# Arrangement -- class of hyperplane arrangements

## Description

A hyperplane is an affine-linear subspace of codimension one. An arrangement is a finite set of hyperplanes.

## Functions and methods returning a hyperplane arrangement :

• arrangement -- create a hyperplane arrangement
• "arrangement(Arrangement,Ring)" -- see arrangement -- create a hyperplane arrangement
• "arrangement(List)" -- see arrangement -- create a hyperplane arrangement
• "arrangement(List,Ring)" -- see arrangement -- create a hyperplane arrangement
• "arrangement(Matrix)" -- see arrangement -- create a hyperplane arrangement
• "arrangement(Matrix,Ring)" -- see arrangement -- create a hyperplane arrangement
• "arrangement(RingElement)" -- see arrangement -- create a hyperplane arrangement
• Arrangement ** Arrangement (missing documentation)
• Arrangement ** Ring (missing documentation)
• Arrangement ^ Flat -- restriction of arrangement to flat
• Arrangement _ Flat -- Subarrangement containing a fixed flat
• arrangement(Flat) (missing documentation)
• arrangement(String) (missing documentation)
• arrangement(String,PolynomialRing) -- look up a built-in hyperplane arrangement
• arrangement(String,Ring) (missing documentation)
• arrangementSum (missing documentation)
• arrangementSum(Arrangement,Arrangement) (missing documentation)
• changeRing (missing documentation)
• changeRing(Arrangement,Ring) (missing documentation)
• compress(Arrangement) -- extract nonzero equations
• deCone -- produce an affine arrangement from a central one
• "deCone(CentralArrangement,RingElement)" -- see deCone -- produce an affine arrangement from a central one
• "deCone(CentralArrangement,ZZ)" -- see deCone -- produce an affine arrangement from a central one
• deletion -- subarrangement given by deleting a hyperplane
• "deletion(Arrangement,RingElement)" -- see deletion -- subarrangement given by deleting a hyperplane
• graphic -- Make a graphic arrangement
• "graphic(List)" -- see graphic -- Make a graphic arrangement
• "graphic(List,PolynomialRing)" -- see graphic -- Make a graphic arrangement
• "graphic(List,Ring)" -- see graphic -- Make a graphic arrangement
• prune(Arrangement) (missing documentation)
• randomArrangement -- generate an arrangement at random
• "randomArrangement(ZZ,ZZ,ZZ)" -- see randomArrangement -- generate an arrangement at random
• restriction -- restriction of arrangement to flat/hyperplane
• "restriction(Arrangement,Flat)" -- see restriction -- restriction of arrangement to flat/hyperplane
• "restriction(Arrangement,Ideal)" -- see restriction -- restriction of arrangement to flat/hyperplane
• "restriction(Arrangement,RingElement)" -- see restriction -- restriction of arrangement to flat/hyperplane
• "restriction(Flat)" -- see restriction -- restriction of arrangement to flat/hyperplane
• restriction(Arrangement,ZZ) (missing documentation)
• subArrangement -- Subarrangement containing a fixed flat
• "subArrangement(Arrangement,Flat)" -- see subArrangement -- Subarrangement containing a fixed flat
• "subArrangement(Flat)" -- see subArrangement -- Subarrangement containing a fixed flat
• trim(Arrangement) -- minimize the generators
• typeA -- Type A reflection arrangement
• "typeA(ZZ)" -- see typeA -- Type A reflection arrangement
• typeA(ZZ,PolynomialRing) -- A_n arrangement with specified coordinate ring
• typeA(ZZ,Ring) -- A_n reflection arrangement with specified coefficient ring
• typeB -- Type B reflection arrangement
• "typeB(ZZ)" -- see typeB -- Type B reflection arrangement
• "typeB(ZZ,PolynomialRing)" -- see typeB -- Type B reflection arrangement
• "typeB(ZZ,Ring)" -- see typeB -- Type B reflection arrangement
• typeD -- Type D reflection arrangement
• "typeD(ZZ)" -- see typeD -- Type D reflection arrangement
• "typeD(ZZ,PolynomialRing)" -- see typeD -- Type D reflection arrangement
• "typeD(ZZ,Ring)" -- see typeD -- Type D reflection arrangement

## Methods that use a hyperplane arrangement :

• Arrangement == Arrangement (missing documentation)
• "circuits(Arrangement)" -- see circuits -- list the circuits of an arrangement
• "closure(Arrangement,List)" -- see closure -- closure operation in the intersection lattice
• closure(Arrangement,Arrangement) (missing documentation)
• closure(Arrangement,Ideal) (missing documentation)
• coefficients(Arrangement) -- create a matrix from the coefficients of the equations of an arrangement
• cone(Arrangement,RingElement) -- Cone of an arrangement
• cone(Arrangement,Symbol) (missing documentation)
• describe(Arrangement) (missing documentation)
• "EPY(Arrangement)" -- see EPY -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
• "EPY(Arrangement,PolynomialRing)" -- see EPY -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
• "euler(Arrangement)" -- see euler(Flat)
• expression(Arrangement) (missing documentation)
• "flat(Arrangement,List)" -- see flat -- make a flat from a list of indices
• "flats(Arrangement)" -- see flats -- list the flats of an arrangement of given rank
• "flats(ZZ,Arrangement)" -- see flats -- list the flats of an arrangement of given rank
• isCentral(Arrangement) (missing documentation)
• matrix(Arrangement) -- create a matrix from the equations of an arrangement
• net(Arrangement) (missing documentation)
• "orlikSolomon(Arrangement)" -- see orlikSolomon -- defining ideal for the Orlik-Solomon algebra
• "orlikSolomon(Arrangement,Ring)" -- see orlikSolomon -- defining ideal for the Orlik-Solomon algebra
• "orlikSolomon(Arrangement,Symbol)" -- see orlikSolomon -- defining ideal for the Orlik-Solomon algebra
• orlikSolomon(Arrangement,PolynomialRing) (missing documentation)
• poincare(Arrangement) (missing documentation)
• rank(Arrangement) -- compute the rank
• ring(Arrangement) -- get the associated ring
• tolist(Arrangement) (missing documentation)

## For the programmer

The object Arrangement is a type, with ancestor classes HashTable < Thing.