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recog

A package for constructive recognition of permutation and matrix groups

1.3.2dev

9 July 2019

Max Neunhöffer
Email: max@9hoeffer.de

Ákos Seress

Copyright

© 2005-2014 by Max Neunhöffer and Ákos Seress

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 FindHomDbPerm
  3.1-7 FindHomMethodsPerm
  3.1-8 SLPforElementFuncsPerm
  3.1-9 FindHomDbMatrix
  3.1-10 FindHomMethodsMatrix
  3.1-11 SLPforElementFuncsMatrix
  3.1-12 FindHomDbProjective
  3.1-13 FindHomMethodsProjective
  3.1-14 SLPforElementFuncsProjective
  3.1-15 FindHomMethodsGeneric
  3.1-16 SLPforElementFuncsGeneric
  3.1-17 TryFindHomMethod

3.2 Recognition info records

  3.2-1 RecognitionInfoFamily
  3.2-2 IsRecognitionInfo
  3.2-3 IsLeaf
  3.2-4 IsReady
  3.2-5 Grp
  3.2-6 Homom
  3.2-7 NiceGens
  3.2-8 pregensfac
  3.2-9 RIFac
  3.2-10 RIKer
  3.2-11 RIParent
  3.2-12 fhmethsel
  3.2-13 slpforelement
  3.2-14 SLPforElement
  3.2-15 StdPresentation
  3.2-16 methodsforfactor
  3.2-17 validatehomominput
  3.2-18 ValidateHomomInput
  3.2-19 calcnicegens
  3.2-20 CalcNiceGensGeneric
  3.2-21 CalcNiceGensHomNode
  3.2-22 CalcNiceGens
  3.2-23 slptonice
  3.2-24 gensN
  3.2-25 findgensNmeth
  3.2-26 FindKernelRandom
  3.2-27 FindKernelDoNothing
  3.2-28 FindKernelFastNormalClosure
  3.2-29 gensNslp
  3.2-30 immediateverification
  3.2-31 forkernel
  3.2-32 forfactor
  3.2-33 isone
  3.2-34 isequal
  3.2-35 order
  3.2-36 Other components of recognition info records

3.3 Methods to find homomorphisms

3.3-1 FindHomomorphism
3.3-2 SLPforElementGeneric

3.4 Conventions for the recognition of permutation groups

3.5 Conventions for the recognition of matrix groups

3.6 Conventions for the recognition of projective groups

4 Method selection

4.1 What are methods?

4.1-1 AddMethod

4.2 How methods are called

4.2-1 CallMethods

5 After successful recognition

5.1 Functions and methods for recognition info records

  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 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

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