  
  [1X7 [33X[0;0YMiscellaneous[133X[101X
  
  [33X[0;0YThis chapter describes various aspects of [5Xrecog[105X that did not fit elsewhere.[133X
  
  
  [1X7.1 [33X[0;0YNaming of groups[133X[101X
  
  [33X[0;0YFor non-constructive recognition of classical matrix groups in their natural
  representation, the following functions are available.[133X
  
  [1X7.1-1 RecogniseClassical[101X
  
  [33X[1;0Y[29X[2XRecogniseClassical[102X( [3Xgrp[103X[, [3Xopt[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya   record   describing   the   outcome  of  the  non-constructive
            recognition procedure.[133X
  
  [33X[0;0YThis  function  implements non-constructive recognition, also called naming,
  for  classical  groups  in  their  natural matrix representation over finite
  fields.  The  implementation is based on the algorithms described in [NP98],
  [NP97],  and [NP99], and uses further ingredients from [CL97a], [CL97b], and
  [Pra99].[133X
  
  [33X[0;0YThe  input  [3Xgrp[103X  must be a matrix group over a finite field. The function is
  intended  for  groups  that  are  classical, or close to classical, in their
  natural representation.[133X
  
  [33X[0;0YThe  optional record [3Xopt[103X can be used to guide the computation. Its component
  [10Xcase[110X   may   be   one   of  [10X"unknown"[110X,  [10X"linear"[110X,  [10X"symplectic"[110X,  [10X"unitary"[110X,
  [10X"orthogonalplus"[110X, or [10X"orthogonalcircle"[110X. Furthermore, [10Xnrrandels[110X controls how
  many random elements are inspected, and [10XinfoLevel[110X sets the [10XInfoMethSel[110X level
  used while running the method selection machinery.[133X
  
  [33X[0;0YThe  returned  record is currently mostly an internal data structure and its
  full  set  of components should not be considered a stable public interface.
  The   most  useful  documented  components  are  the  booleans  [10XisReducible[110X,
  [10XisSLContained[110X,  [10XisSpContained[110X, [10XisSUContained[110X, and [10XisOmegaContained[110X. The four
  [10Xis*Contained[110X  components  indicate  whether  the  given  group  contains the
  corresponding  quasisimple  classical  group  in the natural representation,
  namely [22XSL(d,q)[122X, [22XSp(d,q)[122X, [22XSU(d,q)[122X, and [22XΩ[122X of the appropriate type.[133X
  
  [33X[0;0YTo inspect the full internal record for debugging purposes, use [2XDisplayRecog[102X
  ([14X7.1-2[114X).[133X
  
  [1X7.1-2 DisplayRecog[101X
  
  [33X[1;0Y[29X[2XDisplayRecog[102X( [3Xr[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YPretty-print    selected   information   from   the   record   returned   by
  [2XRecogniseClassical[102X  ([14X7.1-1[114X).  This  is mainly intended as a debugging helper
  for inspecting the internal state accumulated by the recognition procedure.[133X
  
  
  [1X7.2 [33X[0;0YRenaming of [5Xrecog[105X[101X[1X functions and operations[133X[101X
  
  [33X[0;0YMany  of  the  names  in  the  recog package were found to be unintuitive or
  inconsistent  with  other names. For these reasons the names were changed to
  be  more  descriptive and to follow the internal consistency of [5XGAP[105X. In this
  section  a dictionary from old to new names is included. The meanings of the
  old  names for components of a recognition node are described in Section 2.6
  "Components of the recognition node" of the article [NS06].[133X
  
      ┌───────────────────────┬───────────────────────────────────────┐
      │ [13XOld Name[113X              │ [13XNew Name[113X                              │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10XRecognitionInfoFamily[110X │ [2XRecogNodeFamily[102X ([14X4.2-1[114X)               │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10XIsRecognitionInfo[110X     │ [2XIsRecogNode[102X ([14X4.2-2[114X)                   │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10XRIFac[110X                 │ [2XImageRecogNode[102X ([14X4.2-10[114X)               │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10XRIKer[110X                 │ [2XKernelRecogNode[102X ([14X4.2-11[114X)              │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10XRIParent[110X              │ [2XParentRecogNode[102X ([14X4.2-12[114X)              │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10Xmethodsforfactor[110X      │ [2Xmethodsforimage[102X ([14X4.2-18[114X)              │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10Xforfactor[110X             │ [2XInitialDataForImageRecogNode[102X ([14X5.3-1[114X)  │ 
      ├───────────────────────┼───────────────────────────────────────┤
      │ [10Xforkernel[110X             │ [2XInitialDataForKernelRecogNode[102X ([14X5.3-1[114X) │ 
      └───────────────────────┴───────────────────────────────────────┘
  
       [1XTable:[101X Renaming
  
  
