facets of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
points2finetriang
Compute a fine (i.e., using all vertices) triangulation of a point configuration by placing and pushing. Input is read from stdin; output is written to stdout...
points2finetriangs
Compute all fine triangulations of a point configuration that are connected by bistellar flips to a fine seed triangulation. Input is read from stdin; output is...
points2flips
Compute all flips of a point configuration and the seed triangulation. Input is read from stdin; output is written to stdout. The standard options described in...
points2nallfinetriangs
Compute the number of fine triangulations of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in...
points2nalltriangs
Compute the number of triangulations of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in...
points2nfinetriangs
Compute the number of fine triangulations of a point configuration that are connected by bistellar flips to a fine seed triangulation. Input is read from stdin...
points2nflips
Compute the number of flips of a point configuration and the seed triangulation. Input is read from stdin; output is written to stdout. The standard options...
points2ntriangs
Compute the number of triangulations of a point configuration that are connected by bistellar flips to the regular triangulations. Input is read from stdin...
points2placingtriang
Compute the placing triangulation of a point configuration given by the numbering of the elements. Input is read from stdin; output is written to stdout. The...
points2triangs
Compute all triangulations of a point configuration that are connected by bistellar flips to the regular triangulations. Input is read from stdin; output is...
points2volume
Compute the volume of a point configuration. Input is read from stdin; output is written to stdout. The standard options described in TOPCOM(7) are available.
santos_22_triang
Compute a Santos point configuration, its symmetries, and its Santos triangulation without flips from a point configuration. Input is read from stdin; output is...
santos_dim4_triang
Compute a Santos point configuration, its symmetries, and its Santos triangulation without flips from a point configuration. Input is read from stdin; output is...
santos_triang
Compute a Santos point configuration, its symmetries, and its Santos triangulation without flips from a point configuration. Input is read from stdin; output is...
TOPCOM-cross
Compute the vertices of the D-dimensional cross-polytope. The point configuration is written to stdout.
TOPCOM-cube
Compute the vertices and symmetry generators of a cube of dimension D. The output is written to stdout.
TOPCOM-cyclic
Compute the vertices and symmetry generators of the cyclic D-polytope with N vertices. The point configuration is written to stdout.
TOPCOM-hypersimplex
Compute the vertices and symmetry generators of the Kth hypersimplex in dimension D. The output is written to stdout.
TOPCOM-lattice
Compute the permutations of a lattice. The permutations are written to stdout.
Miscellanea (Section 7)
TOPCOM
TOPCOM programs share a command-line parsing library. Therefore, all TOPCOM programs accept the following options. Note that some options are not relevant to...