#############################################################################
##
##  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'
##


BindGlobal(return [;
  local b ,orb,comstabilizer,i,,;
ifnot(.omplement)then
    return ];
  fi
  oc.zero:h if Length(.actorspace)0 then
 b:BaseSteinitzVectors(asisVectors####  This file is part of GAP, a system for computational discrete algebra.
           bas:java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 19
  Length(.)0 then
    u:=  oczero:Zerofi
           bas=;
     orbs then
      u.com[1].orbit  ;(InfoComplement,,fuse ",
    fi;
    (^engthbfactorspace)"classes"java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
  ;
  Info(InfoComplement,2,"fuse ",
    fi;
  if  mats:COAffineCohomologyAction(c,c.omplementGensa,)java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
    auts=[One(ctgrp);
  ;

      :i.vector*.actorspace
  orb:COAffineBlocksactgrp,utsm,rbs;
  com:=[];
  for i in orb do

    coc:=i.vector*b.factorspace;
    #u:=oc.cocycleToComplement(coc);                
    :=ec:=coc,
                #complement:=u,
                stabilizer:=i.       uorbit:i.rbit;i;
    if orbs then u.orbit:    Add(omu;
);
  od;  return recc:com,as:,ats:mats;
o(nfoComplement,,obtain ,(om), orbits";
  return (om=,as=,:mats)
Bin("", functionargjava.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72

BindGlobal( "ComplementClassesRepresentativesSolvableWBG", function      ncomgens,ncen    :(com=rec(cycle:erooneCocycles)java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
local G,,,h q,pi ,com, ,,,pcgs,com,
      ncomgens, ncen, java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 7
      return u;

  G:=arg[2]java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
[]
  
(x
N,(N]java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
    h:=NaturalHomomorphismByNormalSubgroup
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  fistabilizer:=i.stabilizer);
  if Length    if  then     =magesSource(;
    K:f;
  else
    Kfijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
    # build a series only down to K
,java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 36
              (java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 5
     i in [2.Length()}(,(factorpres3,i->(h,PreImagesRepresentativeh)=);
      if Size(i)<Size(Last(slocalG,N,K,s , , fpifactorpres,com,comgens,cen, ocrels, fpcgs, ncom,
          com:=[]java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
      ;
    od;
  fi;

  Info(,1,"of factors:"
ocrels:false

 

  # construct a presentation
h,java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46

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

  if Source(h)=G then:ModuloPcgs
 N:a[2[]java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
  else
    IsElementaryAbelian() 
  fi;    =N(N);
  fpi:=IsomorphismFpGroup:=;
 (,2,    # loop over all complementfar
       pi2] ;
  factorpres
java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 5
      
                    -
  #build a series only down togenerators:=omgensj,
  # initialize
  coms:[[ modulePcgs:=,
  comgens:=[List(factorpres[3],i->PreImagesRepresentativefor i inh{2java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 17
]
       Assert(,ForAll(cr.relators,

  # step down
  foriAddsi)java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
foInfoComplement,1,"Step ",i-1);
    # we know the complements after s[i-1], we want them after s[i].-)
    #fpcgs:=Pcgs(s[i-1]); # the factor pcgs
pcgsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
([       List([1..Length(s),S(/[+1);

    ncom:=[];
    ncomgens]java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
    ncen:=];
    java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
    for  in[.Length) complement:complement];
      nlcom:=[];
      nlcomgens:=[];
      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      # compute complements
           #                         BasisVectors(Basis(ocr.oneCoboundaries)));
               generators:#
               modulePcgs:=fpcgs,
                              factorpresl.actorspace,Zero(ocroneCocycles));
               ;
      ifocrels<#          
        ocr.relators:=ocrels;
        Assert(2,ForAll(ocr.  Info(InfoComplement,2,"using a pre
                        k->            z=ocr.cocycleToList#            for k in [1..Length(z)] do
                              l->ocr.#            Assert(2,ForAll(z,k->k in s[i-1:[FreeGeneratorsOfFpGroup(Range(            z:=ocr.listToCocycle(z);z:=ocr.listToCocycle(z);
                              in si-);
      #              fi;

      OCOneCocycles(ocr,true);
      ocrels:=ocr.relators;

      if java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 1
        # special treatment for trivial case:
        #java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
          java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
                  Zero(cr.),
                  complement:=ocr.complement)];
        else
          #l:=BaseSteinitzVectors(BasisVectors(Basis(ocr.oneCocycles)),
                        java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 76
#
#          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);

nlcom[
#          if Length(l)<>Length(k) then Error("differ!");fi;
        ;

        java.lang.StringIndexOutOfBoundsException: Range [12, 9) out of bounds for length 40
      else
        l:=java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
        ,,"nocomplements";
      fi;

      for k in l ,
        n[-1)
k=
        Assert
                  ;
#

:Normalizer(q,([i]java.lang.StringIndexOutOfBoundsException: Range [41, 5) out of bounds for length 5
afuxg)return (]x^)end
        for jj in l:=[rec(stabilizercen[java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          >otComm,jj   i] 
            :=.]java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
             thecohomology. a  
            # calculation ought to work.#          v:=Enumerator(VectorSpace(LeftActingDomain(ocr.oneCocycles),
            v:=Stabilizer(v#
          fi#
        od;


        Add(ncen,v);
        Add(nlcom,k);
        Add(nlcomgens,GeneratorsOfGroup(k));
      od;

      ncom:=Concatenation(#            Assert(3,z in AsList(v));
      ncomgens:=#            for k in [1..Length(z)] do
      ncen:=Concatenation(ncen,nlcen);
    od;
    com:=ncom;
    comgens:#            od;
    cen:=ncen;
    Info(#            z:=ocr.listToCocycle(z);
  od;

  if K<>fail then
    com:=List(com#            for k in dimran do
  fi;
  #              fi;

end );

InstallMethod#            return z;
  IsIdenticalObj#          end;
  #          k:=ExternalOrbitsStabilizers(cen[j],v,opfun);
  ;