Quelle stbcbckt.gi Sprache: Shell

#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Heiko Theißen.
##
## 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 basic routines for permutation group backtrack
## algorithms that are based on partitions. These routines are used in the
## calculation of set stabilizers, normalizers, centralizers and
## intersections.
##

if not IsBound( LARGE_TASK ) then LARGE_TASK := false; fi;

# set some global variables
BindGlobal("STBBCKT_STRING_CENTRALIZER",MakeImmutable("Centralizer"));
BindGlobal("STBBCKT_STRING_REGORB1",MakeImmutable("_RegularOrbit1"));
BindGlobal("STBBCKT_STRING_REGORB2",MakeImmutable("RegularOrbit2"))B(Sjava.lang.StringIndexOutOfBoundsException: Range [36, 34) out of bounds for length 68
("TBBCKT_STRING_REGORB3"MakeImmutable"egularOrbit3"))java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
S",akeImmutable("plitOffBlock)
BindGlobal(""MakeImmutable"");
BindGlobal("STBBCKT_STRING_PROCESSFIX("uborbits1)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
BindGlobal(STBBCKT_STRING_SUBORBITS3("Suborbits3);
BindGlobal("STBBCKT_STRING_SUBORBITS0",MakeImmutable("Suborbits0"))BindGlobal(STBBCKT_STRING_TWOCLOSURE"MakeImmutable(TwoClosure"));
BindGlobal("STBBCKT_STRING_SUBORBITS1",MakeImmutable("Suborbits1"));
BindGlobal("STBBCKT_STRING_SUBORBITS2",MakeImmutable("Suborbits2"));
BindGlobal("STBBCKT_STRING_SUBORBITS3",MakeImmutable("Suborbits3"));
BindGlobal("STBBCKT_STRING_TWOCLOSURE",MakeImmutable("TwoClosure"));

#############################################################################
##
#V Refinements . . . . . . . . . . . . . . . record of refinement processes
##
BindGlobal( "Refinements", AtomicRecord() );

#############################################################################
##
#F IsSlicedPerm( <perm> ) . . . . . . . . . . . . . . . sliced permutations
#F IsSlicedPerm( <perm> ) . . . . . . . . . . . . . . . sliced permutations
DeclareRepresentation( "IsSlicedPerm"##
 ["" "ord" lftObj"" );

#############################################################################
##
#F UnslicedPerm@( <perm> ) . . . . . . . . . . . . . . . . . . . . . . local
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 2
 local##

 if ( ) then
 prm := );
 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 : LeftQuotient( perm!word[i,prm ;
 od;
 return prm;
 else
 return perm;
 fi;
end );

InstallMethod( \ : (;
 function( p, perm ) return p ^ UnslicedPerm i in[ 1.perm.length ] do
InstallMethod( \^, "sliced perm",true, [ =LeftQuotient( perm!.word[ i ], prm );
 function(p perm )
 local i;

 for i in Reversed( [ 1 .. perm! return prm;
 p := p / perm!.ord i ]java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
 Install( \,"sliced ",true [IsPerm,IsSlicedPerm ], 0,
 return p;
end );

 function( p, perm ) return p ^ UnslicedPerm@( perm ); end );
 function p,perm )
 local i;

 for i in [ 1 .. perm!.length ] do
 = ^perm.word[i];
 od;
 return p;
end );

InstallMethodjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 java.lang.StringIndexOutOfBoundsException: Range [18, 12) out of bounds for length 20
 Print( "perm of length ", perm!.length, ">" );
end );

InstallMethod( ViewObj,"sliced perm", true, [ IsSlicedPerm ], 0,
 function( perm )
 Print( "<perm word of length ", perm!.length, ">" );
endInstallOtherMethod( \/,"sliced perm", true, [ IsObject, IsSlicedPerm ], 0,

java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 14
 "ength","word", "ftObj, "opr" ]);

 od;
 function( p, perm )
 local i;

 for i in [ 1 .. perm!.length ] do
 p = java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 33
 od;
 return p;
end );

InstallMethod( PrintObj,"sliced perm", true Print( "<ermword of length " perm!length, ">" );
 java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 6
 of length ",perm!.length, ">" );
end );

InstallMethod( java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
 unction perm )
 Print( "<perm word of length ", perm!.length, ">" );
end );

