  
  [1X5 [33X[0;0YInteractive ANUPQ functions[133X[101X
  
  [33X[0;0YHere  we  describe  the  interactive functions defined by the [5XANUPQ[105X package,
  i.e. the functions that manipulate and initiate interactive [5XANUPQ[105X processes.
  These  are  functions that extract information via a dialogue with a running
  [10Xanu-pq[110X  process (process used in the UNIX sense). Occasionally, a user needs
  the  [21Xnext step[121X; the functions provided in this chapter make use of data from
  previous  steps  retained  by  the [10Xanu-pq[110X program, thus allowing the user to
  interact  with  the  [10Xanu-pq[110X  program  like  one can when one uses the [10Xanu-pq[110X
  program as a stand-alone (see [10Xguide.dvi[110X in the [10Xstandalone-doc[110X directory).[133X
  
  [33X[0;0YAn  interactive  [5XANUPQ[105X  process  is  initiated by [10XPqStart[110X and terminated via
  [10XPqQuit[110X;  these  functions  are  described  in  ection [14X'[33X[0;0YStarting and Stopping
  Interactive ANUPQ Processes[133X'[114X.[133X
  
  [33X[0;0YEach   interactive  [5XANUPQ[105X  function  that  manipulates  an  already  started
  interactive  [5XANUPQ[105X  process,  has  a  form  where  the first argument is the
  integer [3Xi[103X returned by the initiating [10XPqStart[110X command, and a second form with
  one  argument  fewer  (where  the  integer  [3Xi[103X  is  discovered  by  a default
  mechanism,  namely  by  determining the least integer [3Xi[103X for which there is a
  currently  active interactive [5XANUPQ[105X process). We will thus commonly say that
  [21Xfor  the  [3Xi[103Xth  (or  default)  interactive  [5XANUPQ[105X  process[121X a certain function
  performs  a given action. In each case, it is an error if [3Xi[103X is not the index
  of an active interactive process, or there are no current active interactive
  processes.[133X
  
  [33X[0;0Y[13XNotes[113X: The global method of passing options (via [10XPushOptions[110X), should not be
  used with any of the interactive functions. In fact, the [10XOptionsStack[110X should
  be empty at the time any of the interactive functions is called.[133X
  
  [33X[0;0YOn  [9Xquit[109Xting  [5XGAP[105X,  [10XPqQuitAll();[110X  is  executed,  which terminates all active
  interactive  [5XANUPQ[105X  processes. If [5XGAP[105X is killed without [9Xquit[109Xting, before all
  interactive  [5XANUPQ[105X  processes are terminated, [13Xzombie[113X processes (still living
  [13Xchild[113X processes whose [13Xparents[113X have died), may result. Since zombie processes
  do consume resources, in such an event, the responsible computer user should
  seek  out  and terminate those zombie processes (e.g. on Linux: [10Xps xw | grep
  pq[110X  gives  you  information  on  the  [10Xanu-pq[110X  processes corresponding to any
  interactive [5XANUPQ[105X processes started in a [5XGAP[105X session; you can then do [10Xkill [3XN[103X[10X[110X
  for each number [3XN[103X appearing in the first column of this output).[133X
  
  
  [1X5.1 [33X[0;0YStarting and Stopping Interactive ANUPQ Processes[133X[101X
  
  [1X5.1-1 PqStart[101X
  
  [33X[1;0Y[29X[2XPqStart[102X( [3XG[103X, [3Xworkspace:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqStart[102X( [3XG:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqStart[102X( [3Xworkspace:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqStart[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yactivate  an  iostream for an interactive [5XANUPQ[105X process (i.e. [10XPqStart[110X starts
  up  a  [10Xanu-pq[110X  process and opens a [5XGAP[105X iostream to [21Xtalk[121X to that process) and
  returns an integer [3Xi[103X that can be used to identify that process. The argument
  [3XG[103X  should  be  an  [13Xfp  group[113X or [13Xpc group[113X that the user intends to manipulate
  using  interactive  [5XANUPQ[105X  functions.  If  the  function  is  called without
  specifying   [3XG[103X,   a   group   can   be   read   in  by  using  the  function
  [10XPqRestorePcPresentation[110X (see [2XPqRestorePcPresentation[102X ([14X5.6-3[114X)). If [10XPqStart[110X is
  given  an  integer argument [3Xworkspace[103X, then the [10Xanu-pq[110X program is started up
  with  a  workspace  (an integer array) of size [3Xworkspace[103X (i.e. [22X4 × [3Xworkspace[103X[122X
  bytes in a 32-bit environment); otherwise, the [10Xanu-pq[110X program sets a default
  workspace of [22X10000000[122X.[133X
  
  [33X[0;0YThe  only  [3Xoptions[103X  currently  recognised by [10XPqStart[110X are [10XPrime[110X, [10XExponent[110X and
  [10XRelators[110X  (see  Chapter [14X'[33X[0;0YANUPQ  Options[133X'[114X  for detailed descriptions of these
  options)  and  if  provided  they are essentially global for the interactive
  [5XANUPQ[105X  process,  except  that  any interactive function interacting with the
  process  and  passing new values for these options will over-ride the global
  values.[133X
  
  [1X5.1-2 PqQuit[101X
  
  [33X[1;0Y[29X[2XPqQuit[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqQuit[102X(  ) [32X function[133X
  
  [33X[0;0Ycloses  the  stream  of  the  [3Xi[103Xth  or  default interactive [5XANUPQ[105X process and
  unbinds its [10XANUPQData.io[110X record.[133X
  
  [33X[0;0Y[13XNote:[113X  It  can  happen  that  the [10Xanu-pq[110X process, and hence the [5XGAP[105X iostream
  assigned  to  communicate with it, can die, e.g. by the user typing a [10XCtrl-C[110X
  while  the [10Xanu-pq[110X process is engaged in a long calculation. [10XIsPqProcessAlive[110X
  (see [2XIsPqProcessAlive[102X  ([14X5.2-3[114X))  is  provided to check the status of the [5XGAP[105X
  iostream  (and  hence  the status of the [10Xanu-pq[110X process it was communicating
  with).[133X
  
  [1X5.1-3 PqQuitAll[101X
  
  [33X[1;0Y[29X[2XPqQuitAll[102X(  ) [32X function[133X
  
  [33X[0;0Yis  provided  as  a  convenience,  to terminate all active interactive [5XANUPQ[105X
  processes with a single command. It is equivalent to executing [10XPqQuit([3Xi[103X[10X)[110X for
  all active interactive [5XANUPQ[105X processes [3Xi[103X (see [2XPqQuit[102X ([14X5.1-2[114X)).[133X
  
  
  [1X5.2 [33X[0;0YInteractive ANUPQ Process Utility Functions[133X[101X
  
  [1X5.2-1 PqProcessIndex[101X
  
  [33X[1;0Y[29X[2XPqProcessIndex[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqProcessIndex[102X(  ) [32X function[133X
  
  [33X[0;0YWith  argument [3Xi[103X, which must be a positive integer, [10XPqProcessIndex[110X returns [3Xi[103X
  if it corresponds to an active interactive process, or raises an error. With
  no  arguments  it  returns the default active interactive process or returns
  [9Xfail[109X  and  emits a warning message to [10XInfo[110X at [10XInfoANUPQ[110X or [10XInfoWarning[110X level
  1.[133X
  
  [33X[0;0Y[13XNote:[113X   Essentially,   an   interactive   [5XANUPQ[105X   process  [3Xi[103X  is  [21Xactive[121X  if
  [10XANUPQData.io[[3Xi[103X[10X][110X is bound (i.e. we still have some data telling us about it).
  Also see [2XPqStart[102X ([14X5.1-1[114X).[133X
  
  [1X5.2-2 PqProcessIndices[101X
  
  [33X[1;0Y[29X[2XPqProcessIndices[102X(  ) [32X function[133X
  
  [33X[0;0Yreturns  the  list  of  integer  indices  of  all  active  interactive [5XANUPQ[105X
  processes (see [2XPqProcessIndex[102X ([14X5.2-1[114X) for the meaning of [21Xactive[121X).[133X
  
  [1X5.2-3 IsPqProcessAlive[101X
  
  [33X[1;0Y[29X[2XIsPqProcessAlive[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XIsPqProcessAlive[102X(  ) [32X function[133X
  
  [33X[0;0Yreturn  [9Xtrue[109X  if  the [5XGAP[105X iostream of the [3Xi[103Xth (or default) interactive [5XANUPQ[105X
  process  started  by  [10XPqStart[110X  is  alive  (i.e. can still be written to), or
  [9Xfalse[109X, otherwise. (See the notes for [2XPqStart[102X ([14X5.1-1[114X) and [2XPqQuit[102X ([14X5.1-2[114X).)[133X
  
  [33X[0;0YIf  the user does not yet have a [10Xgap>[110X prompt then usually the [10Xanu-pq[110X program
  is  still  away  doing  something  and  an [5XANUPQ[105X interface function is still
  waiting  for  a  reply.  Typing a [10XCtrl-C[110X (i.e. holding down the [10XCtrl[110X key and
  typing  [10Xc[110X)  will stop the waiting and send [5XGAP[105X into a [10Xbreak[110X-loop, from which
  one  has  no  option  but  to  [10Xquit;[110X.  The  typing  of  [10XCtrl-C[110X,  in  such  a
  circumstance,  usually causes the stream of the interactive [5XANUPQ[105X process to
  die; to check this we provide [10XIsPqProcessAlive[110X (see [2XIsPqProcessAlive[102X).[133X
  
  [33X[0;0YThe [5XGAP[105X iostream of an interactive [5XANUPQ[105X process will also die if the [10Xanu-pq[110X
  program has a segmentation fault. We do hope that this never happens to you,
  but  if  it  does  and the failure is reproducible, then it's a bug and we'd
  like  to  know  about  it.  Please read the [10XREADME[110X that comes with the [5XANUPQ[105X
  package to find out what to include in a bug report and who to email it to.[133X
  
  
  [1X5.3 [33X[0;0YInteractive Versions of Non-interactive ANUPQ Functions[133X[101X
  
  [1X5.3-1 Pq[101X
  
  [33X[1;0Y[29X[2XPq[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPq[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yreturn,  for  the  fp  or pc group (let us call it [3XF[103X), of the [3Xi[103Xth or default
  interactive [5XANUPQ[105X process, the [22Xp[122X-quotient of [3XF[103X specified by [3Xoptions[103X, as a pc
  group;  [3XF[103X  must previously have been given (as first argument) to [10XPqStart[110X to
  start  the  interactive [5XANUPQ[105X process (see [2XPqStart[102X ([14X5.1-1[114X)) or restored from
  file using the function [10XPqRestorePcPresentation[110X (see [2XPqRestorePcPresentation[102X
  ([14X5.6-3[114X)).  Following  the colon [3Xoptions[103X is a selection of the options listed
  for  the  non-interactive  [10XPq[110X function (see [2XPq[102X ([14X4.1-1[114X)), separated by commas
  like record components (see Section [14XReference: Function Call With Options[114X in
  the  [5XGAP[105X Reference Manual), except that the options [10XSetupFile[110X or [10XPqWorkspace[110X
  are  ignored by the interactive [10XPq[110X, and [10XRedoPcp[110X is an option only recognised
  by  the  interactive  [10XPq[110X  i.e. the  following  options are recognised by the
  interactive [10XPq[110X function:[133X
  
  [30X    [33X[0;6Y[10XPrime := [3Xp[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XClassBound := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XExponent := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XRelators := [3Xrels[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XMetabelian[110X[133X
  
  [30X    [33X[0;6Y[10XIdentities := [3Xfuncs[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XGroupName := [3Xname[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XOutputLevel := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XRedoPcp[110X[133X
  
  [33X[0;0YDetailed  descriptions  of  the above options may be found in Chapter [14X'[33X[0;0YANUPQ
  Options[133X'[114X.[133X
  
  [33X[0;0YAs  a minimum the [10XPq[110X function [13Xmust[113X have a value for the [10XPrime[110X option, though
  [10XPrime[110X  need not be passed again in the case it has previously been provided,
  e.g. to [10XPqStart[110X (see [2XPqStart[102X ([14X5.1-1[114X)) when starting the interactive process.[133X
  
  [33X[0;0YThe behaviour of the interactive [10XPq[110X function depends on the current state of
  the pc presentation stored by the [10Xanu-pq[110X program:[133X
  
  [31X1[131X   [33X[0;6YIf  no  pc  presentation  has  yet been computed (the case immediately
        after the [10XPqStart[110X call initiating the process) then the quotient group
        of  the  input  group of the process of largest lower exponent-[3Xp[103X class
        bounded by the value of the [10XClassBound[110X option (see [14X6.2[114X) is returned.[133X
  
  [31X2[131X   [33X[0;6YIf  the  current  pc  presentation  of the process was determined by a
        previous  call  to  [10XPq[110X  or  [10XPqEpimorphism[110X,  and the current call has a
        larger  value  [10XClassBound[110X  then  the  class  is extended as much as is
        possible  and  the quotient group of the input group of the process of
        the new lower exponent-[3Xp[103X class is returned.[133X
  
  [31X3[131X   [33X[0;6YIf  the  current  pc  presentation  of the process was determined by a
        previous  call  to  [10XPqPCover[110X  then  a  consistent pc presentation of a
        quotient  for  the current class is determined before proceeding as in
        2.[133X
  
  [31X4[131X   [33X[0;6YIf  the  [10XRedoPcp[110X  option  is  supplied  the current pc presentation is
        scrapped,  all  options must be re-supplied (in particular, [10XPrime[110X [13Xmust[113X
        be supplied) and then the [10XPq[110X function proceeds as in 1.[133X
  
