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recog

A package for constructive recognition of permutation and matrix groups

1.4.3

16 October 2024

Max Neunhöffer
Email: max@9hoeffer.de

Ákos Seress

Copyright

© 2005-2014 by Max Neunhöffer and Ákos Seress

© 2005-2022 by its authors, see file COPYRIGHT for details.

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or (at your option) any later version.

Contents

1.2 Overview over this manual

1.3 Feedback and support

1.4 Literature (temporary)

2 Installation of the recog package

3 Group recognition

3.1 The recursive procedure

  3.1-1 RecogniseGeneric
  3.1-2 RecognisePermGroup
  3.1-3 RecogniseMatrixGroup
  3.1-4 RecogniseProjectiveGroup
  3.1-5 RecogniseGroup
  3.1-6 TryFindHomMethod

3.2 Recognition nodes

  3.2-1 RecogNodeFamily
  3.2-2 IsRecogNode
  3.2-3 RecogNode
  3.2-4 IsLeaf
  3.2-5 IsReady
  3.2-6 Grp
  3.2-7 Homom
  3.2-8 NiceGens
  3.2-9 pregensfac
  3.2-10 ImageRecogNode
  3.2-11 KernelRecogNode
  3.2-12 ParentRecogNode
  3.2-13 fhmethsel
  3.2-14 slpforelement
  3.2-15 SLPforElement
  3.2-16 StdPresentation
  3.2-17 methodsforimage
  3.2-18 validatehomominput
  3.2-19 ValidateHomomInput
  3.2-20 calcnicegens
  3.2-21 CalcNiceGensGeneric
  3.2-22 CalcNiceGensHomNode
  3.2-23 CalcNiceGens
  3.2-24 slptonice
  3.2-25 gensN
  3.2-26 findgensNmeth
  3.2-27 FindKernelRandom
  3.2-28 FindKernelDoNothing
  3.2-29 FindKernelFastNormalClosure
  3.2-30 gensNslp
  3.2-31 immediateverification
  3.2-32 InitialDataForKernelRecogNode
  3.2-33 InitialDataForImageRecogNode
  3.2-34 isone
  3.2-35 isequal
  3.2-36 OrderFunc
  3.2-37 Other components of recognition nodes

3.3 Methods to find homomorphisms

3.3-1 FindHomomorphism
3.3-2 SLPforElementGeneric

5 After successful recognition

5.1 Functions and methods for recognition nodes

  5.1-1 SLPforNiceGens
  5.1-2 \in
  5.1-3 Size
  5.1-4 DisplayCompositionFactors

6 Methods for recognition

6.1 Methods for generic groups

  6.1-1 FewGensAbelian
  6.1-2 KnownNilpotent
  6.1-3 SnAnUnknownDegree
  6.1-4 TrivialGroup

6.2 Methods for permutation groups

  6.2-1 BalTreeForBlocks
  6.2-2 Giant
  6.2-3 Imprimitive
  6.2-4 LargeBasePrimitive
  6.2-5 MovesOnlySmallPoints
  6.2-6 NonTransitive
  6.2-7 Pcgs
  6.2-8 PcgsForBlocks
  6.2-9 StabChain
  6.2-10 StabilizerChainPerm
  6.2-11 ThrowAwayFixedPoints

6.3 Methods for matrix groups

  6.3-1 BlockDiagonal
  6.3-2 BlockLowerTriangular
  6.3-3 BlockScalar
  6.3-4 DiagonalMatrices
  6.3-5 GoProjective
  6.3-6 KnownStabilizerChain
  6.3-7 LowerLeftPGroup
  6.3-8 NaturalSL
  6.3-9 ReducibleIso
  6.3-10 Scalar

6.5 Unused methods

9 How to write a recognition method

9.1 Leaf methods

9.2 Elements with memory

9.3 Splitting methods

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