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HypArr

Computations with hyperplane arrangements

0.26.05

5 May 2026

Paul Mücksch
Email: paul.muecksch+uni@gmail.com
Homepage: https://paulmuecksch.github.io
Address:
Leibniz Universität Hannover
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Welfengarten 1
30167 Hannover, Germany

Contents

2 Hyperplane arrangements

2.1 Construction of arrangements of hyperplanes

2.1-1 HyperplaneArrangement

2.2 Attributes of arrangements

  2.2-1 Dimension
  2.2-2 Roots
  2.2-3 HArrDefField
  2.2-4 IntersectionLattice
  2.2-5 CharPoly
  2.2-6 ExpArr
  2.2-7 MSetInvL

2.3 Properties of arrangements

  2.3-1 IsReal
  2.3-2 HArrIsIrreducible
  2.3-3 HArrIsGeneric

2.4 Attributes of geometric lattices

  2.4-1 LGroundSet
  2.4-2 LAtoms
  2.4-3 LRank
  2.4-4 LkFlats
  2.4-5 LRankFunction
  2.4-6 LGraph
  2.4-7 LAutGroup
  2.4-8 LMoebius
  2.4-9 LCharPoly
  2.4-10 LBases

2.5 Properties of geometric lattices

  2.5-1 LIsIrreducible
  2.5-2 LIsBoolean
  2.5-3 LIsGeneric

  2.6-1 LIsIsomorphic
  2.6-2 IsLEquiv
  2.6-3 Essentialization
  2.6-4 HArrRestriction
  2.6-5 HArrRestriction
  2.6-6 HArrAddition
  2.6-7 HArrDeletion

3 Special arrangements

3.1 Global methods

  3.1-1 AGpql
  3.1-2 SsS3
  3.1-3 ConnectedSubgraphArr

5 Free arrangements

5.1 Module of logarithmic vector fields aka derivation modules of arrangements

  5.1-1 DerModule
  5.1-2 DerModGenerators
  5.1-3 DerModPRing
  5.1-4 DerModDegreeSequence
  5.1-5 DerModProjDim
  5.1-6 DerModIsFree
  5.1-7 HArrIsFree

5.2 Freeness properties

5.2-1 IsInductivelyFree
5.2-2 IsDivisionallyFree

7 Milnor fibers

  7.1-1 MilnorFiberComplex
  7.1-2 MilnorFiberComplex
  7.1-3 FPtoCWCpx

8.1-1 TopePoset

  8.2-1 TPGroundSet
  8.2-2 TPBaseTope
  8.2-3 TPRankPoly

9 Visualization of real 3-arrangements

9.1 Global methods

  9.1-1 LaTeXDrawProjPicture
  9.1-2 LaTeXDrawSpherePicture
  9.1-3 LaTeXDrawTopeGraph

10 Realization spaces of geometric lattices

10.1 Construction

10.1-1 LRealizationSpace

10.2 Attributes

  10.2-1 LGenSet
  10.2-2 RSLattice
  10.2-3 RSCharacteristic
  10.2-4 RSDefField
  10.2-5 RSCoeffMat
  10.2-6 RSDimension
  10.2-7 RSPRing
  10.2-8 RSIdealMinors
  10.2-9 RSNonMinors
  10.2-10 RSEvalPoint

10.3 Properties

10.3-1 RSIsNonEmpty

10.4 Further (auxillary) Operations

10.4-1 LSubsetGeneratedByS
10.4-2 LIsGenSet

11 Greedy search for arrangements

11.1 Constructions

  11.1-1 HArrGreedySearch
  11.1-2 CharPolySplits
  11.1-3 DistMSetInvL

11.2 Attributes

  11.2-1 GreedySearchRun
  11.2-2 GreedySearchGF
  11.2-3 GreedySearchDimension
  11.2-4 GreedySearchNOfHs
  11.2-5 GreedySearchTargetFct
  11.2-6 GreedySearchMaxIterations

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