  [33X[0;0YSee  Section [14X'[33X[0;0YAttributes  and  a  Property  for  fp and pc p-groups[133X'[114X for the
  attributes  and  property [10XNuclearRank[110X, [10XMultiplicatorRank[110X and [10XIsCapable[110X which
  may be applied to the group returned by [10XPq[110X.[133X
  
  [33X[0;0YThe  following is one of the examples for the non-interactive [10XPq[110X redone with
  the interactive version. Also, we set the option [10XOutputLevel[110X to 1 (see [14X6.2[114X),
  in  order  to see the orders of the quotients of all the classes determined,
  and  we  set  the  [10XInfoANUPQ[110X  level to 2 (see [2XInfoANUPQ[102X ([14X3.3-1[114X)), so that we
  catch the timing information.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup("a", "b");; a := F.1;; b := F.2;;[127X[104X
    [4X[25Xgap>[125X [27XG := F / [a^4, b^4];[127X[104X
    [4X[28X<fp group on the generators [ a, b ]>[128X[104X
    [4X[25Xgap>[125X [27XPqStart(G);[127X[104X
    [4X[28X1[128X[104X
    [4X[25Xgap>[125X [27XSetInfoLevel(InfoANUPQ, 2); #To see timing information[127X[104X
    [4X[25Xgap>[125X [27XPq(: Prime := 2, ClassBound := 3, OutputLevel := 1 );[127X[104X
    [4X[28X#I  Lower exponent-2 central series for [grp][128X[104X
    [4X[28X#I  Group: [grp] to lower exponent-2 central class 1 has order 2^2[128X[104X
    [4X[28X#I  Group: [grp] to lower exponent-2 central class 2 has order 2^5[128X[104X
    [4X[28X#I  Group: [grp] to lower exponent-2 central class 3 has order 2^8[128X[104X
    [4X[28X#I  Computation of presentation took 0.00 seconds[128X[104X
    [4X[28X<pc group of size 256 with 8 generators>[128X[104X
  [4X[32X[104X
  
  [1X5.3-2 PqEpimorphism[101X
  
  [33X[1;0Y[29X[2XPqEpimorphism[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqEpimorphism[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yreturn,  for  the  fp  or pc group (let us call it [3XF[103X), of the [3Xi[103Xth or default
  interactive  [5XANUPQ[105X  process,  an epimorphism from [3XF[103X onto the [22Xp[122X-quotient of [3XF[103X
  specified  by [3Xoptions[103X; [3XF[103X must previously have been given (as first argument)
  to  [10XPqStart[110X  to  start  the interactive [5XANUPQ[105X process (see [2XPqStart[102X ([14X5.1-1[114X)).
  Since  the  underlying  interactions with the [10Xanu-pq[110X program effected by the
  interactive [10XPqEpimorphism[110X are identical to those effected by the interactive
  [10XPq[110X,  everything  said  regarding  the  requirements  and  behaviour  of  the
  interactive   [10XPq[110X  function  (see [2XPq[102X  ([14X5.3-1[114X))  is  also  the  case  for  the
  interactive [10XPqEpimorphism[110X.[133X
  
  [33X[0;0Y[13XNote:[113X See Section [14X'[33X[0;0YAttributes and a Property for fp and pc p-groups[133X'[114X for the
  attributes  and  property [10XNuclearRank[110X, [10XMultiplicatorRank[110X and [10XIsCapable[110X which
  may   be  applied  to  the  image  group  of  the  epimorphism  returned  by
  [10XPqEpimorphism[110X.[133X
  
  [1X5.3-3 PqPCover[101X
  
  [33X[1;0Y[29X[2XPqPCover[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPCover[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yreturn,  for  the  fp  or  pc  group of the [3Xi[103Xth or default interactive [5XANUPQ[105X
  process,  the  [22Xp[122X-covering  group  of  the [22Xp[122X-quotient [10XPq([3Xi[103X[10X : [3Xoptions[103X[10X)[110X or [10XPq(:
  [3Xoptions[103X[10X)[110X, modulo the following:[133X
  
  [31X1[131X   [33X[0;6YIf  no  pc  presentation  has  yet been computed (the case immediately
        after  the [10XPqStart[110X call initiating the process) and the group [3XF[103X of the
        process  is  already  a  [22Xp[122X-group, in the sense that [10XHasIsPGroup([3XF[103X[10X) and
        IsPGroup([3XF[103X[10X)[110X is [9Xtrue[109X, then[133X
  
        [8X[10XPrime[110X[8X[108X
              [33X[0;12Ydefaults    to    [10XPrimePGroup([3XF[103X[10X)[110X,    if    not    supplied   and
              [10XHasPrimePGroup([3XF[103X[10X) = true[110X; and[133X
  
        [8X[10XClassBound[110X[8X[108X
              [33X[0;12Ydefaults  to [10XPClassPGroup([3XF[103X[10X)[110X if [10XHasPClassPGroup([3XF[103X[10X) = true[110X if not
              supplied, or to the usual default of 63, otherwise.[133X
  
  [31X2[131X   [33X[0;6YIf  a pc presentation has been computed and none of [3Xoptions[103X is [10XRedoPcp[110X
        or  if  no pc presentation has yet been computed but 1. does not apply
        then [10XPqPCover([3Xi[103X[10X : [3Xoptions[103X[10X);[110X is equivalent to:[133X
  
  [4X      [32X[104X
          [4XPq(i : options);[104X
          [4XPqPCover(i);[104X
        [4X[32X[104X
  
  [31X3[131X   [33X[0;6YIf  the  [10XRedoPcp[110X  option  is  supplied  the current pc presentation is
        scrapped, and [10XPqPCover[110X proceeds as in 1. or 2. but without the [10XRedoPcp[110X
        option.[133X
  
  [1X5.3-4 PqStandardPresentation[101X
  
  [33X[1;0Y[29X[2XPqStandardPresentation[102X( [[3Xi[103X][3X:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XStandardPresentation[102X( [[3Xi[103X][3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yreturn,  for the [3Xi[103Xth or default interactive [5XANUPQ[105X process, the [3Xp[103X-quotient of
  the group [3XF[103X of the process, specified by [3Xoptions[103X, as an [13Xfp group[113X which has a
  standard  presentation.  Here [3Xoptions[103X is a selection of the options from the
  following list (see Chapter [14X'[33X[0;0YANUPQ Options[133X'[114X for detailed descriptions); this
  list    is    the    same    as   for   the   non-interactive   version   of
  [10XPqStandardPresentation[110X  except  for  the  omission  of options [10XSetupFile[110X and
  [10XPqWorkspace[110X (see [2XPqStandardPresentation[102X ([14X4.2-1[114X)).[133X
  
  [30X    [33X[0;6Y[10XPrime := [3Xp[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XpQuotient := [3XQ[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XClassBound := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XExponent := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XMetabelian[110X[133X
  
  [30X    [33X[0;6Y[10XGroupName := [3Xname[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XOutputLevel := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XStandardPresentationFile := [3Xfilename[103X[10X[110X[133X
  
  [33X[0;0YUnless  [3XF[103X is a pc [3Xp[103X-group, or the option [10XPrime[110X has been passed to a previous
  interactive function for the process to compute a [3Xp[103X-quotient for [3XF[103X, the user
  [13Xmust[113X  supply  either the option [10XPrime[110X or the option [10XpQuotient[110X (if both [10XPrime[110X
  and   [10XpQuotient[110X  are  supplied,  the  prime  [3Xp[103X  is  determined  by  applying
  [10XPrimePGroup[110X  (see [2XPrimePGroup[102X  ([14XReference:  PrimePGroup[114X)  in  the  Reference
  Manual) to the value of [10XpQuotient[110X).[133X
  
  [33X[0;0YTaking   one   of   the   examples   for   the  non-interactive  version  of
  [10XStandardPresentation[110X  (see [2XStandardPresentation[102X  ([14X4.2-1[114X))  that required two
  separate  calls  to  the  [10Xanu-pq[110X  program, we now show how it can be done by
  setting  up  a  dialogue  with  just  the  one  [10Xanu-pq[110X  process,  using  the
  interactive version of [10XStandardPresentation[110X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF4 := FreeGroup( "a", "b", "c", "d" );;[127X[104X
    [4X[25Xgap>[125X [27Xa := F4.1;; b := F4.2;; c := F4.3;; d := F4.4;;[127X[104X
    [4X[25Xgap>[125X [27XG4 := F4 / [ b^4, b^2 / Comm(Comm (b, a), a), d^16,[127X[104X
    [4X[25X>[125X [27X                a^16 / (c * d), b^8 / (d * c^4) ];[127X[104X
    [4X[28X<fp group on the generators [ a, b, c, d ]>[128X[104X
    [4X[25Xgap>[125X [27XSetInfoLevel(InfoANUPQ, 1); #Only essential Info please[127X[104X
    [4X[25Xgap>[125X [27XPqStart(G4); #Start a new interactive process for a new group[127X[104X
    [4X[28X2[128X[104X
    [4X[25Xgap>[125X [27XK := Pq( 2 : Prime := 2, ClassBound := 1 ); #`pq' process no. is 2[127X[104X
    [4X[28X<pc group of size 4 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XStandardPresentation( 2 : pQuotient := K, ClassBound := 14 );[127X[104X
    [4X[28X<fp group with 53 generators>[128X[104X
  [4X[32X[104X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YIn  contrast  to  the function [10XPq[110X (see [2XPq[102X ([14X4.1-1[114X)) which returns a pc group,
  [10XPqStandardPresentation[110X  or [10XStandardPresentation[110X returns an fp group. This is
  because  the  output  is mainly used for isomorphism testing for which an fp
  group  is enough. However, the presentation is a polycyclic presentation and
  if  you need to do any further computation with this group (e.g. to find the
  order)   you   can   use  the  function  [10XPcGroupFpGroup[110X  (see [2XPcGroupFpGroup[102X
  ([14XReference: PcGroupFpGroup[114X) in the [5XGAP[105X Reference Manual) to form a pc group.[133X
  
  [33X[0;0YIf the user does not supply a [3Xp[103X-quotient [3XQ[103X via the [10XpQuotient[110X option, and the
  prime  [3Xp[103X is either supplied, stored, or [3XF[103X is a pc [3Xp[103X-group, then a [3Xp[103X-quotient
  [3XQ[103X  is  computed.  (The value of the prime [3Xp[103X is stored if passed initially to
  [10XPqStart[110X  or  to  a subsequent interactive process.) Note that a stored value
  for  [10XpQuotient[110X  (from  a  prior  call to [10XPq[110X) does [13Xnot[113X have precedence over a
  value  for  the  prime  [3Xp[103X.  If  the  user does supply a [3Xp[103X-quotient [3XQ[103X via the
  [10XpQuotient[110X  option, the package [5XAutPGrp[105X is called to compute the automorphism
  group  of  [3XQ[103X;  an error will occur that asks the user to install the package
  [5XAutPGrp[105X if the automorphism group cannot be computed.[133X
  
  [33X[0;0YIf    any    of    the    interactive    functions   [10XPqStandardPresentation[110X,
  [10XStandardPresentation[110X,          [10XEpimorphismPqStandardPresentation[110X          or
  [10XEpimorphismStandardPresentation[110X   has   been   called   previously   for  an
  interactive  process,  a  subsequent  call to any of these functions for the
  same  process  returns  the  previously  computed value. Note that all these
  functions  compute both an epimorphism and an fp group and store the results
  in  the  [10XSPepi[110X and [10XSP[110X fields of the data record associated with the process.
  See   the   example   for  the  interactive  [10XEpimorphismStandardPresentation[110X
  ([2XEpimorphismStandardPresentation[102X ([14X5.3-5[114X)).[133X
  
  [33X[0;0YThe attributes and property [10XNuclearRank[110X, [10XMultiplicatorRank[110X and [10XIsCapable[110X are
  set for the group returned by [10XPqStandardPresentation[110X or [10XStandardPresentation[110X
  (see Section [14X'[33X[0;0YAttributes and a Property for fp and pc p-groups[133X'[114X).[133X
  
  [1X5.3-5 EpimorphismPqStandardPresentation[101X
  
  [33X[1;0Y[29X[2XEpimorphismPqStandardPresentation[102X( [[3Xi[103X][3X:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XEpimorphismStandardPresentation[102X( [[3Xi[103X][3X:[103X [3Xoptions[103X ) [32X method[133X
  
  [33X[0;0YEach  of  the  above functions accepts the same arguments and options as the
  interactive  form of [10XStandardPresentation[110X (see [2XStandardPresentation[102X ([14X5.3-4[114X))
  and  returns  an epimorphism from the fp or pc group [3XF[103X of the [3Xi[103Xth or default
  interactive  [5XANUPQ[105X  process  onto  the  finitely  presented group given by a
  standard  presentation,  i.e. if [3XS[103X is the standard presentation computed for
  the      [22Xp[122X-quotient      of      [3XF[103X      by     [10XStandardPresentation[110X     then
  [10XEpimorphismStandardPresentation[110X  returns the epimorphism from [3XF[103X to the group
  with presentation [3XS[103X. The group [3XF[103X must have been given (as first argument) to
  [10XPqStart[110X to start the interactive [5XANUPQ[105X process (see [2XPqStart[102X ([14X5.1-1[114X)).[133X
  
