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D.15.2 arr_lib

a library of algorithms for arrangements of hyperplanes

Randolf Scholz (rscholz@rhrk.uni-kl.de),
Patrick Serwene (serwene@mathematik.uni-kl.de),
Lukas Kuehne (lf.kuehne@gmail.com)

= arrAdd assignment
+ arrAdd union of two arrs
[ arrGet access to a single/multiple hyperplane(s) - arrMinus deletes given hyperplanes from the arr <= arrLEQ comparison
>= arrGEQ comparison
== arrEQ comparison
!= arrNEQ comparison
< arrLNEQ comparison
> arrGNEQ comparison

matrix arr2mat coeff matrix
poly arr2poly defining polynomial

variables arrVariables ideal generated by the variables the arr depends on nvars arrNvars number of variables the arr depends on delete arrDelete deletes hyperplanes by indices print arrPrint prints the arr on the screen

homog arrHomog checks if arrangement is homogeneous simplify arrSimplify simplifies arrangement size arrSize number of planes
subst arrSubst substitute variables

= multarrAdd assignement of multarr + multarrAdd union of multarr
poly multarr2poly defining polynomial
size multarrSize number of hyperplanes with mult. print multarrPrint displays multiarr
delete multarrDelete deletes hyperplane


D.15.2.1 arrSet  replaces the k-th Hyperplane with poly p
D.15.2.2 type2arr  converts general input to 'arr' using arrAdd.
D.15.2.3 mat2arr  affine arrangement from coeff matrix
D.15.2.4 mat2carr  central arrangement from coeff matrix
D.15.2.5 arrPrintMatrix  readable output as a coeff matrix
D.15.2.6 varMat  matrix of the corresponding ring_variables
D.15.2.7 varNum  number of given variable (enh. version of varNum in dmod.lib)
D.15.2.8 arrSwapVar  swaps two variables in the arrangement
D.15.2.9 arrLastVar  ring_variable of largest index used in arrangement
D.15.2.10 arrCenter  computes center of an arrangement
D.15.2.11 arrCentral  checks if arrangement is central
D.15.2.12 arrCentered  checks if arrangement is centered
D.15.2.13 arrCentralize  makes centered arrangement central
D.15.2.14 arrCoordChange  performs coordinate change
D.15.2.15 arrCoordNormalize  performs projection onto coordinate hyperplane
D.15.2.16 arrCone  coned arrangement
D.15.2.17 arrDecone  deconed arrangement
D.15.2.18 arrLocalize  localization of an arrangement onto a flat
D.15.2.19 arrRestrict  restricted arrangement onto a flat
D.15.2.20 arrIsEssential  checks if arrangement is essential
D.15.2.21 arrEssentialize  essentialized arragnement
D.15.2.22 arrBoolean  boolean arrangement
D.15.2.23 arrBraid  braid arrangement
D.15.2.24 arrTypeB  type B arrangement
D.15.2.25 arrTypeD  type D arrangement
D.15.2.26 arrRandom  random (affine) arrangement
D.15.2.27 arrRandomCentral  random central arrangement
D.15.2.28 arrEdelmanReiner  Edelman-Reiner arrangement
D.15.2.29 arrOrlikSolomon  Orlik-Solomon algebra of the arrangement
D.15.2.30 arrDer  module of derivation
D.15.2.31 arrIsFree  checks if arrangement is free
D.15.2.32 arrExponents  exponents of a (free) arrangement
D.15.2.33 arr2multarr  converts normal arrangement to multiarrangement
D.15.2.34 multarr2arr  converts multiarrangement to normal arrangement
D.15.2.35 multarrRestrict  restriction of A (as arr) to a flat with multiplicities
D.15.2.36 multarrMultRestrict  restriction of A (as multarr) to a hyperplane with multiplicities
D.15.2.37 arrFlats  intersection lattice
D.15.2.38 arrLattice  computes the intersection lattice / poset
D.15.2.39 moebius  computes moebius values
D.15.2.40 arrCharPoly  characteristic polynomial
D.15.2.41 arrPoincare  poincare polynomial of the arrangement
D.15.2.42 arrChambers  number of chambers of the arrangement
D.15.2.43 arrBoundedChambers  number of bounded chambers of the arrangement
D.15.2.44 printMoebius  displays the moebius values of all the flats in the poset