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HyperplaneArrangements :: HyperplaneArrangements

HyperplaneArrangements -- hyperplane arrangements

Description

HyperplaneArrangement is a package for manipulating hyperplane arrangements.

A hyperplane arrangement is a finite set of hyperplanes in an affine or projective space. In this package, an arrangement is expressed as a list of (linear) defining equations for the hyperplanes. The tools provided allow the user to create new arrangements from old, and to compute various algebraic invariants of arrangements.

Authors

Version

This documentation describes version 0.9 of HyperplaneArrangements.

Source code

The source code from which this documentation is derived is in the file HyperplaneArrangements.m2.

Exports

  • Types
  • Functions and commands
    • arrangement -- create a hyperplane arrangement
    • arrangementSum (missing documentation)
    • changeRing (missing documentation)
    • circuits -- list the circuits of an arrangement
    • closure -- closure operation in the intersection lattice
    • deCone -- produce an affine arrangement from a central one
    • deletion -- subarrangement given by deleting a hyperplane
    • der -- Module of logarithmic derivations
    • EPY -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
    • flat -- make a flat from a list of indices
    • flats -- list the flats of an arrangement of given rank
    • graphic -- Make a graphic arrangement
    • isCentral (missing documentation)
    • isDecomposable -- test if an arrangement is decomposable
    • lct -- Compute the log-canonical threshold of an arrangement
    • meet -- meet operation in intersection lattice
    • multIdeal -- compute a multiplier ideal
    • orlikSolomon -- defining ideal for the Orlik-Solomon algebra
    • orlikTerao -- defining ideal for the Orlik-Terao algebra
    • randomArrangement -- generate an arrangement at random
    • restriction -- restriction of arrangement to flat/hyperplane
    • subArrangement -- Subarrangement containing a fixed flat
    • tolist (missing documentation)
    • typeA -- Type A reflection arrangement
    • typeB -- Type B reflection arrangement
    • typeD -- Type D reflection arrangement
    • vee -- join operation in intersection lattice
  • Methods
    • arrangement(Arrangement,Ring), see arrangement -- create a hyperplane arrangement
    • Arrangement ** Arrangement (missing documentation)
    • Arrangement ** Ring (missing documentation)
    • Arrangement == Arrangement (missing documentation)
    • Arrangement ^ Flat -- restriction of arrangement to flat
    • Arrangement _ Flat -- Subarrangement containing a fixed flat
    • arrangement(Flat) (missing documentation)
    • arrangementSum(Arrangement,Arrangement) (missing documentation)
    • changeRing(Arrangement,Ring) (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 arrangment
    • compress(Arrangement) -- extract nonzero equations
    • cone(Arrangement,RingElement) -- Cone of an arrangement
    • cone(Arrangement,Symbol) (missing documentation)
    • 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(Arrangement,RingElement), see deletion -- subarrangement given by deleting a hyperplane
    • der(CentralArrangement), see der -- Module of logarithmic derivations
    • der(CentralArrangement,List), see der -- Module of logarithmic derivations
    • describe(Arrangement) (missing documentation)
    • dual(CentralArrangement) -- the Gale dual of A
    • 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)
    • euler(Flat)
    • expression(Arrangement) (missing documentation)
    • expression(Flat) (missing documentation)
    • flat(Arrangement,List), see flat -- make a flat from a list of indices
    • Flat == Flat (missing documentation)
    • Flat ^ Flat -- meet operation in intersection lattice
    • Flat | Flat -- join operation in intersection lattice
    • 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)
    • isDecomposable(CentralArrangement), see isDecomposable -- test if an arrangement is decomposable
    • isDecomposable(CentralArrangement,Ring), see isDecomposable -- test if an arrangement is decomposable
    • lct(CentralArrangement), see lct -- Compute the log-canonical threshold of an arrangement
    • matrix(Arrangement) -- create a matrix from the equations of an arrangement
    • meet(Flat,Flat), see meet -- meet operation in intersection lattice
    • multIdeal(QQ,CentralArrangement), see multIdeal -- compute a multiplier ideal
    • multIdeal(QQ,CentralArrangement,List), see multIdeal -- compute a multiplier ideal
    • multIdeal(ZZ,CentralArrangement), see multIdeal -- compute a multiplier ideal
    • multIdeal(ZZ,CentralArrangement,List), see multIdeal -- compute a multiplier ideal
    • net(Arrangement) (missing documentation)
    • net(Flat) (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)
    • orlikSolomon(CentralArrangement,PolynomialRing) (missing documentation)
    • orlikTerao(CentralArrangement), see orlikTerao -- defining ideal for the Orlik-Terao algebra
    • orlikTerao(CentralArrangement,PolynomialRing), see orlikTerao -- defining ideal for the Orlik-Terao algebra
    • orlikTerao(CentralArrangement,Symbol), see orlikTerao -- defining ideal for the Orlik-Terao algebra
    • poincare(Arrangement) (missing documentation)
    • prune(Arrangement) (missing documentation)
    • rank(Arrangement) -- compute the rank
    • rank(Flat) (missing documentation)
    • 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)
    • ring(Arrangement) -- get the associated ring
    • subArrangement(Arrangement,Flat), see subArrangement -- Subarrangement containing a fixed flat
    • subArrangement(Flat), see subArrangement -- Subarrangement containing a fixed flat
    • tolist(Arrangement) (missing documentation)
    • tolist(Flat) (missing documentation)
    • trim(Arrangement) -- minimize the generators
    • vee(Flat,Flat), see vee -- join operation in intersection lattice
  • Symbols
    • HypAtInfinity (missing documentation)
    • NaiveAlgorithm (missing documentation)
  • Other things
    • arrangementLibrary (missing documentation)