  [33X[0;0YTaking          our          earlier         non-interactive         example
  (see [2XEpimorphismPqStandardPresentation[102X  ([14X4.2-2[114X))  and modifying it a little,
  we    illustrate,    as    for    the    interactive    [10XStandardPresentation[110X
  (see [2XStandardPresentation[102X ([14X5.3-4[114X)), how something that required two separate
  calls  to  the  [10Xanu-pq[110X program can now be achieved with a dialogue with just
  one  [10Xanu-pq[110X  process.  Also,  observe  that  calls  to  one  of the standard
  presentation  functions  (as  mentioned in the notes of [2XStandardPresentation[102X
  ([14X5.3-4[114X))  computes  and stores both an fp group with a standard presentation
  and an epimorphism; subsequent calls to a standard presentation function for
  the same process simply return the appropriate stored value.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup(6, "F");;[127X[104X
    [4X[25Xgap>[125X [27Xx := F.1;; y := F.2;; z := F.3;; w := F.4;; a := F.5;; b := F.6;;[127X[104X
    [4X[25Xgap>[125X [27XR := [x^3 / w, y^3 / w * a^2 * b^2, w^3 / b,[127X[104X
    [4X[25X>[125X [27X         Comm (y, x) / z, Comm (z, x), Comm (z, y) / a, z^3 ];[127X[104X
    [4X[28X[ F1^3*F4^-1, F2^3*F4^-1*F5^2*F6^2, F4^3*F6^-1, F2^-1*F1^-1*F2*F1*F3^-1, [128X[104X
    [4X[28X  F3^-1*F1^-1*F3*F1, F3^-1*F2^-1*F3*F2*F5^-1, F3^3 ][128X[104X
    [4X[25Xgap>[125X [27XQ := F / R;[127X[104X
    [4X[28X<fp group on the generators [ F1, F2, F3, F4, F5, F6 ]>[128X[104X
    [4X[25Xgap>[125X [27XPqStart( Q );[127X[104X
    [4X[28X3[128X[104X
    [4X[25Xgap>[125X [27XG := Pq( 3 : Prime := 3, ClassBound := 3 );[127X[104X
    [4X[28X<pc group of size 729 with 6 generators>[128X[104X
    [4X[25Xgap>[125X [27Xlev := InfoLevel(InfoANUPQ);; # Save current InfoANUPQ level[127X[104X
    [4X[25Xgap>[125X [27XSetInfoLevel(InfoANUPQ, 2); # To see computation times[127X[104X
    [4X[25Xgap>[125X [27X# It is not necessary to pass the `Prime' option to[127X[104X
    [4X[25Xgap>[125X [27X# `EpimorphismStandardPresentation' since it was previously[127X[104X
    [4X[25Xgap>[125X [27X# passed to `Pq':[127X[104X
    [4X[25Xgap>[125X [27Xphi := EpimorphismStandardPresentation( 3 : ClassBound := 3 );[127X[104X
    [4X[28X#I  Class 1 3-quotient and its 3-covering group computed in 0.00 seconds[128X[104X
    [4X[28X#I  Order of GL subgroup is 48[128X[104X
    [4X[28X#I  No. of soluble autos is 0[128X[104X
    [4X[28X#I    dim U = 1  dim N = 3  dim M = 3[128X[104X
    [4X[28X#I    nice stabilizer with perm rep[128X[104X
    [4X[28X#I  Computing standard presentation for class 2 took 0.00 seconds[128X[104X
    [4X[28X#I  Computing standard presentation for class 3 took 0.01 seconds[128X[104X
    [4X[28X[ F1, F2, F3, F4, F5, F6 ] -> [ f1*f2^2*f3*f4^2*f5^2, f1*f2*f3*f5, f3^2, [128X[104X
    [4X[28X  f4*f6^2, f5, f6 ][128X[104X
    [4X[25Xgap>[125X [27X# Image of phi should be isomorphic to G ...[127X[104X
    [4X[25Xgap>[125X [27X# let's check the order is correct:[127X[104X
    [4X[25Xgap>[125X [27XSize( Image(phi) );[127X[104X
    [4X[28X729[128X[104X
    [4X[25Xgap>[125X [27X# `StandardPresentation' and `EpimorphismStandardPresentation'[127X[104X
    [4X[25Xgap>[125X [27X# behave like attributes, so no computation is done when[127X[104X
    [4X[25Xgap>[125X [27X# either is called again for the same process ...[127X[104X
    [4X[25Xgap>[125X [27XStandardPresentation( 3 : ClassBound := 3 );[127X[104X
    [4X[28X<fp group of size 729 on the generators [ f1, f2, f3, f4, f5, f6 ]>[128X[104X
    [4X[25Xgap>[125X [27X# No timing data was Info-ed since no computation was done[127X[104X
    [4X[25Xgap>[125X [27XSetInfoLevel(InfoANUPQ, lev); # Restore previous InfoANUPQ level[127X[104X
  [4X[32X[104X
  
  [33X[0;0YA  very similar (essential details are the same) example to the above may be
  executed live, by typing: [10XPqExample( "EpimorphismStandardPresentation-i" );[110X.[133X
  
  [33X[0;0Y[13XNote:[113X   The   notes   for   [10XPqStandardPresentation[110X  or  [10XStandardPresentation[110X
  (see [2XPqStandardPresentation[102X        ([14X5.3-4[114X))        apply       also       to
  [10XEpimorphismPqStandardPresentation[110X  or [10XEpimorphismStandardPresentation[110X except
  that  their return value is an [13Xepimorphism onto[113X an fp group, i.e. one should
  interpret  the  phrase [21Xreturns an fp group[121X as [21Xreturns an epimorphism onto an
  fp group[121X etc.[133X
  
  [1X5.3-6 PqDescendants[101X
  
  [33X[1;0Y[29X[2XPqDescendants[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqDescendants[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yreturn  for  the pc group [3XG[103X of the [3Xi[103Xth or default interactive [5XANUPQ[105X process,
  which  must  be  of  prime  power  order  with  a  confluent pc presentation
  (see [2XIsConfluent[102X ([14XReference: IsConfluent for pc groups[114X) in the [5XGAP[105X Reference
  Manual),  a  list  of  descendants  (pc groups) of [3XG[103X. The group [3XG[103X is usually
  given  as  first  argument  to  [10XPqStart[110X  when starting the interactive [5XANUPQ[105X
  process  (see [2XPqStart[102X  ([14X5.1-1[114X)). Alternatively, one may initiate the process
  with an fp group, use [10XPq[110X interactively (see [2XPq[102X ([14X5.3-1[114X)) to create a pc group
  and  use  [10XPqSetPQuotientToGroup[110X  (see [2XPqSetPQuotientToGroup[102X  ([14X5.3-7[114X)), which
  involves  [13Xno[113X computation, to set the pc group returned by [10XPq[110X as the group of
  the  process.  Note  that  repeating  a  call  to [10XPqDescendants[110X for the same
  interactive  [5XANUPQ[105X process simply returns the list of descendants originally
  calculated;  a warning is emitted at [10XInfoANUPQ[110X level 1 reminding you of this
  should you do this.[133X
  
  [33X[0;0YAfter  the  colon,  [3Xoptions[103X  a  selection  of  the  options  listed  for the
  non-interactive  [10XPqDescendants[110X  function (see [2XPqDescendants[102X ([14X4.4-1[114X)), should
  be given, separated by commas like record components (see Section [14XReference:
  Function  Call  With  Options[114X  in the [5XGAP[105X Reference Manual), except that the
  options   [10XSetupFile[110X   or   [10XPqWorkspace[110X   are   ignored  by  the  interactive
  [10XPqDescendants[110X,  i.e. the following options are recognised by the interactive
  [10XPqDescendants[110X function:[133X
  
  [30X    [33X[0;6Y[10XClassBound := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XRelators := [3Xrels[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XOrderBound := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XStepSize := [3Xn[103X[10X[110X, [10XStepSize := [3Xlist[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XRankInitialSegmentSubgroups := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XSpaceEfficient[110X[133X
  
  [30X    [33X[0;6Y[10XCapableDescendants[110X[133X
  
  [30X    [33X[0;6Y[10XAllDescendants := false[110X[133X
  
  [30X    [33X[0;6Y[10XExponent := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XMetabelian[110X[133X
  
  [30X    [33X[0;6Y[10XGroupName := [3Xname[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XSubList := [3Xsub[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XBasicAlgorithm[110X[133X
  
  [30X    [33X[0;6Y[10XCustomiseOutput := [3Xrec[103X[10X[110X[133X
  
  [33X[0;0Y[13XNotes:[113X  The function [10XPqDescendants[110X uses the automorphism group of [3XG[103X which it
  computes  via  the  package  [5XAutPGrp[105X  if  the automorphism group of [3XG[103X is not
  already  present. If [5XAutPGrp[105X is not installed an error may be raised. If the
  automorphism  group  of  [3XG[103X  is  insoluble  the  [10Xanu-pq[110X program will call [5XGAP[105X
  together with the [5XAutPGrp[105X package for certain orbit-stabilizer calculations.[133X
  
  [33X[0;0YThe attributes and property [10XNuclearRank[110X, [10XMultiplicatorRank[110X and [10XIsCapable[110X are
  set   for   each   group   of   the  list  returned  by  [10XPqDescendants[110X  (see
  Section [14X'[33X[0;0YAttributes and a Property for fp and pc p-groups[133X'[114X).[133X
  
  [33X[0;0YLet  us  now  repeat  the  examples previously given for the non-interactive
  [10XPqDescendants[110X, but this time with the interactive version of [10XPqDescendants[110X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup( "a", "b" );; a := F.1;; b := F.2;;[127X[104X
    [4X[25Xgap>[125X [27XG := PcGroupFpGroup( F / [ a^2, b^2, Comm(b, a) ] );[127X[104X
    [4X[28X<pc group of size 4 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XPqStart(G); #This will now be the 4th interactive process running[127X[104X
    [4X[28X4[128X[104X
    [4X[25Xgap>[125X [27Xdes := PqDescendants( 4 : OrderBound := 6, ClassBound := 5 );;[127X[104X
    [4X[25Xgap>[125X [27XLength(des);[127X[104X
    [4X[28X83[128X[104X
    [4X[25Xgap>[125X [27XList(des, Size);[127X[104X
    [4X[28X[ 8, 8, 8, 16, 16, 16, 32, 16, 16, 16, 16, 16, 32, 32, 64, 64, 32, 32, 32, [128X[104X
    [4X[28X  32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, 32, 64, 64, 64, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64 ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Length( PCentralSeries( d, 2 ) ) - 1 );[127X[104X
    [4X[28X[ 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, [128X[104X
    [4X[28X  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, [128X[104X
    [4X[28X  4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, [128X[104X
    [4X[28X  4, 4, 4, 5, 5, 5, 5, 5 ][128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn  the second example we compute all capable descendants of order 27 of the
  elementary abelian group of order 9.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup( 2, "g" );;[127X[104X
    [4X[25Xgap>[125X [27XG := PcGroupFpGroup( F / [ F.1^3, F.2^3, Comm(F.1, F.2) ] );[127X[104X
    [4X[28X<pc group of size 9 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XPqStart(G); #This will now be the 5th interactive process running[127X[104X
    [4X[28X5[128X[104X
    [4X[25Xgap>[125X [27Xdes := PqDescendants( 5 : OrderBound := 3, ClassBound := 2,[127X[104X
    [4X[25X>[125X [27X                             CapableDescendants );[127X[104X
    [4X[28X[ <pc group of size 27 with 3 generators>, [128X[104X
    [4X[28X  <pc group of size 27 with 3 generators> ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Length( PCentralSeries( d, 3 ) ) - 1 );[127X[104X
    [4X[28X[ 2, 2 ][128X[104X
    [4X[25Xgap>[125X [27X# For comparison let us now compute all descendants[127X[104X
    [4X[25Xgap>[125X [27X# (using the non-interactive Pq function)[127X[104X
    [4X[25Xgap>[125X [27XPqDescendants( G : OrderBound := 3, ClassBound := 2);[127X[104X
    [4X[28X[ <pc group of size 27 with 3 generators>, [128X[104X
    [4X[28X  <pc group of size 27 with 3 generators>, [128X[104X
    [4X[28X  <pc group of size 27 with 3 generators> ][128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn  the  third example, we compute all capable descendants of the elementary
  abelian  group  of order [22X5^2[122X which have exponent-[22X5[122X class at most [22X3[122X, exponent
  [22X5[122X, and are metabelian.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup( 2, "g" );;[127X[104X
    [4X[25Xgap>[125X [27XG := PcGroupFpGroup( F / [ F.1^5, F.2^5, Comm(F.2, F.1) ] );[127X[104X
    [4X[28X<pc group of size 25 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XPqStart(G); #This will now be the 6th interactive process running[127X[104X
    [4X[28X6[128X[104X
    [4X[25Xgap>[125X [27Xdes := PqDescendants( 6 : Metabelian, ClassBound := 3,[127X[104X
    [4X[25X>[125X [27X                             Exponent := 5, CapableDescendants );[127X[104X
    [4X[28X[ <pc group of size 125 with 3 generators>, [128X[104X
    [4X[28X  <pc group of size 625 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 3125 with 5 generators> ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Length( PCentralSeries( d, 5 ) ) - 1 );[127X[104X
    [4X[28X[ 2, 3, 3 ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Length( DerivedSeries( d ) ) );[127X[104X
    [4X[28X[ 3, 3, 3 ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Maximum( List( d, Order ) ) );[127X[104X
    [4X[28X[ 5, 5, 5 ][128X[104X
  [4X[32X[104X
  
  [1X5.3-7 PqSetPQuotientToGroup[101X
  
  [33X[1;0Y[29X[2XPqSetPQuotientToGroup[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSetPQuotientToGroup[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X  process,  set the [22Xp[122X-quotient
  previously  computed  by  the interactive [10XPq[110X function (see [2XPq[102X ([14X5.3-1[114X)) to be
  the  group  of  the  process.  This  function  is  supplied  to  enable  the
  computation  of  descendants  of  a  [22Xp[122X-quotient that is already known to the
  [10Xanu-pq[110X    program,    via    the    interactive    [10XPqDescendants[110X    function
  (see [2XPqDescendants[102X ([14X5.3-6[114X)), thus avoiding the need to re-submit it and have
  the [10Xanu-pq[110X program recompute it.[133X
  
