Quellcode-Bibliothek 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'
##


BindGlobal("COCohomologyAction",function(oc,actgrp,auts,orbs)
  local b, mats, orb, com, stabilizer, i,coc,u;
  if not IsBound(oc.complement) then
    return [];
  fi;if bactorspace)0
  .=Zero;
return           :=
if     (c.)ength(.factorspacejava.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 24
  ifjava.lang.StringIndexOutOfBoundsException: Range [0, 11) out of bounds for length 0
urec:=oZ(.),stabilizer:actgrp),
           bas:=b);
    if orbs then
      .1:[local,N, , ,factorpres com,comgens,cenocrels,pcgs,
    1;
    java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
  fi;
  Info(2
    Characteristic:failjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
    if :=List(s,x->ClosureGroup,);
        s:=[TrivialSubgroup);
  fi s:[[1]java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14

  mats:      Size()Size(Last() 
  orb(ss,);
  =[]java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
  iinorbdo

    coc:=i.vector*b.factorspace;
    #u:=oc.cocycleToComplement(coc);
    u=cocycle:cjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
                elsejava.lang.StringIndexOutOfBoundsException: Range [42, 40) out of bounds for length 46
                =i.;
    iforbs uq:magesSourceh;
        q:=q:java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 12
   fpi:q);
      # build a series only down to K
  return rec(com:     h:=List(s,x->ClosureGroup(K,x)  :[((fpi)java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
end;

BindGlobal                    >PreImagesRepresentativefpi)]fori h{2...h]  Assert1ForAll[]i-ImagehPreImagesRepresentative(,i)i);
local  # #T transfer probably to better group (later, AgCase)
       h:NaturalHomomorphismByNormalSubgroup(N)java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
      l, java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 0

  G
:rg]2
compute a series   
 (N then
    s:[,TrivialSubgroupN]java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
    InfoInfoComplement,2"  sso far
    :       ((([2], generators"java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
  fi;
  if Length(arg)=2 then
    K:;      # compute complements
  else
    K:=arg[3];
     java.lang.StringIndexOutOfBoundsException: Range [13, 11) out of bounds for length 35
    # initialize
    s=h1   =java.lang.StringIndexOutOfBoundsException: Range [33, 34) out of bounds for length 33
     i  h{[.)java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
      if Sizeocrjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
        (java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
      (java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 39
    od;
   ins[])java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42

  Info(InfoComplement,1,"Series of 
1],>ize([]/(1);

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  # construct a presentation:=;
  h:=                  cocycle:= forjin 1.(com]=);

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

   java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
    java.lang.StringIndexOutOfBoundsException: Range [15, 5) out of bounds for length 38
  else
                     fZero(.oneCocycles);
  fi)
  fpiif <          Info(InfoComplement,2,"fuse ",Length(v)," classes; working in dim ",
sentation#
       Length(#            Assert(3,z in AsList(v))-P            :ocr#            for k in [1..Length(
  factorpres=(#            #            Assert(2,z in ocr.oneCocycles);
               #              if IsBound(l.heads[                               [-1])java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
               List(GeneratorsOfGroupif          if Length(l)<>Length(k) then Error("differ!");fi;
                    -                  =.),
  Assert else
  # initialize
  com:=[G];
  comgens:=[List(factorpres[3java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
  cen:=[s        InfoComplement,no java.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 48
  ocrels:=falsejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  # step down
  for i in [
    Info(InfoComplement,1java.lang.StringIndexOutOfBoundsException: Range [0, 9) out of bounds for length 1
     we know the afterjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
    fpcgs:=Pcgs(s[i-1]); # the factor pcgs
    #fpcgs:=fpcgs mod InducedPcgsByGenerators(fpcgs,GeneratorsOfGroup(s[i]));            :=cr.
    fpcgs:#

    #       java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    ncomgens:=[];
    ncen#            Assert(2,z in ocr.#            # sift z
      all#                z:=z-z[k]*l.subspace[-l.heads[k]];
.L(#            od;
               #             z          end;
      gens:[;
      nlcen:#          if Length(l)<>Length(k) then Error("differ!");fi;
      # compute complements
      ocr:=rec(group            v=vCanonicalRightCosetElements[]jj)afu;
               java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length 11
              Info(InfoComplement"complements")
               java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
               );
      if ocrels<false 
        ocr.
        Assert(ForAll(cr.elators,
                        ncomgens=Concatenation(ncomgens,nlcomgens);
                              ;
                              [1))
java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 9

      OCOneCocycles(ocr,true);
relatorsjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27

      if =Normalizer(q,ClosureGroupsi]java.lang.StringIndexOutOfBoundsException: Range [41, 5) out of bounds for length 5
         for trivial case:
fDimensionocr.)Dimension(ocr.        =x (i,^;;
          :=java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 37
                  :=(ocr.oneCocycles-> )s] then
                  complement=ocr.omplement);
        else
          l:=BaseSteinitzVectors(BasisVectors(Basis(ocr.oneCocycles)),
        # andcohomology. 
#
#          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);

          l:=ComplementClassesRepresentativesSolvableWBG));
#          if Length(l)<>Length(k) then Error("differ!");fi;
        fi;

        Info(InfoComplement,2,"splits in ",Length(l)," complements");
      else
        l:=[];
        Info(InfoComplement,2,"no complements");
      fi;

      for k in l do
        q:=k.stabilizer;
        k:=ocr.cocycleToComplement(k.cocycle);
        Assert(3,Length(GeneratorsOfGroup(k))
                  =Length(MappingGeneratorsImages(fpi)[2]));
        # correct stabilizer to obtain centralizer

        v:=Normalizer(q,ClosureGroup(s[i],k));
        afu:=function(x,g) return CanonicalRightCosetElement(s[i],x^g);end;
        for jj in GeneratorsOfGroup(k) do
          if ForAny(GeneratorsOfGroup(v),x->not Comm(x,jj) in s[i]) then
            # we are likely very close as we centralized in the higher level
            # and stabilize the cohomology. Thus a plain stabilizer
            # calculation ought to work.
            v:=Stabilizer(v,CanonicalRightCosetElement(s[i],jj),afu);
          fi;
        od;


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

      ncom:=Concatenation(ncom,nlcom);
      ncomgens:=Concatenation(ncomgens,nlcomgens);
      ncen:=Concatenation(ncen,nlcen);
    od;
    com:=ncom;
    comgens:=ncomgens;
    cen:=ncen;
    Info(InfoComplement,1,Length(com)," complements in total");
  od;

  if K<>fail then
    com:=List(com,x->ClosureGroup(K,x));
  fi;
  return com;

end );

InstallMethod(ComplementClassesRepresentativesSolvableNC,"using cohomology",
  IsIdenticalObj,
  [IsGroup,IsGroup],1,
  ComplementClassesRepresentativesSolvableWBG);