  
  
                                    [1X recog [101X
  
  
   [1X A package for constructive recognition of permutation and matrix groups [101X
  
  
                                     1.4.2
  
  
                               27 September 2022
  
  
                                 Max Neunhöffer
  
                                  Ákos Seress
  
  
  
  Max Neunhöffer
      Email:    [7Xmailto:max@9hoeffer.de[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2005-2014 by Max Neunhöffer and Ákos Seress[133X
  
  [33X[0;0Y© 2005-2022 by its authors, see file [11XCOPYRIGHT[111X for details.[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 3 or (at your option) any later version.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (recog)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YPhilosophy[133X
    1.2 [33X[0;0YOverview over this manual[133X
    1.3 [33X[0;0YFeedback and support[133X
    1.4 [33X[0;0YLiterature (temporary)[133X
  2 [33X[0;0YInstallation of the [5Xrecog[105X package[133X
  3 [33X[0;0YGroup recognition[133X
    3.1 [33X[0;0YThe recursive procedure[133X
      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 [33X[0;0YRecognition nodes[133X
      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 [33X[0;0YOther components of recognition nodes[133X
    3.3 [33X[0;0YMethods to find homomorphisms[133X
      3.3-1 FindHomomorphism
      3.3-2 SLPforElementGeneric
  4 [33X[0;0YMethod selection[133X
    4.1 [33X[0;0YWhat are methods?[133X
      4.1-1 IsRecogMethod
      4.1-2 RecogMethod
      4.1-3 BindRecogMethod
      4.1-4 Stamp
      4.1-5 Comment
      4.1-6 CallRecogMethod
    4.2 [33X[0;0YMethod Databases[133X
      4.2-1 AddMethod
      4.2-2 FindHomDbPerm
      4.2-3 FindHomDbMatrix
      4.2-4 FindHomDbProjective
    4.3 [33X[0;0YHow methods are called[133X
      4.3-1 CallMethods
    4.4 [33X[0;0YGlobal records storing functions[133X
      4.4-1 FindHomMethodsPerm
      4.4-2 FindHomMethodsMatrix
      4.4-3 FindHomMethodsProjective
      4.4-4 FindHomMethodsGeneric
      4.4-5 SLPforElementFuncsPerm
      4.4-6 SLPforElementFuncsMatrix
      4.4-7 SLPforElementFuncsProjective
      4.4-8 SLPforElementFuncsGeneric
  5 [33X[0;0YAfter successful recognition[133X
    5.1 [33X[0;0YFunctions and methods for recognition nodes[133X
      5.1-1 SLPforNiceGens
      5.1-2 \in
      5.1-3 Size
      5.1-4 DisplayCompositionFactors
  6 [33X[0;0YMethods for recognition[133X
    6.1 [33X[0;0YMethods for generic groups[133X
      6.1-1 [33X[0;0Y[10XFewGensAbelian[110X[133X
      6.1-2 [33X[0;0Y[10XKnownNilpotent[110X[133X
      6.1-3 [33X[0;0Y[10XSnAnUnknownDegree[110X[133X
      6.1-4 [33X[0;0Y[10XTrivialGroup[110X[133X
    6.2 [33X[0;0YMethods for permutation groups[133X
      6.2-1 [33X[0;0Y[10XBalTreeForBlocks[110X[133X
      6.2-2 [33X[0;0Y[10XGiant[110X[133X
      6.2-3 [33X[0;0Y[10XImprimitive[110X[133X
      6.2-4 [33X[0;0Y[10XLargeBasePrimitive[110X[133X
      6.2-5 [33X[0;0Y[10XMovesOnlySmallPoints[110X[133X
      6.2-6 [33X[0;0Y[10XNonTransitive[110X[133X
      6.2-7 [33X[0;0Y[10XPcgs[110X[133X
      6.2-8 [33X[0;0Y[10XPcgsForBlocks[110X[133X
      6.2-9 [33X[0;0Y[10XStabChain[110X[133X
      6.2-10 [33X[0;0Y[10XStabilizerChainPerm[110X[133X
      6.2-11 [33X[0;0Y[10XThrowAwayFixedPoints[110X[133X
    6.3 [33X[0;0YMethods for matrix groups[133X
      6.3-1 [33X[0;0Y[10XBlockDiagonal[110X[133X
      6.3-2 [33X[0;0Y[10XBlockLowerTriangular[110X[133X
      6.3-3 [33X[0;0Y[10XBlockScalar[110X[133X
      6.3-4 [33X[0;0Y[10XDiagonalMatrices[110X[133X
      6.3-5 [33X[0;0Y[10XGoProjective[110X[133X
      6.3-6 [33X[0;0Y[10XKnownStabilizerChain[110X[133X
      6.3-7 [33X[0;0Y[10XLowerLeftPGroup[110X[133X
      6.3-8 [33X[0;0Y[10XNaturalSL[110X[133X
      6.3-9 [33X[0;0Y[10XReducibleIso[110X[133X
      6.3-10 [33X[0;0Y[10XScalar[110X[133X
    6.4 [33X[0;0YMethods for projective groups[133X
      6.4-1 [33X[0;0Y[10XAltSymBBByDegree[110X[133X
      6.4-2 [33X[0;0Y[10XBiggerScalarsOnly[110X[133X
      6.4-3 [33X[0;0Y[10XBlockScalarProj[110X[133X
      6.4-4 [33X[0;0Y[10XBlocks[110X[133X
      6.4-5 [33X[0;0Y[10XBlocksBackToMats[110X[133X
      6.4-6 [33X[0;0Y[10XBlocksModScalars[110X[133X
      6.4-7 [33X[0;0Y[10XC3C5[110X[133X
      6.4-8 [33X[0;0Y[10XC6[110X[133X
      6.4-9 [33X[0;0Y[10XClassicalNatural[110X[133X
      6.4-10 [33X[0;0Y[10XComputeSimpleSocle[110X[133X
      6.4-11 [33X[0;0Y[10XD247[110X[133X
      6.4-12 [33X[0;0Y[10XDoBaseChangeForBlocks[110X[133X
      6.4-13 [33X[0;0Y[10XFindElmOfEvenNormal[110X[133X
      6.4-14 [33X[0;0Y[10XKroneckerKernel[110X[133X
      6.4-15 [33X[0;0Y[10XKroneckerProduct[110X[133X
      6.4-16 [33X[0;0Y[10XLieTypeNonConstr[110X[133X
      6.4-17 [33X[0;0Y[10XLowIndex[110X[133X
      6.4-18 [33X[0;0Y[10XNameSporadic[110X[133X
      6.4-19 [33X[0;0Y[10XNotAbsolutelyIrred[110X[133X
      6.4-20 [33X[0;0Y[10XProjDeterminant[110X[133X
      6.4-21 [33X[0;0Y[10XPrototypeForC2C4[110X[133X
      6.4-22 [33X[0;0Y[10XSporadicsByOrders[110X[133X
      6.4-23 [33X[0;0Y[10XStabilizerChainProj[110X[133X
      6.4-24 [33X[0;0Y[10XSubfield[110X[133X
      6.4-25 [33X[0;0Y[10XTensorDecomposable[110X[133X
      6.4-26 [33X[0;0Y[10XThreeLargeElOrders[110X[133X
    6.5 [33X[0;0YUnused methods[133X
  7 [33X[0;0YExamples[133X
  8 [33X[0;0YRenaming[133X
  9 [33X[0;0YHow to write a recognition method[133X
    9.1 [33X[0;0YLeaf methods[133X
    9.2 [33X[0;0YElements with memory[133X
    9.3 [33X[0;0YSplitting methods[133X
  
  
  [32X