  [33X[0;0Y[13XNote:[113X   See   the  function  [10XPqPGSetDescendantToPcp[110X  ([2XPqPGSetDescendantToPcp[102X
  ([14X5.9-4[114X))  for  a mechanism to make (the [22Xp[122X-cover of) a particular descendants
  the current group of the process.[133X
  
  [33X[0;0YThe  following  example  of  the  usage  of  [10XPqSetPQuotientToGroup[110X, which is
  essentially     equivalent     to    what    is    obtained    by    running
  [10XPqExample("PqDescendants-1-i");[110X,  redoes  the first example of [2XPqDescendants[102X
  ([14X5.3-6[114X) (which computes the descendants of the Klein four group).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XF := FreeGroup( "a", "b" );[127X[104X
    [4X[28X<free group on the generators [ a, b ]>[128X[104X
    [4X[25Xgap>[125X [27XprocId := PqStart( F : Prime := 2 );[127X[104X
    [4X[28X7[128X[104X
    [4X[25Xgap>[125X [27XPq( procId : ClassBound := 1 );[127X[104X
    [4X[28X<pc group of size 4 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XPqSetPQuotientToGroup( procId );[127X[104X
    [4X[25Xgap>[125X [27Xdes := PqDescendants( procId : OrderBound := 6, ClassBound := 5 );;[127X[104X
    [4X[25Xgap>[125X [27XLength(des);[127X[104X
    [4X[28X83[128X[104X
    [4X[25Xgap>[125X [27XList(des, Size);[127X[104X
    [4X[28X[ 8, 8, 8, 16, 16, 16, 32, 16, 16, 16, 16, 16, 32, 32, 64, 64, 32, 32, 32, [128X[104X
    [4X[28X  32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, 32, 64, 64, 64, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, [128X[104X
    [4X[28X  64, 64, 64, 64, 64, 64, 64 ][128X[104X
    [4X[25Xgap>[125X [27XList(des, d -> Length( PCentralSeries( d, 2 ) ) - 1 );[127X[104X
    [4X[28X[ 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, [128X[104X
    [4X[28X  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, [128X[104X
    [4X[28X  4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, [128X[104X
    [4X[28X  4, 4, 4, 5, 5, 5, 5, 5 ][128X[104X
  [4X[32X[104X
  
  
  [1X5.4  [33X[0;0YLow-level  Interactive  ANUPQ  functions  based on menu items of the pq[101X
  [1Xprogram[133X[101X
  
  [33X[0;0YThe  [10Xanu-pq[110X  program  has  5 menus, the details of which the reader will not
  normally  need  to  know,  but if she wishes to know the details they may be
  found  in  the  standalone  manual: [10Xguide.dvi[110X. Both [10Xguide.dvi[110X and the [10Xanu-pq[110X
  program  refer  to  the  items  of  these  5  menus as [21Xoptions[121X, which do [13Xnot[113X
  correspond  in  any way to the options used by any of the [5XGAP[105X functions that
  interface with the [10Xanu-pq[110X program.[133X
  
  [33X[0;0Y[13XWarning:[113X  The  commands  provided  in  this  section are intended to provide
  something  like  the  interactive  functionality  one  has  when running the
  standalone,  from  within  [5XGAP[105X.  The  [10Xanu-pq[110X  standalone (in particular, its
  [21Xadvanced[121X  menus)  assumes  some expertise of the user; doing the [21Xwrong[121X thing
  can  cause  the  program  to  crash.  While a number of safeguards have been
  provided  in  the  [5XGAP[105X  interface  to  the  [10Xanu-pq[110X  program,  these  are [13Xnot[113X
  foolproof,  and  the  user should exercise care and ensure pre-requisites of
  the various commands are met.[133X
  
  
  [1X5.5 [33X[0;0YGeneral commands[133X[101X
  
  [33X[0;0YThe  following commands either use a menu item from whatever menu is [21Xcurrent[121X
  for  the  [10Xanu-pq[110X program, or have general application and are not associated
  with just one menu item of the [10Xanu-pq[110X program.[133X
  
  [1X5.5-1 PqNrPcGenerators[101X
  
  [33X[1;0Y[29X[2XPqNrPcGenerators[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqNrPcGenerators[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or default interactive [5XANUPQ[105X process, return the number of pc
  generators  of  the  lower  exponent [22Xp[122X-class quotient of the group currently
  determined  by  the process. This also applies if the pc presentation is not
  consistent.[133X
  
  [1X5.5-2 PqFactoredOrder[101X
  
  [33X[1;0Y[29X[2XPqFactoredOrder[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqFactoredOrder[102X(  ) [32X function[133X
  
  [33X[0;0Yfor the [3Xi[103Xth or default interactive [5XANUPQ[105X process, return an integer pair [10X[[3Xp[103X[10X,
  [3Xn[103X[10X][110X   where   [3Xp[103X   is   a   prime  and  [3Xn[103X  is  the  number  of  pc  generators
  (see [2XPqNrPcGenerators[102X  ([14X5.5-1[114X)) in the pc presentation of the quotient group
  currently  determined  by  the  process. If this presentation is consistent,
  then  [22Xp^n[122X  is the order of the quotient group. Otherwise (if tails have been
  added  but  the necessary consistency checks, relation collections, exponent
  law checks and redundant generator eliminations have not yet been done), [22Xp^n[122X
  is an upper bound for the order of the group.[133X
  
  [1X5.5-3 PqOrder[101X
  
  [33X[1;0Y[29X[2XPqOrder[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqOrder[102X(  ) [32X function[133X
  
  [33X[0;0Yfor the [3Xi[103Xth or default interactive [5XANUPQ[105X process, return [22Xp^n[122X where [10X[[3Xp[103X[10X, [3Xn[103X[10X][110X is
  the pair as returned by [10XPqFactoredOrder[110X (see [2XPqFactoredOrder[102X ([14X5.5-2[114X)).[133X
  
  [1X5.5-4 PqPClass[101X
  
  [33X[1;0Y[29X[2XPqPClass[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPClass[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, return the lower exponent
  [22Xp[122X-class of the quotient group currently determined by the process.[133X
  
  [1X5.5-5 PqWeight[101X
  
  [33X[1;0Y[29X[2XPqWeight[102X( [3Xi[103X, [3Xj[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqWeight[102X( [3Xj[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth or default interactive [5XANUPQ[105X process, return the weight of the
  [3Xj[103Xth  pc  generator  of  the  lower  exponent  [22Xp[122X-class  quotient of the group
  currently determined by the process, or [9Xfail[109X if there is no such numbered pc
  generator.[133X
  
  [1X5.5-6 PqCurrentGroup[101X
  
  [33X[1;0Y[29X[2XPqCurrentGroup[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCurrentGroup[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, return the group whose pc
  presentation  is determined by the process as a [5XGAP[105X pc group (either a lower
  exponent  [22Xp[122X-class  quotient  of  the  start  group  or the [22Xp[122X-cover of such a
  quotient).[133X
  
  [33X[0;0Y[13XNotes:[113X  See  Section [14X'[33X[0;0YAttributes  and a Property for fp and pc p-groups[133X'[114X for
  the  attributes  and  property  [10XNuclearRank[110X, [10XMultiplicatorRank[110X and [10XIsCapable[110X
  which may be applied to the group returned by [10XPqCurrentGroup[110X.[133X
  
  [1X5.5-7 PqDisplayPcPresentation[101X
  
  [33X[1;0Y[29X[2XPqDisplayPcPresentation[102X( [3Xi:[103X [[3XOutputLevel[103X [3X:=[103X [3Xlev[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqDisplayPcPresentation[102X( [3X:[103X [[3XOutputLevel[103X [3X:=[103X [3Xlev[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to display the pc presentation of the lower exponent [22Xp[122X-class quotient of the
  group currently determined by the process.[133X
  
  [33X[0;0YExcept  if  the  last  command  communicating  with the [10Xanu-pq[110X program was a
  [22Xp[122X-group generation command (for which there is only a verbose output level),
  to  set the amount of information this command displays you may wish to call
  [10XPqSetOutputLevel[110X  first (see [2XPqSetOutputLevel[102X ([14X5.5-8[114X)), or equivalently pass
  the option [10XOutputLevel[110X (see [14X6.2[114X).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqDisplayPcPresentation[110X
  performs menu item 4 of the current menu of the [10Xanu-pq[110X program.[133X
  
  [1X5.5-8 PqSetOutputLevel[101X
  
  [33X[1;0Y[29X[2XPqSetOutputLevel[102X( [3Xi[103X, [3Xlev[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSetOutputLevel[102X( [3Xlev[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to set the output level of the [10Xanu-pq[110X program to [3Xlev[103X.[133X
  
  [33X[0;0Y[13XNote:[113X  For those familiar with the [10Xanu-pq[110X program, [10XPqSetOutputLevel[110X performs
  menu  item  5  of  the  main  (or advanced) [22Xp[122X-Quotient menu, or the Standard
  Presentation menu.[133X
  
  [1X5.5-9 PqEvaluateIdentities[101X
  
  [33X[1;0Y[29X[2XPqEvaluateIdentities[102X( [3Xi:[103X [[3XIdentities[103X [3X:=[103X [3Xfuncs[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqEvaluateIdentities[102X( [3X:[103X [[3XIdentities[103X [3X:=[103X [3Xfuncs[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth or default interactive [5XANUPQ[105X process, invoke the evaluation of
  identities  defined by the [10XIdentities[110X option, and eliminate any redundant pc
  generators formed. Since a previous value of [10XIdentities[110X is saved in the data
  record  of  the  process,  it  is  unnecessary to pass the [10XIdentities[110X if set
  previously.[133X
  
  [33X[0;0Y[13XNote:[113X  This  function  is  mainly  implemented at the [5XGAP[105X level. It does not
  correspond to a menu item of the [10Xanu-pq[110X program.[133X
  
  
  [1X5.6 [33X[0;0YCommands from the Main [22Xp[122X[101X[1X-Quotient menu[133X[101X
  
  [1X5.6-1 PqPcPresentation[101X
  
  [33X[1;0Y[29X[2XPqPcPresentation[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPcPresentation[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compute  the  pc presentation of the quotient (determined by [3Xoptions[103X) of
  the   group   of   the   process,   which   for   process  [3Xi[103X  is  stored  as
  [10XANUPQData.io[[3Xi[103X[10X].group[110X.[133X
  
  [33X[0;0YThe possible [3Xoptions[103X are the same as for the interactive [10XPq[110X (see [2XPq[102X ([14X5.3-1[114X))
  function,  except  for  [10XRedoPcp[110X  (which, in any case, would be superfluous),
  namely:   [10XPrime[110X,  [10XClassBound[110X,  [10XExponent[110X,  [10XRelators[110X,  [10XGroupName[110X,  [10XMetabelian[110X,
  [10XIdentities[110X  and  [10XOutputLevel[110X  (see  Chapter [14X'[33X[0;0YANUPQ  Options[133X'[114X  for a detailed
  description  for these options). The option [10XPrime[110X is required unless already
  provided to [10XPqStart[110X.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YThe pc presentation is held by the [10Xanu-pq[110X program. In contrast to [10XPq[110X (see [2XPq[102X
  ([14X5.3-1[114X)),  no  [5XGAP[105X  pc group is returned; see [10XPqCurrentGroup[110X ([2XPqCurrentGroup[102X
  ([14X5.5-6[114X)) if you need the corresponding [5XGAP[105X pc group.[133X
  
  [33X[0;0Y[10XPqPcPresentation([3Xi[103X[10X:   [3Xoptions[103X[10X);[110X  is  roughly  equivalent  to  the  following
  sequence of low-level commands:[133X
  
  [4X[32X[104X
    [4XPqPcPresentation(i: opts); #class 1 call[104X
    [4Xfor c in [2 .. class] do[104X
    [4X    PqNextClass(i);[104X
    [4Xod;[104X
  [4X[32X[104X
  
  [33X[0;0Ywhere  [3Xopts[103X is [3Xoptions[103X except with the [10XClassBound[110X option set to 1, and [3Xclass[103X
  is  either  the maximum class of a [3Xp[103X-quotient of the group of the process or
  the  user-supplied value of the option [10XClassBound[110X (whichever is smaller). If
  the  [10XIdentities[110X option has been set, both the first [10XPqPcPresentation[110X class 1
  call  and  the  [10XPqNextClass[110X  calls  invoke [10XPqEvaluateIdentities([3Xi[103X[10X);[110X as their
  final step.[133X
  
  [33X[0;0YFor  those  familiar with the [10Xanu-pq[110X program, [10XPqPcPresentation[110X performs menu
  item 1 of the main [22Xp[122X-Quotient menu.[133X
  
  [1X5.6-2 PqSavePcPresentation[101X
  
  [33X[1;0Y[29X[2XPqSavePcPresentation[102X( [3Xi[103X, [3Xfilename[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSavePcPresentation[102X( [3Xfilename[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  save  the  pc  presentation  previously computed for the quotient of the
  group of that process to the file with name [3Xfilename[103X. If the first character
  of  the  string  [3Xfilename[103X  is not [10X/[110X, [3Xfilename[103X is assumed to be the path of a
  writable  file  relative  to the directory in which [5XGAP[105X was started. A saved
  file may be restored by [10XPqRestorePcPresentation[110X (see [2XPqRestorePcPresentation[102X
  ([14X5.6-3[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the  [10Xanu-pq[110X program, [10XPqSavePcPresentation[110X
  performs menu item 2 of the main [22Xp[122X-Quotient menu.[133X
  
  [1X5.6-3 PqRestorePcPresentation[101X
  
  [33X[1;0Y[29X[2XPqRestorePcPresentation[102X( [3Xi[103X, [3Xfilename[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqRestorePcPresentation[102X( [3Xfilename[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to   restore   the   pc   presentation  previously  saved  to  [3Xfilename[103X,  by
  [10XPqSavePcPresentation[110X   (see [2XPqSavePcPresentation[102X   ([14X5.6-2[114X)).  If  the  first
  character  of  the  string  [3Xfilename[103X is not [10X/[110X, [3Xfilename[103X is assumed to be the
  path of a readable file relative to the directory in which [5XGAP[105X was started.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqRestorePcPresentation[110X
  performs menu item 3 of the main [22Xp[122X-Quotient menu.[133X
  
