Topcom -- interface to selected functions from topcom package

Topcom is mathematical software written by Jorg Rambau for computing and manipulating triangulations of polytopes and chirotopes.

This Macaulay2 package provides an interface for some of the functionality of this software.

The package is meant as an internal package, to be called by packages such as Polyhedra. It is highly recommended to use those packages, rather than calling this package directly.

Example use of Topcom

• An example use of TopCom -- interface to selected functions from topcom package

Generating triangulations

• topcomAllTriangulations(Matrix) -- generate all triangulations of a point or vector configuration
• topcomNumTriangulations(Matrix) -- the number of triangulations of a point or vector configuration

Useful functions involving specific triangulations

• topcomRegularFineTriangulation(Matrix) -- compute a regular triangulation using all of the given points
• topcomIsTriangulation(Matrix,List) -- determine if a set of subsets is a triangulation of a point set
• topcomIsRegularTriangulation(Matrix,List) -- determine if a given triangulation is a regular triangulation
• topcomRegularTriangulationWeights(Matrix,List) -- find a list of heights of a regular triangulation

Useful functions involving bistellar flips

• topcomFlips(Matrix,List) -- find the neighboring triangulations (bistellar flips) of a triangulation
• topcomNumFlips(Matrix,List) -- find the number of neighboring triangulations (bistellar flips) of a triangulation

Chirotope functions

The chirotope of a point set (or vector set), consisting of the columns of the $d \times n$ matrix $A$, is the function which assigns to each $d+1 \times d+1$ minor of $\overline{A}$ the sign of its determinant. Topcom encodes this into a string. See chirotopeString for details about the output of this function.

• chirotopeString(Matrix) -- compute the chirotope string of a point or vector configuration
• naiveChirotopeString(Matrix) -- compute the chirotope string of a point or vector configuration
• orientedCircuits(String) -- compute the oriented circuits of an oriented matroid or point or vector configuration
• orientedCocircuits(String) -- compute the oriented cocircuits of an oriented matroid

Author

• Mike Stillman <[email protected]>

Version

This documentation describes version 0.95 of Topcom.

Source code

The source code from which this documentation is derived is in the file Topcom.m2.

Exports