HyperplaneArrangements : Table of Contents

• HyperplaneArrangements -- manipulating hyperplane arrangements
• Arrangement -- the class of all hyperplane arrangements
• Arrangement ** Ring -- change the coefficient ring of an arrangement
• Arrangement == Arrangement -- whether two hyperplane arrangements are equal
• arrangement(Flat) -- get the hyperplane arrangement to which a flat belongs
• arrangement(List,Ring) -- make a hyperplane arrangement
• arrangement(Matrix,Ring) -- make a hyperplane arrangement
• arrangement(String,Ring) -- access a database of classic hyperplane arrangements
• arrangementSum(Arrangement,Arrangement) -- make the direct sum of two arrangements
• CentralArrangement -- the class of all central hyperplane arrangements
• circuits(CentralArrangement) -- list the circuits of an arrangement
• closure(Arrangement,List) -- closure operation in the intersection lattice
• coefficients(Arrangement) -- make a matrix from the coefficients of the defining equations
• compress(Arrangement) -- extract nonzero equations
• cone(Arrangement,RingElement) -- creates an associated central hyperplane arrangement
• deCone(CentralArrangement,RingElement) -- produce an affine arrangement from a central one
• deletion(Arrangement,RingElement) -- deletion of a subset of an arrangement
• der(CentralArrangement,List) -- compute the module of logarithmic derivations
• dual(CentralArrangement,Ring) -- the Gale dual of an arrangement
• EPY(Arrangement,PolynomialRing) -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
• euler(CentralArrangement) -- compute the Euler characteristic of the projective complement
• eulerRestriction(CentralArrangement,List,ZZ) -- form the Euler restriction of a central multiarrangement
• Flat -- intersection of hyperplanes
• Flat == Flat -- whether two flats are equal
• flat(Arrangement,List) -- make a flat from a list of indices
• flats(ZZ,Arrangement) -- list the flats of an arrangement of a given rank
• genericArrangement(ZZ,ZZ,Ring) -- realize the uniform matroid using points on the monomial curve
• graphic(List,List,PolynomialRing) -- make a graphic arrangement
• hyperplanes(Arrangement) -- the defining linear forms of an arrangement
• isCentral(Arrangement) -- test to see if a hyperplane arrangement is central
• isDecomposable(CentralArrangement,Ring) -- whether a hyperplane arrangement decomposable in the sense of Papadima-Suciu
• logCanonicalThreshold(CentralArrangement) -- compute the log-canonical threshold of an arrangement
• makeEssential(CentralArrangement) -- make an essential arrangement out of an arbitrary one
• matrix(Arrangement) -- make a matrix from the defining equations
• matroid(CentralArrangement) -- get the matroid of a central arrangement
• meet(Flat,Flat) -- compute the meet operation in the intersection lattice
• multiplierIdeal(QQ,CentralArrangement,List) -- compute a multiplier ideal
• orlikSolomon(Arrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Solomon algebra
• orlikTerao(CentralArrangement,PolynomialRing) -- compute the defining ideal for the Orlik-Terao algebra
• poincare(Arrangement) -- compute the Poincaré polynomial of an arrangement
• prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring
• randomArrangement(ZZ,PolynomialRing,ZZ) -- generate an arrangement at random
• rank(CentralArrangement) -- compute the rank of a central hyperplane arrangement
• rank(Flat) -- compute the rank of a flat
• restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• ring(Arrangement) -- get the underlying ring of a hyperplane arrangement
• subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• substitute(Arrangement,RingMap) -- change the ring of an arrangement
• toList(Flat) -- the indices of a flat
• trim(Arrangement) -- make a simple hyperplane arrangement
• typeA(ZZ,Ring) -- make the hyperplane arrangement defined by a type $A_n$ root system
• typeB(ZZ,Ring) -- make the hyperplane arrangement defined by a type $B_n$ root system
• typeD(ZZ,Ring) -- make the hyperplane arrangement defined by a type $D_n$ root system
• vee(Flat,Flat) -- compute the vee operation in the intersection lattice