#############################################################################
##
#F PreImageWord( , <word> ) . . . . . . preimage under sliced permutation
##
InstallGlobalFunction( PreImageWord, function( p, word )
 local i;

 for i in Reversed( [ 1 .. Length( word )
 p: p / word[[i];
 od;
 return p;
end )java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6

#############################################################################
##
#F ExtendedT( <t>, <pnt>, <img>, <G> ) . . prescribe one more image for <t>
##
InstallGlobalFunction( ExtendedTPrint( "permword of length ", perm!.length, ">" );
 local bpt,end )

 # Map the image with the part <t> that is already known.
 if simg=0 then img : img /t
 elsePrint <perm word length ", perm!.length, ">" );


 # = <img>.
 bpt := BasePoint##
 if bpt <> pnt then
 if pnt <>##
 returnfalse;
 fi;

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 return false;
 elif IsSlicedPerm( t ) then
len:=t!.ength;
 while img <> bpt do
 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 13
 edg Ijava.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 66
 img := img ^ edg bpt, len,edg;
# t!.rgtObj := t!.opr( t!.rgtObj, edg );
 t!.word ifsimg=0 img : img t;
 od;
 t!.length := len;
 elseelse img := simg; fi;
 If <G> fixes <pnt>, nothing more can be changed, so test whether <pnt>
 fi;

 return t;
end );

#############################################################################
##
#F MeetPartitionStrat( <rbase>,<image>,<S>,<strat> ) . meet acc. to <strat>
##
InstallGlobalFunction( MeetPartitionStrat return false;
local

 if Length( strat ) = 0 then return false;
 return false;
 IsSlicedPerm( t )then

 img>do
p stratdo
 if p[1] = 0 and
not(image p[] FixpointCellNoP [3 java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
 or p[1] <> 0 and
 SplitCell( P p[],S,p[2]g p[] ) <> p[3]then
 return false;
 fi;
 od;
 return true;
endod;

#############################################################################
##
#F StratMeetPartition( <rbase>, , <S>, <g> ) . construct a meet strategy
##
## Entries in <strat> have the following meaning:
## [p,s,i] (p<>0) means that `0 < |P[p]\cap S[s]/g| = i < |P[p]|',
## i.e., a new cell with points was appended to 
## (and these have been taken out of `P[p]'),
## [0,a,p] means that fixpoint <a> was mapped to fixpoint in `P[p]',
## i.e., `P[p]' has become a one-point cell.
##
InstallGlobalFunction( StratMeetPartition, function( arg )
 local local P p;
 g, # permutation such that meet <S> / <g> is constructed
, # R-base record, which records processing of fixpoints
 strat, # meet strategy, the result
 p return false;
 i, # result of call to `SpliltCell'

 P : image.artition;
 blist, #/ see explanation below
 splits,
 lS,
 cell, nrcells;

 if not IsPartition( arg[ 1 ] ) then rbase := arg[ 1 ]; p := 2;
 else rbase:=false; := 1 fi;
 P := or p[1] <>0 and
 S : arg[ p +1];
 if Length( arg ) = p + 2 then g := arg[ p + 2 ];
 else fi;
 strat := [ ];

 od;
 # `Set(cellsP{S[s]})' is the set of (numbers of) cells of that
 # contain a point from `S[s]/g'. A cell splits iff it contains points for
 # two such values of <s>.
 if #############################################################################
 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 2
 else
 java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 2
 for i in## [p,s,i] (p<>0) means that `0 < |P[p]\cap S[s]/g| = i < |P[p]|',
 cell := Cell( P, i );
 cellsP{ OnTuples(## i.e., `P[p]' has become a one-point cell.
 od;
 ;

 If <S> is just a set, it is interpreted as partition ( <S>|<S>^compl ).g, permutation such that meet <S> / <g> is constructed
 if IsPartition( S ) then
 nrcells := NumberCells( S ) - 1;
 lS:=S;
 else
 nrcells := 1;
 blist(1.P)] {S})java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
 p : p s # indices looping over the cells of resp. <S>
 if p <> fail
 ( blist,BlistList( 1. NumberCells(P )],
 cellsP Difference 1 . Length(Pcellno)] )} ));
 p := Position( blist splits,
 fi;
 lS:=S;
 S lS,
 fi;

 for s in [ 1 .. nrcells ] do
 java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
 if S=false then
 =arg[p]

 p:Cell(S);
 fi;
 p:=cellsP{p}; # the affected P-cells
 p=Collected(p);
 splits:=[];
 for i in p do
 # a cell will split iff it contains more points than are in the
 # s-cell
 if P.lengths[i[1]]>i[2] then
 (plits,i[1];
 fi;
 od;

