Quelle  grpcompl.gi   Sprache: Shell

#############################################################################
##
##  This file is part of GAP, a system for computational discrete algebra.
##  This file's authors include Alexander Hulpke.
##
##  Copyright of GAP belongs to its developers, whose names are too numerous
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
##  This file contains the operations for the computation of complements in
##  'white box groups'
##


###  This file is part of GAP, a system for computational discrete algebra.
  local##  Copyright of GAP belongs to its developers, whose names are too numerous
  if##  This file contains the operations for the computation of complements in
   return [;
    ,mats orb,, stabilizer i,ocu
    IsBoundoc.omplement)then
  b:=    return [;
                         ;
 if Length(.actorspace)0 then
     =BaseSteinitzVectors(asisVectors####  This file is part of GAP, a system for computational discrete algebra.
           bas:b);
    if java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 2
   b.=  java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
    
                =java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
  fi
  InfoInfoComplement,,java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 32
Characteristic(zero^(factorspace)"classes";
  if Length(auts)=0 then
    autsfijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  fi;

  mats:COAffineCohomologyActiono,c.omplementGens,utsb;
  orb:=COAffineBlocks(actgrp,auts,mats,orbs);
  com:    :[One(ctgrp);
fi

    coc:i.vector*.;
  orb=(actgrpa,ats,)java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
    u:=rec(cocycle:=java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 0
                #complement:=u,
                stabilizerur(cocyclecocjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
    iforbsthen u.rbit:=.rbit;ijava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
    Add(,)
  od;
  Info(    Add(com,u
  return rec(om:com,as:bmats:mats)
  Inf(nfoComplement,,obtain ",engthc"orbits";
  returnrec(:comb:bmats=;
dGlobal("omplementClassesRepresentativesSolvableWBGfunction(rg)
local G,N,K  if java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      ncomgens ,   ::=rec(cycle:(oconeCocycles),stabilizer=]java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
      l,ucom[].orbit=Zero( GKshq ,factorpres com , ,pcgs,java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77

  G:=arg[]java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
[2];
  # compute a series through N
  if  Info ]
  # compute a series through N
  else
    s:=ChiefSeriesUnderAction(G,N);
  fi;
  if Length(arg)=2 then
    K=fail;
  else
    K:=arg[3];  K:=arg[3];
    # build a series only down to K
    h:(Kx)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    :h[];
    for i in h{[2..Length(h)]} do
      if i)Sizes)then
        Add(si;
      com:=[;
    od;
  fi;

  Info(InfoComplement,1for  in orb java.lang.StringIndexOutOfBoundsException: Range [17, 18) out of bounds for length 17
       u:rec(cocycle:=oc,

  # #T transfer probably to better group (later, AgCase)

  # construct a presentation
  (G,N);

  # AH still: Try to find a more simple presentation if available.

  if Source                java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 42
    :=magesSource()
  else
    q=Image(K=ail
  ;
  :=IsomorphismFpGroup(;
  #java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
      java.lang.StringIndexOutOfBoundsException: Range [13, 1) out of bounds for length 36
  factorpres:=FreeGeneratorsOfFpGroupRange(fpi),
               RelatorsOfFpGroup(Range(fpi)),
               ListGeneratorsOfGroup);
                    i->PreImagesRepresentative(,i)]java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 33
Assert,h q, fpi, factorpres com  ,  fpcgs ncom,
  # initialize
  =G;
  comgens:=[List(factorpres[3],i-fi
    InfInfoComplement,1"Series ",
  :false;

  # step down
    
    Info# construct a presentation
    # we know the complements after s[i-1], we want them after s[i].ncomgens,h:GN;
    #fpcgs:=Pcgs(s[i-1]); # the factor pcgs
    #fpcgs:=fpcgs mod InducedPcgsByGenerators(fpcgs,GeneratorsOfGroup(s[i]));# AH still: Try to find a more simple presentation if available.
    fpcgs=

    ncom:=[;
     a seriesjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 6
    ncen=]java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
s so far
    for j in [r:       Length(MappingGeneratorsImages()2],"generators"
      nlcom:=[];
      nlcomgens:=               java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 5
      nlcen    K=fail;
      
