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Macaulay2 web site
Arrangement -- class of hyperplane arrangements
Description
A hyperplane is a linear subspace of codimension one. An arrangement is a finite set of hyperplanes.
Functions and methods returning a hyperplane arrangement :
arrangement
-- create a hyperplane arrangement
arrangement(Arrangement,Ring), see
arrangement
-- create a hyperplane arrangement
arrangement(List), see
arrangement
-- create a hyperplane arrangement
arrangement(List,Ring), see
arrangement
-- create a hyperplane arrangement
arrangement(Matrix), see
arrangement
-- create a hyperplane arrangement
arrangement(Matrix,Ring), see
arrangement
-- create a hyperplane arrangement
Arrangement ** Arrangement
(missing documentation)
Arrangement ** Ring
(missing documentation)
Arrangement ^ Flat
-- restriction of arrangement to flat
Arrangement _ Flat
-- Subarrangement containing a fixed flat
arrangement(Flat)
(missing documentation)
arrangement(String)
(missing documentation)
arrangement(String,PolynomialRing)
-- look up a built-in hyperplane arrangement
arrangement(String,Ring)
(missing documentation)
arrangementSum
(missing documentation)
arrangementSum(Arrangement,Arrangement)
(missing documentation)
changeRing
(missing documentation)
changeRing(Arrangement,Ring)
(missing documentation)
compress(Arrangement)
-- extract nonzero equations
cone(Arrangement,RingElement)
(missing documentation)
cone(Arrangement,Symbol)
(missing documentation)
deletion
-- subarrangement given by deleting a hyperplane
deletion(Arrangement,RingElement), see
deletion
-- subarrangement given by deleting a hyperplane
dual(Arrangement)
-- the Gale dual of A
graphic
-- Make a graphic arrangement
graphic(List), see
graphic
-- Make a graphic arrangement
graphic(List,PolynomialRing), see
graphic
-- Make a graphic arrangement
graphic(List,Ring), see
graphic
-- Make a graphic arrangement
randomArrangement
-- generate an arrangement at random
randomArrangement(ZZ,ZZ,ZZ), see
randomArrangement
-- generate an arrangement at random
restriction
-- restriction of arrangement to flat/hyperplane
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
subArrangement
-- Subarrangement containing a fixed flat
subArrangement(Arrangement,Flat), see
subArrangement
-- Subarrangement containing a fixed flat
subArrangement(Flat), see
subArrangement
-- Subarrangement containing a fixed flat
trim(Arrangement)
-- minimize the generators
typeA
-- Type A reflection arrangement
typeA(ZZ), see
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
typeB(ZZ), see
typeB
-- Type B reflection arrangement
typeB(ZZ,PolynomialRing), see
typeB
-- Type B reflection arrangement
typeB(ZZ,Ring), see
typeB
-- Type B reflection arrangement
typeD
-- Type D reflection arrangement
typeD(ZZ), see
typeD
-- Type D reflection arrangement
typeD(ZZ,PolynomialRing), see
typeD
-- Type D reflection arrangement
typeD(ZZ,Ring), see
typeD
-- Type D reflection arrangement
Methods that use a hyperplane arrangement :
Arrangement == Arrangement
(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
crit(Arrangement)
(missing documentation)
der(Arrangement), see
der
-- Module of logarithmic derivations
der(Arrangement,List), see
der
-- Module of logarithmic derivations
describe(Arrangement)
(missing documentation)
dlogPhi(Arrangement,List)
(missing documentation)
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 characteristic
expression(Arrangement)
(missing documentation)
flat(Arrangement,List), see
flat
-- make a flat from a list of indices
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
freeDlogPhi(Arrangement,List)
(missing documentation)
isDecomposable(Arrangement), see
isDecomposable
-- test if an arrangement is decomposable
isDecomposable(Arrangement,Ring), see
isDecomposable
-- test if an arrangement is decomposable
matrix(Arrangement)
-- create a matrix from the equations of an arrangement
multIdeal(Number,Arrangement), see
multIdeal
-- compute a multiplier ideal
multIdeal(Number,Arrangement,List), see
multIdeal
-- compute a multiplier ideal
multIdeal(RR,Arrangement), see
multIdeal
-- compute a multiplier ideal
multIdeal(RR,Arrangement,List), see
multIdeal
-- compute a multiplier ideal
net(Arrangement)
(missing documentation)
omega(Arrangement)
(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)
poincare(Arrangement)
(missing documentation)
rank(Arrangement)
-- compute the rank
ring(Arrangement)
-- get the associated ring
tolist(Arrangement)
(missing documentation)
For the programmer
The object
Arrangement
is
a
type
, with ancestor classes
HashTable
<
Thing
.