 # this code is new, the extensive construction of blists in the old
 # version was awfully slow in larger degrees. ahulpke 11-aug-00
 for p in splits do
 # Last argument `true' means that the cell will split.
 i := SplitCell( P, p, lS, s, # two such values of <s>.
 cellsP .;
cell=Cell(P NumberCells))
 cellsP{ OnTuples( cell, g ) } := NumberCells( P ) + 0 * fori in [1 ..NumberCells( P ) ] do
 fi;

 if rbase <> false then
 Add( strat, [ p, s, i ] );

 # If we have one or two new fixpoints, put them into the
 # base.
 if i = then
 pnt := FixpointCellNo( P IsPartition( S ) then
 ProcessFixpoint - 1;
 Add( strat, [ :=;
 if IsTrivialRBase( rbase ) then
 return strat;
 fi;
 fi;
 if P.lengths[ p p: ( blist ;
pnt=,)
 ProcessFixpoint(blist ([1 .NumberCells ,
 Add cellsP{Difference .Length(c ,S) ;
 if IsTrivialRBase( rbase )

 fi;
 fi;

 fi;
# p := Position( blist, true, p );
 od;
 od;
 return strat;
end # now split with cell number s of S.

# the following functions are for suborbits given by blists, by element
 p:=lS;
InstallGlobalFunction(SuboLiBlifunction(an)
 if (b)then
 return [b];
 elif IsBlistRep(fi
Blist(ran,b);
 fi;
n b;
end);

InstallGlobalFunction(SuboSiBli,function(b)
 if IsInt(b) then
 return 1;
 elif IsBlistRep(b) then
 return SizeBlist(b);
 else
 return (plits,i[];
 fi;
end);

InstallGlobalFunction(SuboTruePos,function(ran,b)
 if od;
 # this code is new, the extensive construction of blists in the old
 elif # versionwas awfully slow in larger . ahulpke 11-aug-00
 return Position(,true)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 elif HasIsSSortedList(b)and IsSSortedList(b) then
 return Position(ran,MinimumList(b));
 else if IsOne g) then
 return First :Cell(P NumberCells( P) );
 fi;
end);

InstallGlobalFunction(SuboUniteBlist,function( fi;
 if IsInt(b) then
(ran,)]=true;
 elif IsBlistRep(b) then
 UniteBlist(a,b);
 else
 #UniteBlist(a,BlistList(ran,b));
 UniteBlistList(ran,a
 fi
end);

# sb is a list of length 3: [points,subs,blists]. The function returns a
# cell as sorted list of points
 pnt FixpointCellNo(P,NumberCells( P ) );
local b,i;
 if Length ProcessFixpoint(rbase, pnt );
 # blists are used
 :=hallowCopy(sb[]1)java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 for i in [2..Length(sb[3])] do
 UniteBlist(b,sb[3][i]);
 od
 UniteBlistList(ran,b,sb[1]);
 for i in sb[2 fi;
 UniteBlistList(ran,b,i);
 od;
 return ListBlist(ran,b);
 elif Length(sb[2])>0 then
 # blists are not used but worth using
 =sb[];
 for i in sb ,[, ])
 UniteBlistList( if IsTrivialRBase( rbase ) then
 od;
 return ListBlist(ran,b);
 else
 b:=ShallowCopy(sb[1]);
 for i in sb[2]do
 UniteSet fi;
 od;
 return b;
 fi;
end);

#############################################################################
##
#F Suborbits( <G>, <tofix>, , <Omega> ) . . . . . . . . . . . . suborbits
##
## Returns a record with the following components:
##
## domain: the set <Omega>
## stabChainTop: top level of stabilizer chain for $G_tofix$ (pointwise stabilizer) with
## base point <a> (may be different from )
## conj: an element mapping to <a>
## which: a list whose th entry is the number of the suborbit
## containing 
## lengths: a (not strictly) sorted list of suborbit lengths (subdegrees)
## byLengths: a list whose th entry is the set of numbers of suborbits of
## the th distinct length appearing in `lengths'
## partition: the partition into unions of suborbits of equal length
## The next three entries are lists whose <k> entry refers to the <k>th
## suborbit.
## blists: the suborbits as boolean lists
## reps: a transversal in <G> s.t. $a.reps[k]$ lies in the <k>th
## suborbit (reps[k] = `false' if this is impossible)
## orbitalPartitions:
## a list to store the `OrbitalPartition' for each suborbit in
##
java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
ix, b, Omega, , , bylen,
 G, GG, a, conj, ran, subs, all, k, pnt, orb, gen,
 perm, omega, P, cell, part, p, i, la
repte

 the arguments
 H (,();
 tofix := arg[ 2 ];
 b (1.(an]i>[i] in);
 Omega := arg[ fi
 java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0
 if b Positionb]:truejava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 part : true; ;

