  
  [1X3 [33X[0;0YLINS Search[133X[101X
  
  [33X[0;0YThis  chapter  is  for  advanced  users  and  those  interested  in  a brief
  introduction to the mathematical background of [5XLINS[105X.[133X
  
  [33X[0;0Y[12X(NOTE: The internal options below might change during further development!)[112X[133X
  
  
  [1X3.1 [33X[0;0YLINS Search Options[133X[101X
  
  [33X[0;0YThe  method  [10XLowIndexNormalSubgroupsSearch[110X  allows an optional argument [3Xopts[103X
  which  must  be  a  record and modifies the search for the execution of only
  this single command.[133X
  
  [33X[0;0YThe following components of [3Xopts[103X are supported.[133X
  
  [8X[10XDoSetParent[110X[8X[108X
        [33X[0;6Y[9Xtrue[109X  to set parent of every subgroup to the group [3XG[103X that is contained
        in   the  root  of  the  search  graph.  It  also  sets  the  property
        [10XIsNormalInParent[110X to [9Xtrue[109X for every subgroup.[133X
  
        [33X[0;6YThis should be only disabled for debugging or testing purposes.[133X
  
  [8X[10XInitGraph[110X[8X[108X
        [33X[0;6Ya  function that takes as an argument a [9XLinsGraph[109X [3Xgr[103X. It can popullate
        the  record  object  [3Xgr[103X  via  calls  like [10Xgr!.NAME = VALUE[110X in order to
        initialize  certain components that might be needed by other functions
        later on (see option [10XDoTerminate[110X).[133X
  
  [8X[10XDoCut[110X[8X[108X
        [33X[0;6Ya function that takes as arguments a [9XLinsGraph[109X [3Xgr[103X and a [9XLinsNode[109X [3XrH[103X.[133X
  
        [33X[0;6YReturns  [9Xtrue[109X  if  subgroups under [3XrH[103X should not be computed, i.e. the
        branch will be cut under the node [3XrH[103X.[133X
  
  [8X[10XDoTerminate[110X[8X[108X
        [33X[0;6Ya function that takes as arguments a [9XLinsGraph[109X [3Xgr[103X and two [9XLinsNodes[109X [3XrH[103X
        and  [3XrK[103X.  We  are currently computing the subgroups under [3XrH[103X and found
        the normal subgroup [3XrK[103X.[133X
  
        [33X[0;6YThis  function  may  write  data to [10Xgr!.ComputedNormalSubgroups`[110X. Make
        sure  to  initalize  this  via the option [10XInitGraph[110X (for example to an
        empty list), since it is not bound by default.[133X
  
        [33X[0;6YReturns [9Xtrue[109X if the search can be terminated.[133X
  
  [8X[10XUseLIS[110X[8X[108X
        [33X[0;6Y[9Xfalse[109X   to   use   the   new   procedure   with   [10XGQuotient[110X  calls  in
        [10XLINS_FindTQuotients[110X.[133X
  
        [33X[0;6Y[9Xtrue[109X  to use the old procedure with a [10XLowIndexSubgroupsFpGroup[110X call in
        [10XLINS_FindTQuotients[110X.[133X
  
  [8X[10XFilterTQuotients[110X[8X[108X
        [33X[0;6Ya  function  that  takes  as  an argument a [9XLinsGraph[109X [3Xgr[103X and a list of
        [3Xtargets[103X following the specifications of [10XLINS_FindTQuotients[110X.[133X
  
        [33X[0;6YThe  value  of  [10Xtargets[110X  in  a  call via [10XLowIndexNormalSubgroupsSearch[110X
        depends on the value of the option [10XUseLIS[110X.[133X
  
        [33X[0;6YIf [10XUseLIS[110X is false, we have [10Xtargets = LINS_TargetsQuotient[110X.[133X
  
        [33X[0;6YIf [10XUseLIS[110X is true, we have [10Xtargets = LINS_TargetsQuotientUseLIS[110X.[133X
  
        [33X[0;6YReturns   a   sublist   from   [3Xtargets[103X,   that   will   be   used   by
        [10XLINS_FindTQuotients[110X.[133X
  
  [8X[10XDoIntersection[110X[8X[108X
        [33X[0;6Ya  function that takes as an argument a [9XLinsGraph[109X [3Xgr[103X, two [9XLinsNodes[109X [3XrH[103X
        and [3XrK[103X, and a positive integer [3Xi[103X. Let [22XG[122X be the group that is contained
        in the root of the search graph.[133X
  
        [33X[0;6YReturns  [9Xtrue[109X  if  the  intersection [22XU[122X of the groups in [3XrH[103X and [3XrK[103X with
        index [22X[G : U] = i[122X should be computed.[133X
  
  [8X[10XDoPQuotient[110X[8X[108X
        [33X[0;6Ya function that takes as an argument a [9XLinsGraph[109X [3Xgr[103X, a [9XLinsNode[109X [3XrH[103X and
        a prime [3Xp[103X.[133X
  
        [33X[0;6YReturns  [9Xtrue[109X if [3Xp[103X-quotients under [3XrH[103X should be computed for the prime
        [3Xp[103X.[133X
  
  [8X[10XDoPModule[110X[8X[108X
        [33X[0;6Ya  function that takes as an argument a [9XLinsGraph[109X [3Xgr[103X, a [9XLinsNode[109X [3XrH[103X, a
        prime [3Xp[103X and a positive integer [3Xi[103X. Let [22XG[122X be the group that is contained
        in the root of the search graph.[133X
  
        [33X[0;6YReturns  [9Xtrue[109X  if  the  normal  subgroup  [22XK[122X  of index [22X[G : K] = i[122X with
        elementary abelian [3Xp[103X-quotient in [3XrH[103X should be computed.[133X
  