  [1X5.6-4 PqNextClass[101X
  
  [33X[1;0Y[29X[2XPqNextClass[102X( [3Xi:[103X [[3XQueueFactor[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqNextClass[102X( [3X:[103X [[3XQueueFactor[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to calculate the next class of [10XANUPQData.io[[3Xi[103X[10X].group[110X.[133X
  
  [33X[0;0Y[10XPqNextClass[110X  accepts the option [10XQueueFactor[110X (see also [14X6.2[114X) which should be a
  positive  integer  if  automorphisms  have  been previously supplied. If the
  [10Xanu-pq[110X  program  requires a queue factor and none is supplied via the option
  [10XQueueFactor[110X a default of 15 is taken.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YThe single command: [10XPqNextClass([3Xi[103X[10X);[110X is equivalent to executing[133X
  
  [4X[32X[104X
    [4XPqComputePCover(i);[104X
    [4XPqCollectDefiningRelations(i);[104X
    [4XPqDoExponentChecks(i);[104X
    [4XPqEliminateRedundantGenerators(i);[104X
  [4X[32X[104X
  
  [33X[0;0YIf  the [10XIdentities[110X option is set the [10XPqEliminateRedundantGenerators([3Xi[103X[10X);[110X step
  is  essentially  replaced by [10XPqEvaluateIdentities([3Xi[103X[10X);[110X (which invokes its own
  elimination of redundant generators).[133X
  
  [33X[0;0YFor those familiar with the [10Xanu-pq[110X program, [10XPqNextClass[110X performs menu item 6
  of the main [22Xp[122X-Quotient menu.[133X
  
  [1X5.6-5 PqComputePCover[101X
  
  [33X[1;0Y[29X[2XPqComputePCover[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqComputePCover[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X processi, directi, the [10Xanu-pq[110X
  program  to  compute  the  [22Xp[122X-covering  group  of  [10XANUPQData.io[[3Xi[103X[10X].group[110X.  In
  contrast to the function [10XPqPCover[110X (see [2XPqPCover[102X ([14X4.1-3[114X)), this function does
  not return a [5XGAP[105X pc group.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YThe single command: [10XPqComputePCover([3Xi[103X[10X);[110X is equivalent to executing[133X
  
  [4X[32X[104X
    [4XPqSetupTablesForNextClass(i);[104X
    [4XPqTails(i, 0);[104X
    [4XPqDoConsistencyChecks(i, 0, 0);[104X
    [4XPqEliminateRedundantGenerators(i);[104X
  [4X[32X[104X
  
  [33X[0;0YFor  those  familiar  with the [10Xanu-pq[110X program, [10XPqComputePCover[110X performs menu
  item 7 of the main [22Xp[122X-Quotient menu.[133X
  
  
  [1X5.7 [33X[0;0YCommands from the Advanced [22Xp[122X[101X[1X-Quotient menu[133X[101X
  
  [1X5.7-1 PqCollect[101X
  
  [33X[1;0Y[29X[2XPqCollect[102X( [3Xi[103X, [3Xword[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCollect[102X( [3Xword[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X  process, instruct the [10Xanu-pq[110X
  program to do a collection on [3Xword[103X, a word in the current pc generators (the
  form  of  [3Xword[103X required is described below). [10XPqCollect[110X returns the resulting
  word  of  the  collection as a list of generator number, exponent pairs (the
  same form as the second allowed input form of [3Xword[103X; see below).[133X
  
  [33X[0;0YThe argument [3Xword[103X may be input in either of the following ways:[133X
  
  [31X1[131X   [33X[0;6Y[3Xword[103X may be a string, where the [3Xi[103Xth pc generator is represented by [10Xx[3Xi[103X[10X[110X,
        e.g. [10X"x3*x2^2*x1"[110X.  This  way  is  quite  versatile as parentheses and
        left-normed  commutators  -- using square brackets, in the same way as
        [10XPqGAPRelators[110X  (see [2XPqGAPRelators[102X  ([14X3.4-2[114X))  -- are permitted; [3Xword[103X is
        checked for correct syntax via [10XPqParseWord[110X (see [2XPqParseWord[102X ([14X3.4-3[114X)).[133X
  
  [31X2[131X   [33X[0;6YOtherwise,  [3Xword[103X must be a list of generator number, exponent pairs of
        integers,  i.e.  each pair represents a [21Xsyllable[121X so that [10X[ [3, 1], [2,
        2], [1, 1] ][110X represents the same word as that of the example given for
        the first allowed form of [3Xword[103X.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqCollect[110X performs menu
  item 1 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-2 PqSolveEquation[101X
  
  [33X[1;0Y[29X[2XPqSolveEquation[102X( [3Xi[103X, [3Xa[103X, [3Xb[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSolveEquation[102X( [3Xa[103X, [3Xb[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  solve [22X[3Xa[103X * [3Xx[103X = [3Xb[103X[122X for [3Xx[103X, where [3Xa[103X and [3Xb[103X are words in the pc generators. For
  the  representation  of  these  words  see  the  description of the function
  [10XPqCollect[110X ([2XPqCollect[102X ([14X5.7-1[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqSolveEquation[110X performs
  menu item 2 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-3 PqCommutator[101X
  
  [33X[1;0Y[29X[2XPqCommutator[102X( [3Xi[103X, [3Xwords[103X, [3Xpow[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCommutator[102X( [3Xwords[103X, [3Xpow[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X  process, instruct the [10Xanu-pq[110X
  program  to compute the left normed commutator of the list [3Xwords[103X of words in
  the  current  pc  generators raised to the integer power [3Xpow[103X, and return the
  resulting  word  as  a  list  of  generator number, exponent pairs. The form
  required  for  each  word of [3Xwords[103X is the same as that required for the [3Xword[103X
  argument  of  [10XPqCollect[110X (see [2XPqCollect[102X ([14X5.7-1[114X)). The form of the output word
  is also the same as for [10XPqCollect[110X.[133X
  
  [33X[0;0Y[13XNote:[113X For those familiar with the [10Xanu-pq[110X program, [10XPqCommutator[110X performs menu
  item 3 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-4 PqSetupTablesForNextClass[101X
  
  [33X[1;0Y[29X[2XPqSetupTablesForNextClass[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSetupTablesForNextClass[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to   set   up   tables   for  the  next  class.  As  as  side-effect,  after
  [10XPqSetupTablesForNextClass([3Xi[103X[10X)[110X  the  value returned by [10XPqPClass([3Xi[103X[10X)[110X will be one
  more than it was previously.[133X
  
  [33X[0;0Y[13XNote:[113X  For those familiar with the [10Xanu-pq[110X program, [10XPqSetupTablesForNextClass[110X
  performs menu item 6 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-5 PqTails[101X
  
  [33X[1;0Y[29X[2XPqTails[102X( [3Xi[103X, [3Xweight[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqTails[102X( [3Xweight[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compute and add tails of weight [3Xweight[103X if [3Xweight[103X is in the integer range
  [10X[2  ..  PqPClass([3Xi[103X[10X)][110X  (assuming  [3Xi[103X is the number of the process, even in the
  default case) or for all weights if [10X[3Xweight[103X[10X = 0[110X.[133X
  
  [33X[0;0YIf  [3Xweight[103X  is  non-zero,  then tails that introduce new generators for only
  weight  [3Xweight[103X  are  computed  and  added,  and in this case and if [10X[3Xweight[103X[10X <
  PqPClass([3Xi[103X[10X)[110X,  it is assumed that the tails that introduce new generators for
  each  weight  from  [10XPqPClass([3Xi[103X[10X)[110X  down to weight [10X[3Xweight[103X[10X + 1[110X have already been
  added.  You  may wish to call [10XPqSetMetabelian[110X (see [2XPqSetMetabelian[102X ([14X5.7-16[114X))
  prior to calling [10XPqTails[110X.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YFor  its  use  in  the  context  of  finding  the next class see [2XPqNextClass[102X
  ([14X5.6-4[114X);    in    particular,    a    call    to   [10XPqSetupTablesForNextClass[110X
  (see [2XPqSetupTablesForNextClass[102X  ([14X5.7-4[114X))  needs  to  have been made prior to
  calling [10XPqTails[110X.[133X
  
  [33X[0;0YThe single command: [10XPqTails([3Xi[103X[10X, [3Xweight[103X[10X);[110X is equivalent to[133X
  
  [4X[32X[104X
    [4XPqComputeTails(i, weight);[104X
    [4XPqAddTails(i, weight);[104X
  [4X[32X[104X
  
  [33X[0;0YFor  those familiar with the [10Xanu-pq[110X program, [10XPqTails[110X uses menu item 7 of the
  Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-6 PqComputeTails[101X
  
  [33X[1;0Y[29X[2XPqComputeTails[102X( [3Xi[103X, [3Xweight[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqComputeTails[102X( [3Xweight[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compute  tails  of weight [3Xweight[103X if [3Xweight[103X is in the integer range [10X[2 ..
  PqPClass([3Xi[103X[10X)][110X  (assuming  [3Xi[103X is the number of the process, even in the default
  case)  or  for  all weights if [10X[3Xweight[103X[10X = 0[110X. See [10XPqTails[110X ([2XPqTails[102X ([14X5.7-5[114X)) for
  more details.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqComputeTails[110X uses menu
  item 7 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-7 PqAddTails[101X
  
  [33X[1;0Y[29X[2XPqAddTails[102X( [3Xi[103X, [3Xweight[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqAddTails[102X( [3Xweight[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  add  the  tails  of weight [3Xweight[103X, previously computed by [10XPqComputeTails[110X
  (see [2XPqComputeTails[102X  ([14X5.7-6[114X)),  if  [3Xweight[103X  is  in  the  integer range [10X[2 ..
  PqPClass([3Xi[103X[10X)][110X  (assuming  [3Xi[103X is the number of the process, even in the default
  case)  or  for  all weights if [10X[3Xweight[103X[10X = 0[110X. See [10XPqTails[110X ([2XPqTails[102X ([14X5.7-5[114X)) for
  more details.[133X
  
  [33X[0;0Y[13XNote:[113X  For those familiar with the [10Xanu-pq[110X program, [10XPqAddTails[110X uses menu item
  7 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-8 PqDoConsistencyChecks[101X
  
  [33X[1;0Y[29X[2XPqDoConsistencyChecks[102X( [3Xi[103X, [3Xweight[103X, [3Xtype[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqDoConsistencyChecks[102X( [3Xweight[103X, [3Xtype[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, do consistency checks for
  weight [3Xweight[103X if [3Xweight[103X is in the integer range [10X[3 .. PqPClass([3Xi[103X[10X)][110X (assuming
  [3Xi[103X  is  the  number of the process) or for all weights if [10X[3Xweight[103X[10X = 0[110X, and for
  type  [3Xtype[103X if [3Xtype[103X is in the range [10X[1, 2, 3][110X (see below) or for all types if
  [10X[3Xtype[103X[10X  =  0[110X.  (For  its  use  in  the  context  of finding the next class see
  [2XPqNextClass[102X ([14X5.6-4[114X).)[133X
  
  [33X[0;0YThe    [13Xtype[113X    of    a    consistency   check   is   defined   as   follows.
  [10XPqDoConsistencyChecks([3Xi[103X[10X,  [3Xweight[103X[10X, [3Xtype[103X[10X)[110X for [3Xweight[103X in [10X[3 .. PqPClass([3Xi[103X[10X)][110X and
  the   given   value   of  [3Xtype[103X  invokes  the  equivalent  of  the  following
  [10XPqDoConsistencyCheck[110X calls (see [2XPqDoConsistencyCheck[102X ([14X5.7-17[114X)):[133X
  
  [8X[10X[3Xtype[103X[8X[10X = 1[110X[8X:[108X
        [33X[0;6Y[10XPqDoConsistencyCheck([3Xi[103X[10X,  [3Xa[103X[10X,  [3Xa[103X[10X,  [3Xa[103X[10X)[110X  checks  [10X2  * PqWeight([3Xi[103X[10X, [3Xa[103X[10X) + 1 =
        [3Xweight[103X[10X[110X, for pc generators of index [3Xa[103X.[133X
  
  [8X[10X[3Xtype[103X[8X[10X = 2[110X[8X:[108X
        [33X[0;6Y[10XPqDoConsistencyCheck([3Xi[103X[10X,  [3Xb[103X[10X,  [3Xb[103X[10X, [3Xa[103X[10X)[110X checks for pc generators of indices
        [3Xb[103X,  [3Xa[103X satisfyingx both [10X[3Xb[103X[10X > [3Xa[103X[10X[110X and [10XPqWeight([3Xi[103X[10X, [3Xb[103X[10X) + PqWeight([3Xi[103X[10X, [3Xa[103X[10X) + 1 =
        [3Xweight[103X[10X[110X.[133X
  
  [8X[10X[3Xtype[103X[8X[10X = 3[110X[8X:[108X
        [33X[0;6Y[10XPqDoConsistencyCheck([3Xi[103X[10X,  [3Xc[103X[10X,  [3Xb[103X[10X, [3Xa[103X[10X)[110X checks for pc generators of indices
        [3Xc[103X,  [3Xb[103X,  [3Xa[103X  satisfying  [10X[3Xc[103X[10X  >  [3Xb[103X[10X > [3Xa[103X[10X[110X and the sum of the weights of these
        generators equals [3Xweight[103X.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0Y[10XPqWeight([3Xi[103X[10X,  [3Xj[103X[10X)[110X  returns  the  weight of the [3Xj[103Xth pc generator, for process [3Xi[103X
  (see [2XPqWeight[102X ([14X5.5-5[114X)).[133X
  
