HyperplaneArrangements : Index

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