  
  [1X2 [33X[0;0YExecuting a search[133X[101X
  
  
  [1X2.1 [33X[0;0YInformation and diagnostics[133X[101X
  
  [33X[0;0Y[5XGraphBacktracking[105X  reports  diagnostic  information  through  the info class
  [10XInfoGB[110X,  which  is  set  equal  to  the  [5XBacktrackKit[105X  info  class [2XInfoBTKit[102X
  ([14XBacktrackKit:  InfoBTKit[114X);  raising the level of either (with [10XSetInfoLevel[110X)
  therefore  raises  both. Higher levels print progressively more detail about
  the progress of the search.[133X
  
  
  [1X2.2 [33X[0;0YThe main search interface[133X[101X
  
  [33X[0;0YThese   three   functions  are  the  graph  backtracking  analogues  of  the
  [5XBacktrackKit[105X     search    functions    [2XBTKit_SimpleSearch[102X    ([14XBacktrackKit:
  BTKit_SimpleSearch[114X),       [2XBTKit_SimpleSinglePermSearch[102X       ([14XBacktrackKit:
  BTKit_SimpleSinglePermSearch[114X)  and  [2XBTKit_SimpleAllPermSearch[102X ([14XBacktrackKit:
  BTKit_SimpleAllPermSearch[114X),  and  take  the same arguments. Each begins from
  the   ordered   partition   stack   [3Xps[103X  (see  [2XPartitionStack[102X  ([14XBacktrackKit:
  PartitionStack[114X))  and  searches  for  the  permutations  that  satisfy every
  refiner  in the list [3Xconlist[103X. Refiners may be built with the constructors in
  the  [10XGB_Con[110X  record  (see  [14X3[114X) or with any [5XBacktrackKit[105X refiner. The optional
  final  argument  [3Xconf[103X  is  a configuration record; the recognised fields are
  [10XcellSelector[110X  (the branch-cell selector) and [10Xconsolidator[110X (the function used
  to make the graph stack equitable, see [14X4[114X).[133X
  
  [1X2.2-1 GB_SimpleSearch[101X
  
  [33X[1;0Y[29X[2XGB_SimpleSearch[102X( [3Xps[103X, [3Xconlist[103X[, [3Xconf[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya permutation group[133X
  
  [33X[0;0YReturns the group of all permutations that satisfy every refiner in [3Xconlist[103X.
  This  is  correct only when that set of permutations is in fact a group (for
  example,  an  intersection  of  groups,  a stabiliser, or a normaliser); use
  [2XGB_SimpleSinglePermSearch[102X ([14X2.2-2[114X) when the solution set is a coset.[133X
  
  [1X2.2-2 GB_SimpleSinglePermSearch[101X
  
  [33X[1;0Y[29X[2XGB_SimpleSinglePermSearch[102X( [3Xps[103X, [3Xconlist[103X[, [3Xconf[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya permutation, or [9Xfail[109X[133X
  
  [33X[0;0YReturns a single permutation satisfying every refiner in [3Xconlist[103X, or [9Xfail[109X if
  no  such  permutation  exists.  This  is  the  function to use for coset and
  transporter problems (group or coset intersection, conjugacy, and so on).[133X
  
  [1X2.2-3 GB_SimpleAllPermSearch[101X
  
  [33X[1;0Y[29X[2XGB_SimpleAllPermSearch[102X( [3Xps[103X, [3Xconlist[103X[, [3Xconf[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya list of permutations[133X
  
  [33X[0;0YReturns  the  complete  list  of  permutations  satisfying  every refiner in
  [3Xconlist[103X.  This enumerates the whole solution set and is therefore very slow;
  it is intended for testing and exploration on small examples.[133X
  
  
  [1X2.3 [33X[0;0YInspecting the initial graph stack[133X[101X
  
  [33X[0;0YThese  functions  expose  the graph stack that is built before any branching
  takes place. They are used mainly for testing and for understanding how much
  a  set  of  refiners  deduces  [21Xfor  free[121X,  and  are unlikely to be needed in
  ordinary use.[133X
  
  [1X2.3-1 GB_CheckInitialGroup[101X
  
  [33X[1;0Y[29X[2XGB_CheckInitialGroup[102X( [3Xps[103X, [3Xconlist[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record[133X
  
  [33X[0;0YBuilds  the  initial  graph  stack  for  [3Xconlist[103X  and  returns a record with
  components  [10Xgens[110X (generators of the automorphism group of the initial stack,
  as  permutations)  and [10Xanswer[110X ([9Xtrue[109X if every one of those generators already
  satisfies  [3Xconlist[103X, so that no search is required; [9Xfalse[109X otherwise, in which
  case the group is a supergroup of the solutions).[133X
  
  [1X2.3-2 GB_CheckInitialCoset[101X
  
  [33X[1;0Y[29X[2XGB_CheckInitialCoset[102X( [3Xps[103X, [3Xconlist[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record[133X
  
  [33X[0;0YThe coset analogue of [2XGB_CheckInitialGroup[102X ([14X2.3-1[114X). Builds the initial graph
  stack  down  both  the  left  and the right branch and returns a record with
  components  [10Xgraph1[110X,  [10Xgraph2[110X  (the two canonically-labelled graph stacks) and
  [10Xequal[110X (whether they coincide).[133X
  
