Arrangement -- the class of all hyperplane arrangements

Types of hyperplane arrangement:

• CentralArrangement -- the class of all central hyperplane arrangements

Functions and methods returning a hyperplane arrangement:

• Arrangement ** Ring -- change the coefficient ring of an arrangement
• arrangement(Flat) -- get the hyperplane arrangement to which a flat belongs
• arrangement -- see arrangement(List,Ring) -- make a hyperplane arrangement
• arrangement(List) -- see arrangement(List,Ring) -- make a hyperplane arrangement
• arrangement(List,Ring) -- make a hyperplane arrangement
• arrangement(RingElement) -- see arrangement(List,Ring) -- make a hyperplane arrangement
• arrangement(Matrix) -- see arrangement(Matrix,Ring) -- make a hyperplane arrangement
• arrangement(Matrix,Ring) -- make a hyperplane arrangement
• arrangement(String) -- see arrangement(String,Ring) -- access a database of classic hyperplane arrangements
• arrangement(String,PolynomialRing) -- see arrangement(String,Ring) -- access a database of classic hyperplane arrangements
• arrangement(String,Ring) -- access a database of classic hyperplane arrangements
• Arrangement ++ Arrangement -- see arrangementSum(Arrangement,Arrangement) -- make the direct sum of two arrangements
• arrangementSum(Arrangement,Arrangement) -- make the direct sum of two arrangements
• compress(Arrangement) -- extract nonzero equations
• deCone(CentralArrangement,RingElement) -- produce an affine arrangement from a central one
• deCone(CentralArrangement,ZZ) -- see deCone(CentralArrangement,RingElement) -- produce an affine arrangement from a central one
• deletion(Arrangement,List) -- see deletion(Arrangement,RingElement) -- deletion of a subset of an arrangement
• deletion(Arrangement,RingElement) -- deletion of a subset of an arrangement
• deletion(Arrangement,Set) -- see deletion(Arrangement,RingElement) -- deletion of a subset of an arrangement
• deletion(Arrangement,ZZ) -- see deletion(Arrangement,RingElement) -- deletion of a subset of an arrangement
• genericArrangement -- see genericArrangement(ZZ,ZZ,Ring) -- realize the uniform matroid using points on the monomial curve
• genericArrangement(ZZ,ZZ) -- see genericArrangement(ZZ,ZZ,Ring) -- realize the uniform matroid using points on the monomial curve
• genericArrangement(ZZ,ZZ,Ring) -- realize the uniform matroid using points on the monomial curve
• graphic(List) -- see graphic(List,List,PolynomialRing) -- make a graphic arrangement
• graphic(List,PolynomialRing) -- see graphic(List,List,PolynomialRing) -- make a graphic arrangement
• graphic(List,Ring) -- see graphic(List,List,PolynomialRing) -- make a graphic arrangement
• prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring
• randomArrangement(ZZ,PolynomialRing,ZZ) -- generate an arrangement at random
• randomArrangement(ZZ,ZZ,ZZ) -- see randomArrangement(ZZ,PolynomialRing,ZZ) -- generate an arrangement at random
• Arrangement ^ Flat -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,Flat) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,List) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,RingElement) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,Set) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,ZZ) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Flat) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• Arrangement _ Flat -- see subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• subArrangement -- see subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• subArrangement(Flat) -- see subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• Arrangement ** RingMap -- see substitute(Arrangement,RingMap) -- change the ring of an arrangement
• substitute(Arrangement,Ring) -- see substitute(Arrangement,RingMap) -- change the ring of an arrangement
• substitute(Arrangement,RingMap) -- change the ring of an arrangement
• trim(Arrangement) -- make a simple hyperplane arrangement
• typeA(ZZ) -- see typeA(ZZ,Ring) -- make the hyperplane arrangement defined by a type $A_n$ root system
• typeA(ZZ,PolynomialRing) -- see typeA(ZZ,Ring) -- make the hyperplane arrangement defined by a type $A_n$ root system
• typeA(ZZ,Ring) -- make the hyperplane arrangement defined by a type $A_n$ root system
• typeB(ZZ) -- see typeB(ZZ,Ring) -- make the hyperplane arrangement defined by a type $B_n$ root system
• typeB(ZZ,PolynomialRing) -- see typeB(ZZ,Ring) -- make the hyperplane arrangement defined by a type $B_n$ root system
• typeB(ZZ,Ring) -- make the hyperplane arrangement defined by a type $B_n$ root system
• typeD(ZZ) -- see typeD(ZZ,Ring) -- make the hyperplane arrangement defined by a type $D_n$ root system
• typeD(ZZ,PolynomialRing) -- see typeD(ZZ,Ring) -- make the hyperplane arrangement defined by a type $D_n$ root system
• typeD(ZZ,Ring) -- make the hyperplane arrangement defined by a type $D_n$ root system

Methods that use a hyperplane arrangement:

• Arrangement == Arrangement -- whether two hyperplane arrangements are equal
• closure(Arrangement,Ideal) -- see closure(Arrangement,List) -- closure operation in the intersection lattice
• closure(Arrangement,List) -- closure operation in the intersection lattice
• coefficients(Arrangement) -- make a matrix from the coefficients of the defining equations
• cone(Arrangement,RingElement) -- creates an associated central hyperplane arrangement
• cone(Arrangement,Symbol) -- see cone(Arrangement,RingElement) -- creates an associated central hyperplane arrangement
• EPY(Arrangement) -- see EPY(Arrangement,PolynomialRing) -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
• EPY(Arrangement,PolynomialRing) -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
• flat(Arrangement,List) -- make a flat from a list of indices
• flats(Arrangement) -- see flats(ZZ,Arrangement) -- list the flats of an arrangement of a given rank
• flats(ZZ,Arrangement) -- list the flats of an arrangement of a given rank
• hyperplanes(Arrangement) -- the defining linear forms of an arrangement
• toList(Arrangement) -- see hyperplanes(Arrangement) -- the defining linear forms of an arrangement
• isCentral(Arrangement) -- test to see if a hyperplane arrangement is central
• matrix(Arrangement) -- make a matrix from the defining equations
• orlikSolomon(Arrangement) -- see orlikSolomon(Arrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Solomon algebra
• orlikSolomon(Arrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Solomon algebra
• orlikSolomon(Arrangement,Ring) -- see orlikSolomon(Arrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Solomon algebra
• orlikSolomon(Arrangement,Symbol) -- see orlikSolomon(Arrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Solomon algebra
• poincare(Arrangement) -- compute the Poincaré polynomial of an arrangement
• ring(Arrangement) -- get the underlying ring of a hyperplane arrangement

For the programmer

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:1087:0.