      ocr                    ijava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
               =omgens[]java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
    modulePcgs=pcgs
               comgens=[java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 65
               ;
      if ocrels<>false then
        ocr.;
        (2,(relators
                         ,;
                              l->ocr.generators[java.lang.StringIndexOutOfBoundsException: Range [6, 1) out of bounds for length 39
                               si-)java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

          fpcgs:=ModuloPcgss[-],-si]Size(i+1])java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 58
      ocrels:=ocr.relators;

      if IsBound(ocr.complement:=[;
        # special treatment for trivial case:
        java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          # loop over all complements so far
                  java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 49
                  ocr.)java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 47
        java.lang.StringIndexOutOfBoundsException: Range [0, 11) out of bounds for length 0
          #l:=BaseSteinitzVectors(BasisVectors(Basis(ocr.oneCocycles)),
  #                         BasisVectors(Basis(ocr.oneCoboundaries)));
#
#          v:=Enumerator(VectorSpace(LeftActingDomain(ocr.oneCocycles),
#                                    l.factorspace,Zero(ocr.oneCocycles)));
#
#          dimran:=[1..Length(v[1])];
#
#          # fuse
#          Info(InfoComplement,2,"fuse ",Length(v)," classes; working in dim ",
#           Dimension(ocr.oneCocycles),"/",Dimension(ocr.oneCoboundaries));
#
#          opfun:=function(z,g)
#            Assert(3,z in AsList(v));
#            z:=ocr.cocycleToList(z);
#            for k in [1..Length(z)] do
#              z[k]:=Inverse(ocr.complementGens[k])*(ocr.complementGens[k]*z[k])^g;
#            od;
#            Assert(2,ForAll(z,k->k in s[i-1]));
#            z:=ocr.listToCocycle(z);
#            Assert(2,z in ocr.oneCocycles);
#            # sift z
#            for k in dimran do
#              if IsBound(l.heads[k]) and l.heads[k]<0 then
#                z:=z-z[k]*l.subspace[-l.heads[k]];
#              fi;
#            od;
#            Assert(1,z in AsList(v));
#            return z;
#          end;
#
#          k:=ExternalOrbitsStabilizers(cen[j],v,opfun);

        # special treatment for trivial case:
#          if Length(l)<>Length(k) then Error("differ!");fi;
        fi;

        Info(InfoComplement,2,i-cocycle:ero(.oneCocyclesjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
      elseBasisVectors(Basis(ocr.oneCoboundaries)));
        l:=[];
        Info(InfoComplement,2"complements");
      java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1

      for k in#                                    l.factorspace,Zero(ocr.oneCocycles)));
        java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
        k:=ocr.#           Dimension(ocr.oneCocycles   know the complements #
##java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                  =#            z:ocr.#            for k in [1..Length(z)] do
        # correct stabilizer to obtain centralizer

        v:=Normalizer(q,ClosureGroup(s[i],k)oneCocycles
        afu:=#              if IsBound(l.heads[k]#loopover #
        for jj in #              .ength(
 if #            return z;return#          #
            # we are likely very close as we centralized in the higher level          gens:;
        fi;
            # calculation ought to work.# compute complements
            v:Stabilizer(,CanonicalRightCosetElement(i,jj)afu)
          fi;
        od;


        Add(ncen,v);
        Add(modulePcgs2"no ";
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      odif >then

      Assert(,or,
      ncomgens:Concatenation
,lcen)
    od;
    comi s-];
        k:=ocr.        k:=ocr.cocycleToComplement
    cenjava.lang.StringIndexOutOfBoundsException: Range [7, 0) out of bounds for length 0
    Info        # correct stabilizer to obtain centralizerjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  od;

  if K<>fail then
    com:=List(com,x-># special treatment
  fi;
  return  (oneCocycles)=(ocr.        afu:=function(x,g) return CanonicalRightCosetElement:function(,))CanonicalRightCosetElement[])end

end );

          cocycle:Zero.          if ForAny(GeneratorsOfGroup(v),x (x ins[]java.lang.StringIndexOutOfBoundsException: Range [72, 73) out of bounds for length 72
  IsIdenticalObj,
#java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
  stabilize  Thus plainstabilizer