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# Homogenize -- an optional argument to most functions in Topcom to indicate whether to homogenize the matrix

## Description

Most functions in this package take a $d \times n$ matrix $A$, representing a point or vector configuration: the columns are the points or vectors. Topcom's input is always a matrix representing a vector configuration. A matrix $A$ whose columns represent a point configuration can be "homogenized" to a vector configuration by adding a row of ones to $A$, forming a $(d+1) \times n$ matrix $A^h$.

## Functions with optional argument named Homogenize :

• chirotopeString(...,Homogenize=>...) -- see chirotopeString(Matrix) -- compute the chirotope string of a point or vector configuration
• naiveChirotopeString(...,Homogenize=>...) -- see naiveChirotopeString(Matrix) -- compute the chirotope string of a point or vector configuration
• orientedCircuits(...,Homogenize=>...) -- see orientedCircuits -- compute the oriented circuits of an oriented matroid or point or vector configuration
• orientedCocircuits(...,Homogenize=>...) -- see orientedCocircuits -- compute the oriented cocircuits of an oriented matroid
• topcomAllTriangulations(...,Homogenize=>...) -- see topcomAllTriangulations(Matrix) -- generate all triangulations of a point or vector configuration
• topcomFlips(...,Homogenize=>...) -- see topcomFlips(Matrix,List) -- find the neighboring triangulations (bistellar flips) of a triangulation
• topcomIsRegularTriangulation(...,Homogenize=>...) -- see topcomIsRegularTriangulation -- determine if a given triangulation is a regular triangulation
• topcomIsTriangulation(...,Homogenize=>...) -- see topcomIsTriangulation(Matrix,List) -- determine if a set of subsets is a triangulation of a point set
• topcomNumFlips(...,Homogenize=>...) -- see topcomNumFlips(Matrix,List) -- find the number of neighboring triangulations (bistellar flips) of a triangulation
• topcomNumTriangulations(...,Homogenize=>...) -- see topcomNumTriangulations(Matrix) -- the number of triangulations of a point or vector configuration
• topcomRegularFineTriangulation(...,Homogenize=>...) -- see topcomRegularFineTriangulation(Matrix) -- compute a regular triangulation using all of the given points
• topcomRegularTriangulationWeights(...,Homogenize=>...) -- see topcomRegularTriangulationWeights(Matrix,List) -- find a list of heights of a regular triangulation

## For the programmer

The object Homogenize is .