  [33X[0;0YIt is assumed that tails for the given weight (or weights) have already been
  added (see [2XPqTails[102X ([14X5.7-5[114X)).[133X
  
  [33X[0;0YFor  those  familiar with the [10Xanu-pq[110X program, [10XPqDoConsistencyChecks[110X performs
  menu item 8 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-9 PqCollectDefiningRelations[101X
  
  [33X[1;0Y[29X[2XPqCollectDefiningRelations[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCollectDefiningRelations[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  collect the images of the defining relations of the original fp group of
  the  process, with respect to the current pc presentation, in the context of
  finding  the next class (see [2XPqNextClass[102X ([14X5.6-4[114X)). If the tails operation is
  not complete then the relations may be evaluated incorrectly.[133X
  
  [33X[0;0Y[13XNote:[113X For those familiar with the [10Xanu-pq[110X program, [10XPqCollectDefiningRelations[110X
  performs menu item 9 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-10 PqCollectWordInDefiningGenerators[101X
  
  [33X[1;0Y[29X[2XPqCollectWordInDefiningGenerators[102X( [3Xi[103X, [3Xword[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCollectWordInDefiningGenerators[102X( [3Xword[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth or default interactive [5XANUPQ[105X process, take a user-defined word
  [3Xword[103X in the defining generators of the original presentation of the fp or pc
  group  of  the  process.  Each  generator  is  mapped  into  the  current pc
  presentation,  and  the  resulting  word  is  collected  with respect to the
  current  pc presentation. The result of the collection is returned as a list
  of generator number, exponent pairs.[133X
  
  [33X[0;0YThe  [3Xword[103X  argument  may  be  input  in either of the two ways described for
  [10XPqCollect[110X (see [2XPqCollect[102X ([14X5.7-1[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X     For     those     familiar     with     the     [10Xanu-pq[110X    program,
  [10XPqCollectDefiningGenerators[110X performs menu item 23 of the Advanced [22Xp[122X-Quotient
  menu.[133X
  
  [1X5.7-11 PqCommutatorDefiningGenerators[101X
  
  [33X[1;0Y[29X[2XPqCommutatorDefiningGenerators[102X( [3Xi[103X, [3Xwords[103X, [3Xpow[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCommutatorDefiningGenerators[102X( [3Xwords[103X, [3Xpow[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X process, take a list [3Xwords[103X of
  user-defined  words  in the defining generators of the original presentation
  of  the  fp  or  pc  group  of  the  process, and an integer power [3Xpow[103X. Each
  generator  is  mapped  into  the  current pc presentation. The list [3Xwords[103X is
  interpreted  as  a  left-normed  commutator  which is then raised to [3Xpow[103X and
  collected  with  respect  to  the current pc presentation. The result of the
  collection is returned as a list of generator number, exponent pairs.[133X
  
  [33X[0;0Y[13XNote[113X     For     those     familiar     with     the     [10Xanu-pq[110X     program,
  [10XPqCommutatorDefiningGenerators[110X   performs  menu  item  24  of  the  Advanced
  [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-12 PqDoExponentChecks[101X
  
  [33X[1;0Y[29X[2XPqDoExponentChecks[102X( [3Xi:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqDoExponentChecks[102X( [3X:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to do exponent checks for weights (inclusively) between the bounds of [10XBounds[110X
  or  for  all  weights  if  [10XBounds[110X  is  not  given.  The value [3Xlist[103X of [10XBounds[110X
  (assuming  the  interactive  process  is numbered [3Xi[103X) should be a list of two
  integers  [3Xlow[103X,  [3Xhigh[103X  satisfying  [22X1 ≤ [3Xlow[103X ≤ [3Xhigh[103X ≤[122X [10XPqPClass([3Xi[103X[10X)[110X (see [2XPqPClass[102X
  ([14X5.5-4[114X)).  If  no  exponent  law  has been specified, no exponent checks are
  performed.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the  [10Xanu-pq[110X  program,  [10XPqDoExponentChecks[110X
  performs menu item 10 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-13 PqEliminateRedundantGenerators[101X
  
  [33X[1;0Y[29X[2XPqEliminateRedundantGenerators[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqEliminateRedundantGenerators[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to eliminate redundant generators of the current [22Xp[122X-quotient.[133X
  
  [33X[0;0Y[13XNote:[113X     For     those     familiar     with     the     [10Xanu-pq[110X    program,
  [10XPqEliminateRedundantGenerators[110X   performs  menu  item  11  of  the  Advanced
  [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-14 PqRevertToPreviousClass[101X
  
  [33X[1;0Y[29X[2XPqRevertToPreviousClass[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqRevertToPreviousClass[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to abandon the current class and revert to the previous class.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqRevertToPreviousClass[110X
  performs menu item 12 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-15 PqSetMaximalOccurrences[101X
  
  [33X[1;0Y[29X[2XPqSetMaximalOccurrences[102X( [3Xi[103X, [3Xnoccur[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSetMaximalOccurrences[102X( [3Xnoccur[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  set maximal occurrences of the weight 1 generators in the definitions of
  pcp  generators  of  the group of the process. This can be used to avoid the
  definition  of  generators  of  which one knows for theoretical reasons that
  they would be eliminated later on.[133X
  
  [33X[0;0YThe  argument  [3Xnoccur[103X  must be a list of non-negative integers of length the
  number  of  weight  1 generators (i.e. the rank of the class 1 [22Xp[122X-quotient of
  the  group  of  the  process).  An  entry  of  [10X0[110X  for a particular generator
  indicates  that  there  is  no  limit  on  the number of occurrences for the
  generator.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqSetMaximalOccurrences[110X
  performs menu item 13 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-16 PqSetMetabelian[101X
  
  [33X[1;0Y[29X[2XPqSetMetabelian[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSetMetabelian[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to enforce metabelian-ness.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqSetMetabelian[110X performs
  menu item 14 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-17 PqDoConsistencyCheck[101X
  
  [33X[1;0Y[29X[2XPqDoConsistencyCheck[102X( [3Xi[103X, [3Xc[103X, [3Xb[103X, [3Xa[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqDoConsistencyCheck[102X( [3Xc[103X, [3Xb[103X, [3Xa[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqJacobi[102X( [3Xi[103X, [3Xc[103X, [3Xb[103X, [3Xa[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqJacobi[102X( [3Xc[103X, [3Xb[103X, [3Xa[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to do the consistency check for the pc generators with indices [3Xc[103X, [3Xb[103X, [3Xa[103X which
  should be non-increasing positive integers, i.e. [22X[3Xc[103X ≥ [3Xb[103X ≥ [3Xa[103X[122X.[133X
  
  [33X[0;0YThere are 3 types of consistency checks:[133X
  
  
  [24X[33X[0;6Y\begin{array}{rclrl}  (a^n)a  &=&  a(a^n)  &&  {\rm (Type\ 1)} \\ (b^n)a &=&
  b^{(n-1)}(ba),  b(a^n) = (ba)a^{(n-1)} && {\rm (Type\ 2)} \\ c(ba) &=& (cb)a
  && {\rm (Type\ 3)} \\ \end{array}[133X
  
  [124X
  
  [33X[0;0YThe  reason  some  people talk about Jacobi relations instead of consistency
  checks becomes clear when one looks at the consistency check of type 3:[133X
  
  
  [24X[33X[0;6Y\begin{array}{rcl} c(ba) &=& a c[c,a] b[b,a] = acb [c,a][c,a,b][b,a] = \dots
  \\  (cb)a  &=&  b  c[c,b]  a = a b[b,a] c[c,a] [c,b][c,b,a] \\ &=& abc [b,a]
  [b,a,c] [c,a] [c,b] [c,b,a] = \dots \\ \end{array}[133X
  
  [124X
  
  [33X[0;0YEach  collection  would  normally  carry on further. But one can see already
  that  no other commutators of weight 3 will occur. After all terms of weight
  one and weight two have been moved to the left we end up with:[133X
  
  
  [24X[33X[0;6Y\begin{array}{rcl}  &  &abc  [b,a] [c,a] [c,b] [c,a,b] \dots \\ &=&abc [b,a]
  [c,a] [c,b] [c,b,a] [b,a,c] \dots \\ \end{array}[133X
  
  [124X
  
  [33X[0;0YModulo terms of weight 4 this is equivalent to[133X
  
  
  [24X[33X[0;6Y[c,a,b] [b,c,a] [a,b,c] = 1[133X
  
  [124X
  
  [33X[0;0Ywhich is the Jacobi identity.[133X
  
  [33X[0;0YSee also [10XPqDoConsistencyChecks[110X ([2XPqDoConsistencyChecks[102X ([14X5.7-8[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqDoConsistencyCheck[110X and
  [10XPqJacobi[110X perform menu item 15 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-18 PqCompact[101X
  
  [33X[1;0Y[29X[2XPqCompact[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqCompact[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  do a compaction of its work space. This function is safe to perform only
  at certain points in time.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqCompact[110X performs menu
  item 16 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-19 PqEchelonise[101X
  
  [33X[1;0Y[29X[2XPqEchelonise[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqEchelonise[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  echelonise the word most recently collected by [10XPqCollect[110X or [10XPqCommutator[110X
  against  the relations of the current pc presentation, and return the number
  of  the generator made redundant or [9Xfail[109X if no generator was made redundant.
  A    call    to    [10XPqCollect[110X   (see [2XPqCollect[102X   ([14X5.7-1[114X))   or   [10XPqCommutator[110X
  (see [2XPqCommutator[102X  ([14X5.7-3[114X))  needs  to  be  performed  prior  to  using this
  command.[133X
  
  [33X[0;0Y[13XNote:[113X For those familiar with the [10Xanu-pq[110X program, [10XPqEchelonise[110X performs menu
  item 17 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-20 PqSupplyAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqSupplyAutomorphisms[102X( [3Xi[103X, [3Xmlist[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSupplyAutomorphisms[102X( [3Xmlist[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or default interactive [5XANUPQ[105X process, supply the automorphism
  data  provided  by  the  list  [3Xmlist[103X  of  matrices with non-negative integer
  coefficients.  Each  matrix  in  [3Xmlist[103X  describes  one  automorphism  in the
  following way.[133X
  
  [30X    [33X[0;6YThe rows of each matrix correspond to the pc generators of weight one.[133X
  
  [30X    [33X[0;6YEach  row  is  the  exponent  vector of the image of the corresponding
        weight one generator under the respective automorphism.[133X
  
  [33X[0;0Y[13XNote:[113X For those familiar with the [10Xanu-pq[110X program, [10XPqSupplyAutomorphisms[110X uses
  menu item 18 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-21 PqExtendAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqExtendAutomorphisms[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqExtendAutomorphisms[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  extend  automorphisms  of  the  [22Xp[122X-quotient  of the previous class to the
  [22Xp[122X-quotient of the present class.[133X
  
  [33X[0;0Y[13XNote:[113X For those familiar with the [10Xanu-pq[110X program, [10XPqExtendAutomorphisms[110X uses
  menu item 18 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-22 PqApplyAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqApplyAutomorphisms[102X( [3Xi[103X, [3Xqfac[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqApplyAutomorphisms[102X( [3Xqfac[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to apply automorphisms; [3Xqfac[103X is the queue factor e.g. [10X15[110X.[133X
  
  [33X[0;0Y[13XNote:[113X  For those familiar with the [10Xanu-pq[110X program, [10XPqCloseRelations[110X performs
  menu item 19 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-23 PqDisplayStructure[101X
  
  [33X[1;0Y[29X[2XPqDisplayStructure[102X( [3Xi:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqDisplayStructure[102X( [3X:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  display  the  structure  for  the  pcp generators numbered (inclusively)
  between  the  bounds of [10XBounds[110X or for all generators if [10XBounds[110X is not given.
  The  value  [3Xlist[103X  of [10XBounds[110X (assuming the interactive process is numbered [3Xi[103X)
  should  be  a  list  of  two  integers [3Xlow[103X, [3Xhigh[103X satisfying [22X1 ≤ [3Xlow[103X ≤ [3Xhigh[103X ≤[122X
  [10XPqNrPcGenerators([3Xi[103X[10X)[110X  (see [2XPqNrPcGenerators[102X ([14X5.5-1[114X)). [10XPqDisplayStructure[110X also
  accepts the option [10XOutputLevel[110X (see [14X6.2[114X).[133X
  
  [33X[0;0Y[13XExplanation of output[113X[133X
  
  [33X[0;0YNew  generators  are  defined  as  commutators  of  previous  generators and
  generators  of  class 1 or as [22Xp[122X-th powers of generators that have themselves
  been defined as [22Xp[122X-th powers. A generator is never defined as [22Xp[122X-th power of a
  commutator.[133X
  
  [33X[0;0YTherefore,  there  are  two cases: all the numbers on the righthand side are
  either  the  same  or  they  differ.  Below,  [10Xg[3Xi[103X[10X[110X  refers to the [3Xi[103Xth defining
  generator.[133X
  
  [30X    [33X[0;6YIf  the righthand side numbers are all the same, then the generator is
        a  [22Xp[122X-th  power  (of a [22Xp[122X-th power of a [22Xp[122X-th power, etc.). The number of
        repeated digits say how often a [22Xp[122X-th power has to be taken.[133X
  
        [33X[0;6YIn  the  following  example,  the  generator number 31 is the eleventh
        power of generator 17 which in turn is an eleventh power and so on:[133X
  
        [33X[0;6Y\begintt  #I 31 is defined on 17^11 = 1 1 1 1 1 \endtt So generator 31
        is obtained by taking the eleventh power of generator 1 five times.[133X
  
  [30X    [33X[0;6YIf  the  numbers  are  not all the same, the generator is defined by a
        commutator.  If  the first two generator numbers differ, the generator
        is  defined  as a left-normed commutator of the weight one generators,
        e.g.[133X
  
