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HyperplaneArrangements : Table of Contents
HyperplaneArrangements
-- hyperplane arrangements
Arrangement
-- class of hyperplane arrangements
arrangement
-- create a hyperplane arrangement
Arrangement ^ Flat
-- restriction of arrangement to flat
Arrangement _ Flat
-- Subarrangement containing a fixed flat
arrangement(String,PolynomialRing)
-- look up a built-in hyperplane arrangement
arrangementLibrary
(missing documentation)
arrangementSum
(missing documentation)
CentralArrangement
-- class of central hyperplane arrangements
changeRing
(missing documentation)
circuits
-- list the circuits of an arrangement
closure
-- closure operation in the intersection lattice
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
deCone
-- produce an affine arrangement from a central one
deletion
-- subarrangement given by deleting a hyperplane
der
-- Module of logarithmic derivations
der(..., Strategy => ...)
dual(CentralArrangement)
-- the Gale dual of A
EPY
-- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement
euler(Flat)
-- Euler characteristic
Flat
-- intersection of hyperplanes
flat
-- make a flat from a list of indices
Flat ^ Flat
-- meet operation in intersection lattice
Flat | Flat
-- join operation in intersection lattice
flats
-- list the flats of an arrangement of given rank
graphic
-- Make a graphic arrangement
HypAtInfinity
(missing documentation)
isCentral
(missing documentation)
isDecomposable
-- test if an arrangement is decomposable
lct
-- Compute the log-canonical threshold of an arrangement
matrix(Arrangement)
-- create a matrix from the equations of an arrangement
meet
-- meet operation in intersection lattice
multIdeal
-- compute a multiplier ideal
NaiveAlgorithm
(missing documentation)
orlikSolomon
-- defining ideal for the Orlik-Solomon algebra
orlikSolomon(..., HypAtInfinity => ...)
-- hyperplane at infinity
orlikSolomon(..., Projective => ...)
-- specify projective complement
orlikTerao
-- defining ideal for the Orlik-Terao algebra
randomArrangement
-- generate an arrangement at random
rank(Arrangement)
-- compute the rank
restriction
-- restriction of arrangement to flat/hyperplane
ring(Arrangement)
-- get the associated ring
subArrangement
-- Subarrangement containing a fixed flat
tolist
(missing documentation)
trim(Arrangement)
-- minimize the generators
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
typeD
-- Type D reflection arrangement
vee
-- join operation in intersection lattice