        [33X[0;6Y\begintt  #I  19  is  defined  on  [11,  1]  =  2 1 1 1 1 \endtt Here,
        generator  19  is  defined  as  the  commutator  of  generator  11 and
        generator  1  which is the same as the left-normed commutator [10X[x2, x1,
        x1,  x1,  x1][110X.  One  can  check this by tracing back the definition of
        generator 11 until one gets to a generator of class 1.[133X
  
  [30X    [33X[0;6YIf  the  first two generator numbers are identical, then the left most
        component of the left-normed commutator is a [22Xp[122X-th power, e.g.[133X
  
        [33X[0;6Y\begintt #I 25 is defined on [14, 1] = 1 1 2 1 1 \endtt[133X
  
        [33X[0;6YIn this example, generator 25 is defined as commutator of generator 14
        and generator 1. The left-normed commutator is[133X
  
  
  [24X      [33X[0;6Y[(x1^{11})^{11}, x2, x1, x1][133X
  
  [124X
  
        [33X[0;6YAgain, this can be verified by tracing back the definitions.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the  [10Xanu-pq[110X  program,  [10XPqDisplayStructure[110X
  performs menu item 20 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-24 PqDisplayAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqDisplayAutomorphisms[102X( [3Xi:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqDisplayAutomorphisms[102X( [3X:[103X [[3XBounds[103X [3X:=[103X [3Xlist[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to   display  the  automorphism  actions  on  the  pcp  generators  numbered
  (inclusively)  between  the bounds of [10XBounds[110X or for all generators if [10XBounds[110X
  is  not given. The value [3Xlist[103X of [10XBounds[110X (assuming the interactive process is
  numbered  [3Xi[103X) should be a list of two integers [3Xlow[103X, [3Xhigh[103X satisfying [22X1 ≤ [3Xlow[103X ≤
  [3Xhigh[103X      ≤[122X      [10XPqNrPcGenerators([3Xi[103X[10X)[110X     (see [2XPqNrPcGenerators[102X     ([14X5.5-1[114X)).
  [10XPqDisplayStructure[110X also accepts the option [10XOutputLevel[110X (see [14X6.2[114X).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with the [10Xanu-pq[110X program, [10XPqDisplayAutomorphisms[110X
  performs menu item 21 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  [1X5.7-25 PqWritePcPresentation[101X
  
  [33X[1;0Y[29X[2XPqWritePcPresentation[102X( [3Xi[103X, [3Xfilename[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqWritePcPresentation[102X( [3Xfilename[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to write a pc presentation of a previously-computed quotient of the group of
  that process, to the file with name [3Xfilename[103X. Here the group of a process is
  the  one  given  as  first argument when [10XPqStart[110X was called to initiate that
  process (for process [3Xi[103X the group is stored as [10XANUPQData.io[[3Xi[103X[10X].group[110X). If the
  first  character  of the string [3Xfilename[103X is not [10X/[110X, [3Xfilename[103X is assumed to be
  the  path  of  a  writable  file  relative to the directory in which [5XGAP[105X was
  started. If a pc presentation has not been previously computed by the [10Xanu-pq[110X
  program,  then  [10Xanu-pq[110X  is  called to compute it first, effectively invoking
  [10XPqPcPresentation[110X (see [2XPqPcPresentation[102X ([14X5.6-1[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the [10Xanu-pq[110X program, [10XPqPcWritePresentation[110X
  performs menu item 25 of the Advanced [22Xp[122X-Quotient menu.[133X
  
  
  [1X5.8 [33X[0;0YCommands from the Standard Presentation menu[133X[101X
  
  [1X5.8-1 PqSPComputePcpAndPCover[101X
  
  [33X[1;0Y[29X[2XPqSPComputePcpAndPCover[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSPComputePcpAndPCover[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor the [3Xi[103Xth or default interactive [5XANUPQ[105X process, directs the [10Xanu-pq[110X program
  to  compute  for  the  group  of  that  process  a pc presentation up to the
  [22Xp[122X-quotient  of  maximum  class or the value of the option [10XClassBound[110X and the
  [22Xp[122X-cover  of  that  quotient,  and  sets  up tabular information required for
  computation  of  a standard presentation. Here the group of a process is the
  one given as first argument when [10XPqStart[110X was called to initiate that process
  (for process [3Xi[103X the group is stored as [10XANUPQData.io[[3Xi[103X[10X].group[110X).[133X
  
  [33X[0;0YThe  possible  [3Xoptions[103X are [10XPrime[110X, [10XClassBound[110X, [10XRelators[110X, [10XExponent[110X, [10XMetabelian[110X
  and  [10XOutputLevel[110X  (see  Chapter [14X'[33X[0;0YANUPQ Options[133X'[114X for detailed descriptions of
  these options). The option [10XPrime[110X is normally determined via [10XPrimePGroup[110X, and
  so  is  not  required  unless  the  group  doesn't  know  it's a [22Xp[122X-group and
  [10XHasPrimePGroup[110X returns [9Xfalse[109X.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqSPComputePcpAndPCover[110X
  performs option 1 of the Standard Presentation menu.[133X
  
  [1X5.8-2 PqSPStandardPresentation[101X
  
  [33X[1;0Y[29X[2XPqSPStandardPresentation[102X( [3Xi[103X[, [3Xmlist[103X][3X:[103X [[3Xoptions[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqSPStandardPresentation[102X( [[3Xmlist[103X][3X:[103X [[3Xoptions[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X process, inputs data given by
  [3Xoptions[103X to compute a standard presentation for the group of that process. If
  argument  [3Xmlist[103X  is  given  it  is assumed to be the automorphism group data
  required.  Otherwise it is assumed that a call to either [10XPq[110X (see [2XPq[102X ([14X5.3-1[114X))
  or  [10XPqEpimorphism[110X (see [2XPqEpimorphism[102X ([14X5.3-2[114X)) has generated a [22Xp[122X-quotient and
  that  [5XGAP[105X  can  compute  its  automorphism  group  from  which the necessary
  automorphism  group data can be derived. The group of the process is the one
  given as first argument when [10XPqStart[110X was called to initiate the process (for
  process [3Xi[103X the group is stored as [10XANUPQData.io[[3Xi[103X[10X].group[110X and the [22Xp[122X-quotient if
  existent  is stored as [10XANUPQData.io[[3Xi[103X[10X].pQuotient[110X). If [3Xmlist[103X is not given and
  a  [22Xp[122X-quotient  of  the  group  has  not  been  previously computed a class 1
  [22Xp[122X-quotient is computed.[133X
  
  [33X[0;0Y[10XPqSPStandardPresentation[110X accepts three options, all optional:[133X
  
  [30X    [33X[0;6Y[10XClassBound := [3Xn[103X[10X[110X[133X
  
  [30X    [33X[0;6Y[10XPcgsAutomorphisms[110X[133X
  
  [30X    [33X[0;6Y[10XStandardPresentationFile := [3Xfilename[103X[10X[110X[133X
  
  [33X[0;0YIf [10XClassBound[110X is omitted it defaults to 63.[133X
  
  [33X[0;0YDetailed  descriptions  of  the above options may be found in Chapter [14X'[33X[0;0YANUPQ
  Options[133X'[114X.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the  [10Xanu-pq[110X  program,  [10XPqSPPcPresentation[110X
  performs menu item 2 of the Standard Presentation menu.[133X
  
  [1X5.8-3 PqSPSavePresentation[101X
  
  [33X[1;0Y[29X[2XPqSPSavePresentation[102X( [3Xi[103X, [3Xfilename[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSPSavePresentation[102X( [3Xfilename[103X ) [32X function[133X
  
  [33X[0;0Yfor the [3Xi[103Xth or default interactive [5XANUPQ[105X process, directs the [10Xanu-pq[110X program
  to  save the standard presentation previously computed for the group of that
  process  to the file with name [3Xfilename[103X, where the group of a process is the
  one  given  as  first  argument  when  [10XPqStart[110X  was  called to initiate that
  process. If the first character of the string [3Xfilename[103X is not [10X/[110X, [3Xfilename[103X is
  assumed to be the path of a writable file relative to the directory in which
  [5XGAP[105X was started.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar  with  the  [10Xanu-pq[110X program, [10XPqSPSavePresentation[110X
  performs menu item 3 of the Standard Presentation menu.[133X
  
  [1X5.8-4 PqSPCompareTwoFilePresentations[101X
  
  [33X[1;0Y[29X[2XPqSPCompareTwoFilePresentations[102X( [3Xi[103X, [3Xf1[103X, [3Xf2[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSPCompareTwoFilePresentations[102X( [3Xf1[103X, [3Xf2[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compare  the presentations in the files with names [3Xf1[103X and [3Xf2[103X and returns
  [9Xtrue[109X  if  they are identical and [9Xfalse[109X otherwise. For each of the strings [3Xf1[103X
  and  [3Xf2[103X, if the first character is not a [10X/[110X then it is assumed to be the path
  of a readable file relative to the directory in which [5XGAP[105X was started.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YThe  presentations in files [3Xf1[103X and [3Xf2[103X must have been generated by the [10Xanu-pq[110X
  program  but  they  do  [13Xnot[113X  need  to  be  [13Xstandard[113X presentations. If If the
  presentations    in    files    [3Xf1[103X   and   [3Xf2[103X   [13Xhave[113X   been   generated   by
  [10XPqSPStandardPresentation[110X (see [2XPqSPStandardPresentation[102X ([14X5.8-2[114X)) then a [9Xfalse[109X
  response  from  [10XPqSPCompareTwoFilePresentations[110X  says  the groups defined by
  those presentations are [13Xnot[113X isomorphic.[133X
  
  [33X[0;0YFor  those familiar with the [10Xanu-pq[110X program, [10XPqSPCompareTwoFilePresentations[110X
  performs menu item 6 of the Standard Presentation menu.[133X
  
  [1X5.8-5 PqSPIsomorphism[101X
  
  [33X[1;0Y[29X[2XPqSPIsomorphism[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqSPIsomorphism[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compute  the  isomorphism mapping from the [22Xp[122X-group of the process to its
  standard  presentation. This function provides a description only; for a [5XGAP[105X
  object,                  use                 [10XEpimorphismStandardPresentation[110X
  (see [2XEpimorphismStandardPresentation[102X ([14X5.3-5[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqSPIsomorphism[110X performs
  menu item 8 of the Standard Presentation menu.[133X
  
  
  [1X5.9 [33X[0;0YCommands from the Main [22Xp[122X[101X[1X-Group Generation menu[133X[101X
  
  [33X[0;0YNote  that  the  [22Xp[122X-group  generation  commands  can only be applied once the
  [10Xanu-pq[110X  program has produced a pc presentation of some quotient group of the
  [21Xgroup of the process[121X.[133X
  
  [1X5.9-1 PqPGSupplyAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqPGSupplyAutomorphisms[102X( [3Xi[103X[, [3Xmlist[103X][3X:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGSupplyAutomorphisms[102X( [[3Xmlist[103X][3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, supply the [10Xanu-pq[110X program
  with  the  automorphism  group  data  needed for the current quotient of the
  group   of   that   process   (for   process   [3Xi[103X  the  group  is  stored  as
  [10XANUPQData.io[[3Xi[103X[10X].group[110X).   For   a   description   of  the  format  of  [3Xmlist[103X
  see [2XPqSupplyAutomorphisms[102X     ([14X5.7-20[114X).    The    options    possible    are
  [10XNumberOfSolubleAutomorphisms[110X  and  [10XRelativeOrders[110X. (Detailed descriptions of
  these options may be found in Chapter [14X'[33X[0;0YANUPQ Options[133X'[114X.)[133X
  
  [33X[0;0YIf  [3Xmlist[103X  is omitted, the automorphism data is determined from the group of
  the process which must have been a [22Xp[122X-group in pc presentation.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqPGSupplyAutomorphisms[110X
  performs menu item 1 of the main [22Xp[122X-Group Generation menu.[133X
  
  [1X5.9-2 PqPGExtendAutomorphisms[101X
  
  [33X[1;0Y[29X[2XPqPGExtendAutomorphisms[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGExtendAutomorphisms[102X(  ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  compute  the  extensions  of  the automorphisms of the [22Xp[122X-quotient of the
  previous  class  to the [22Xp[122X-quotient of the current class. You may wish to set
  the  [10XInfoLevel[110X  of  [10XInfoANUPQ[110X to 2 (or more) in order to see the output from
  the [10Xanu-pq[110X program (see [2XInfoANUPQ[102X ([14X3.3-1[114X)).[133X
  
  [33X[0;0Y[13XNote:[113X  For  those  familiar with the [10Xanu-pq[110X program, [10XPqPGExtendAutomorphisms[110X
  performs menu item 2 of the main or advanced [22Xp[122X-Group Generation menu.[133X
  
  [1X5.9-3 PqPGConstructDescendants[101X
  
  [33X[1;0Y[29X[2XPqPGConstructDescendants[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGConstructDescendants[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  construct  descendants  prescribed  by [3Xoptions[103X, and return the number of
  descendants   constructed   (compare  function [2XPqDescendants[102X  ([14X4.4-1[114X)  which
  returns  the  list  of  descendants).  The  options possible are [10XClassBound[110X,
  [10XOrderBound[110X,    [10XStepSize[110X,   [10XPcgsAutomorphisms[110X,   [10XRankInitialSegmentSubgroups[110X,
  [10XSpaceEfficient[110X,  [10XCapableDescendants[110X,  [10XAllDescendants[110X,  [10XExponent[110X, [10XMetabelian[110X,
  [10XBasicAlgorithm[110X, [10XCustomiseOutput[110X. (Detailed descriptions of these options may
  be found in Chapter [14X'[33X[0;0YANUPQ Options[133X'[114X.)[133X
  
  [33X[0;0Y[10XPqPGConstructDescendants[110X  requires  that  the  [10Xanu-pq[110X program has previously
  computed  a  pc presentation and a [22Xp[122X-cover for a [22Xp[122X-quotient of some class of
  the group of the process.[133X
  
  [33X[0;0Y[13XNote:[113X  For  those familiar with the [10Xanu-pq[110X program, [10XPqPGConstructDescendants[110X
  performs menu item 5 of the main [22Xp[122X-Group Generation menu.[133X
  
  [1X5.9-4 PqPGSetDescendantToPcp[101X
  
  [33X[1;0Y[29X[2XPqPGSetDescendantToPcp[102X( [3Xi[103X, [3Xcls[103X, [3Xn[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGSetDescendantToPcp[102X( [3Xcls[103X, [3Xn[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGSetDescendantToPcp[102X( [3Xi:[103X [[3XFilename[103X [3X:=[103X [3Xname[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGSetDescendantToPcp[102X( [3X:[103X [[3XFilename[103X [3X:=[103X [3Xname[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGRestoreDescendantFromFile[102X( [3Xi[103X, [3Xcls[103X, [3Xn[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGRestoreDescendantFromFile[102X( [3Xcls[103X, [3Xn[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGRestoreDescendantFromFile[102X( [3Xi:[103X [[3XFilename[103X [3X:=[103X [3Xname[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqPGRestoreDescendantFromFile[102X( [3X:[103X [[3XFilename[103X [3X:=[103X [3Xname[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  restore  group [3Xn[103X of class [3Xcls[103X from a temporary file, where [3Xcls[103X and [3Xn[103X are
  positive  integers,  or the group stored in [3Xname[103X. [10XPqPGSetDescendantToPcp[110X and
  [10XPqPGRestoreDescendantFromFile[110X  are  synonyms;  they  make sense only after a
  prior   call   to  construct  descendants  by  say  [10XPqPGConstructDescendants[110X
  (see [2XPqPGConstructDescendants[102X  ([14X5.9-3[114X))  or  the  interactive  [10XPqDescendants[110X
  (see [2XPqDescendants[102X  ([14X5.3-6[114X)).  In  the  [10XFilename[110X  option  forms,  the option
  defaults  to  the  last  filename  in which a presentation was stored by the
  [10Xanu-pq[110X program.[133X
  
  [33X[0;0Y[13XNotes[113X[133X
  
  [33X[0;0YSince   the  [10XPqPGSetDescendantToPcp[110X  and  [10XPqPGRestoreDescendantFromFile[110X  are
  intended to be used in calculation of further descendants the [10Xanu-pq[110X program
  computes  the [22Xp[122X-cover of the restored descendant. Hence, [10XPqCurrentGroup[110X used
  immediately  after one of these commands returns the [22Xp[122X-cover of the restored
  descendant rather than the descendant itself.[133X
  
  [33X[0;0YFor  those  familiar  with  the  [10Xanu-pq[110X  program, [10XPqPGSetDescendantToPcp[110X and
  [10XPqPGRestoreDescendantFromFile[110X  perform  menu  item 3 of the main or advanced
  [22Xp[122X-Group Generation menu.[133X
  
  
  [1X5.10 [33X[0;0YCommands from the Advanced [22Xp[122X[101X[1X-Group Generation menu[133X[101X
  
  [33X[0;0YThe    functions    below    perform    the    component    algorithms    of
  [10XPqPGConstructDescendants[110X (see [2XPqPGConstructDescendants[102X ([14X5.9-3[114X)). You can get
  some idea of their usage by trying [10XPqExample("Nott-APG-Rel-i");[110X. You can get
  some  idea of the breakdown of [10XPqPGConstructDescendants[110X into these functions
  by comparing the previous output with [10XPqExample("Nott-PG-Rel-i");[110X.[133X
  
  [33X[0;0YThese  functions  are  intended  for use only by [21Xexperts[121X; please contact the
  authors  of  the  package if you genuinely have a need for them and need any
  amplified descriptions.[133X
  
  [1X5.10-1 PqAPGDegree[101X
  
  [33X[1;0Y[29X[2XPqAPGDegree[102X( [3Xi[103X, [3Xstep[103X, [3Xrank:[103X [[3XExponent[103X [3X:=[103X [3Xn[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XPqAPGDegree[102X( [3Xstep[103X, [3Xrank:[103X [[3XExponent[103X [3X:=[103X [3Xn[103X] ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  invoke  menu  item  6  of the Advanced [22Xp[122X-Group Generation menu. Here the
  step-size [3Xstep[103X and the rank [3Xrank[103X are positive integers and are the arguments
  required  by  the  [10Xanu-pq[110X  program.  See [14X6.2[114X  for  the one recognised option
  [10XExponent[110X.[133X
  
  [1X5.10-2 PqAPGPermutations[101X
  
  [33X[1;0Y[29X[2XPqAPGPermutations[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqAPGPermutations[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the [3Xi[103Xth or default interactive [5XANUPQ[105X process, direct the [10Xanu-pq[110X program
  to  perform  menu  item  7 of the Advanced [22Xp[122X-Group Generation menu. Here the
  options    [3Xoptions[103X   recognised   are   [10XPcgsAutomorphisms[110X,   [10XSpaceEfficient[110X,
  [10XPrintAutomorphisms[110X  and  [10XPrintPermutations[110X  (see Chapter [14X'[33X[0;0YANUPQ Options[133X'[114X for
  details).[133X
  
  [1X5.10-3 PqAPGOrbits[101X
  
  [33X[1;0Y[29X[2XPqAPGOrbits[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqAPGOrbits[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X process, direct the [10Xanu-pq[110X to
  perform menu item 8 of the Advanced [22Xp[122X-Group Generation menu.[133X
  
  [33X[0;0YHere  the  options  [3Xoptions[103X recognised are [10XPcgsAutomorphisms[110X, [10XSpaceEfficient[110X
  and  [10XCustomiseOutput[110X  (see  Chapter [14X'[33X[0;0YANUPQ  Options[133X'[114X  for  details). For the
  [10XCustomiseOutput[110X  option  only  the  setting  of the [10Xorbit[110X is recognised (all
  other fields if set are ignored).[133X
  
  [1X5.10-4 PqAPGOrbitRepresentatives[101X
  
  [33X[1;0Y[29X[2XPqAPGOrbitRepresentatives[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqAPGOrbitRepresentatives[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X process, direct the [10Xanu-pq[110X to
  perform item 9 of the Advanced [22Xp[122X-Group Generation menu.[133X
  
  [33X[0;0YThe   options   [3Xoptions[103X   may   be   any   selection   of   the   following:
  [10XPcgsAutomorphisms[110X,  [10XSpaceEfficient[110X, [10XExponent[110X, [10XMetabelian[110X, [10XCapableDescendants[110X
  (or  [10XAllDescendants[110X),  [10XCustomiseOutput[110X  (where  only  the [10Xgroup[110X and [10Xautgroup[110X
  fields  are  recognised)  and  [10XFilename[110X  (see  Chapter [14X'[33X[0;0YANUPQ  Options[133X'[114X  for
  details).  If [10XFilename[110X is omitted the reduced [22Xp[122X-cover is written to the file
  [10X"redPCover"[110X   in   the   temporary   directory   whose  name  is  stored  in
  [10XANUPQData.tmpdir[110X.[133X
  
  [1X5.10-5 PqAPGSingleStage[101X
  
  [33X[1;0Y[29X[2XPqAPGSingleStage[102X( [3Xi:[103X [3Xoptions[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqAPGSingleStage[102X( [3X:[103X [3Xoptions[103X ) [32X function[133X
  
  [33X[0;0Yfor  the  [3Xi[103Xth  or  default  interactive  [5XANUPQ[105X process, direct the [10Xanu-pq[110X to
  perform option 5 of the Advanced [22Xp[122X-Group Generation menu.[133X
  
  [33X[0;0YThe      possible      options      are     [10XStepSize[110X,     [10XPcgsAutomorphisms[110X,
  [10XRankInitialSegmentSubgroups[110X,       [10XSpaceEfficient[110X,       [10XCapableDescendants[110X,
  [10XAllDescendants[110X,  [10XExponent[110X,  [10XMetabelian[110X,  [10XBasicAlgorithm[110X and [10XCustomiseOutput[110X.
  (Detailed  descriptions  of  these  options  may  be found in Chapter [14X'[33X[0;0YANUPQ
  Options[133X'[114X.)[133X
  
  
  [1X5.11 [33X[0;0YPrimitive Interactive ANUPQ Process Read/Write Functions[133X[101X
  
  [33X[0;0YFor  those familiar with using the [10Xanu-pq[110X program as a standalone we provide
  primitive read/write tools to communicate directly with an interactive [5XANUPQ[105X
  process,  started  via  [10XPqStart[110X.  For the most part, it is up to the user to
  translate the output strings from [10Xanu-pq[110X program into a form useful in [5XGAP[105X.[133X
  
  [1X5.11-1 PqRead[101X
  
  [33X[1;0Y[29X[2XPqRead[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqRead[102X(  ) [32X function[133X
  
  [33X[0;0Yread  a  complete  line of [5XANUPQ[105X output, from the [3Xi[103Xth or default interactive
  [5XANUPQ[105X  process,  if  there  is output to be read and returns [9Xfail[109X otherwise.
  When  successful,  the  line  is returned as a string complete with trailing
  newline,  colon, or question-mark character. Please note that it is possible
  to  be [21Xtoo quick[121X (i.e. the return can be [9Xfail[109X purely because the output from
  [5XANUPQ[105X is not there yet), but if [10XPqRead[110X finds any output at all, it waits for
  a  complete  line.  [10XPqRead[110X  also  writes the line read via [10XInfo[110X at [10XInfoANUPQ[110X
  level  2.  It  doesn't  try to distinguish banner and menu output from other
  output of the [10Xanu-pq[110X program.[133X
  
  [1X5.11-2 PqReadAll[101X
  
  [33X[1;0Y[29X[2XPqReadAll[102X( [3Xi[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqReadAll[102X(  ) [32X function[133X
  
  [33X[0;0Yread  and  return  as  many  [13Xcomplete[113X lines of [5XANUPQ[105X output, from the [3Xi[103Xth or
  default  interactive  [5XANUPQ[105X process, as there are to be read, [13Xat the time of
  the  call[113X,  as  a  list  of  strings  with any trailing newlines removed and
  returns  the  empty list otherwise. [10XPqReadAll[110X also writes each line read via
  [10XInfo[110X  at  [10XInfoANUPQ[110X  level  2. It doesn't try to distinguish banner and menu
  output  from  other  output  of the [10Xanu-pq[110X program. Whenever [10XPqReadAll[110X finds
  only  a  partial  line,  it waits for the complete line, thus increasing the
  probability that it has captured all the output to be had from [5XANUPQ[105X.[133X
  
  [1X5.11-3 PqReadUntil[101X
  
  [33X[1;0Y[29X[2XPqReadUntil[102X( [3Xi[103X, [3XIsMyLine[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqReadUntil[102X( [3XIsMyLine[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqReadUntil[102X( [3Xi[103X, [3XIsMyLine[103X, [3XModify[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqReadUntil[102X( [3XIsMyLine[103X, [3XModify[103X ) [32X function[133X
  
  [33X[0;0Yread  complete  lines  of  [5XANUPQ[105X output, from the [3Xi[103Xth or default interactive
  [5XANUPQ[105X  process,  [21Xchomps[121X  them (i.e. removes any trailing newline character),
  emits  them  to  [10XInfo[110X  at  [10XInfoANUPQ[110X  level 2 (without trying to distinguish
  banner and menu output from other output of the [10Xanu-pq[110X program), and applies
  the  function [3XModify[103X (where [3XModify[103X is just the identity map/function for the
  first  two forms) until a [21Xchomped[121X line [3Xline[103X for which [10X[3XIsMyLine[103X[10X( [3XModify[103X[10X([3Xline[103X[10X)
  )[110X is true. [10XPqReadUntil[110X returns the list of [3XModify[103X-ed [21Xchomped[121X lines read.[133X
  
  [33X[0;0Y[13XNotes:[113X When provided by the user, [3XModify[103X should be a function that accepts a
  single string argument.[133X
  
  [33X[0;0Y[3XIsMyLine[103X  should  be  a function that is able to accept the output of [3XModify[103X
  (or  take  a  single string argument when [3XModify[103X is not provided) and should
  return a boolean.[133X
  
  [33X[0;0YIf   [10X[3XIsMyLine[103X[10X(   [3XModify[103X[10X([3Xline[103X[10X)   )[110X  is  never  true,  [10XPqReadUntil[110X  will  wait
  indefinitely.[133X
  
  [1X5.11-4 PqWrite[101X
  
  [33X[1;0Y[29X[2XPqWrite[102X( [3Xi[103X, [3Xstring[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPqWrite[102X( [3Xstring[103X ) [32X function[133X
  
  [33X[0;0Ywrite [3Xstring[103X to the [3Xi[103Xth or default interactive [5XANUPQ[105X process; [3Xstring[103X must be
  in  exactly the form the [5XANUPQ[105X standalone expects. The command is echoed via
  [10XInfo[110X   at   [10XInfoANUPQ[110X   level   3   (with   a   [21X[10XToPQ>   [110X[121X   prompt);  i.e. do
  [10XSetInfoLevel(InfoANUPQ,  3);[110X  to  see  what  is  transmitted  to  the [10Xanu-pq[110X
  program.  [10XPqWrite[110X returns [9Xtrue[109X if successful in writing to the stream of the
  interactive [5XANUPQ[105X process, and [9Xfail[109X otherwise.[133X
  
  [33X[0;0Y[13XNote:[113X If [10XPqWrite[110X returns [9Xfail[109X it means that the [5XANUPQ[105X process has died.[133X
  