 G := java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 6
 :(aseStabChain))
 conj )

 # Replace <H> by the stabilizer of all elements of <tofix> except the
 # last.
 len =Length )
 b,;
conj : InverseRepresentative(G,tofixi])
 G used
 od;

 if len <> 0 then
 b := b ^
 java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 20
 else
 if not IsBound( H!.suborbits ) then
 =(s[1)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 fi;
 suborbits := H!.suborbits;
 fi;


#java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
 if not IsInBasicOrbit [2]
ptyStabChain]One ) b )
 AddGeneratorsExtendSchreierTree, . )java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
)
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 fi;
 a :=##

 rep:=InverseRepresentative(GG,b);
 rep2:=InverseRepresentative(GG,a)^-1##
 conj := conj * rep*rep2;

 # try whether a and b are in the same path
 #conj := conj * InverseRepresentative( GG, b ) /
 # InverseRepresentative( GG, a );## base point <a> (may be different from )

 ran := ## containing 
## byLengths: a list whose th entry is the set of numbers of suborbits of

 k:=1;
 The next three entries are lists ## suborbit.
 and (suborbits[k][1## suborbit (reps[k] = `false' if this is impossible)
 k:=k+1;
 od;
 , , , java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
java.lang.StringIndexOutOfBoundsException: Range [25, 23) out of bounds for length 32
 Info(java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 0
 else
 Info(InfoBckt,2,"nter suborbits ",ize,:";

 # Construct the suborbits rooted at <a>.
 # GG is a head of a stabilizer chain with base orbit containing = arg[3 ];
 # b with min elm a
 if not IsIdenticalObj(G,GG) then
 GG:=CopyStabChain( G );
 ChangeStabChain( GG, [ a ], false );
 te:=GG.transversal;
 stabgens:=GG.stabilizer.generators;
 0 then part := false;b :=[ 1]java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
 else
 G := StabChainMutableH)
 # now conjugate with rep, so that we get things based at 'a'
 rep2 maps the basepointto aa
 te:=ShallowCopy(G.transversal);
 te[
te]=G.identity;
 stabgens:=List(stabgens,i->i^rep2);
 fi;

 subsconj= G ;
 transversal:=te,
 ;
 domain =^java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 20
which : , ,
 reps := [ G.java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 9
 :=,
 lengths := [ 1 ],
 orbitalPartitions not (G,b then
 subs.lists[1]=ajava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 subs.which[ a ] := 1;
 IsRangeOmega)and1 inOmega java.lang.StringIndexOutOfBoundsException: Range [45, 46) out of bounds for length 45
all=,];
 else
);
 rep2java.lang.StringIndexOutOfBoundsException: Range [28, 22) out of bounds for length 28

 all : java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
 la:=Length k=()

 k := 1;
 pnt := Position( all, :+
 > java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 k :Info,"java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 45
 = ;
 all[ pnt ] := true;
 for p
 for gen in stabgens do
 i := p ^ gen;
 if # b with min
 Add(orb i );
 [ : true;
 fi;
 od;
 od;
 te=Gtjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 subs.whichjava.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 44
 #if IsInBasicOrbit( G, pnt ) then
nt]
 subs.reps[ k ] := true;
 subs.lengths[ k ] := Length( orb );
 else
#
 subs.reps[ k ] := false:List-r;

 fi;
 #UniteBlist( all, sublique );transversal=,
 if QuoInt(Length(ran),Length(orb))>100 thenidentity=.,
 if Length(orb)= : ListWithIdenticalEntries( Length(ran) ),
 subs.lists k] := orb[1];
 else
 subs.blists[ k ] := Immutable(Set(orb));
 fi;
 else
 subs.blists[ k lengths : [1 ],
 fi;
 if la=0 then
 pnt:.=;
 java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 29
 =,)
 fi;
 od;
 SubtractBlist java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 56

 la:=Length(all)-1;
 if :1java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
 for +;
 : java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 25
 od;
 suborbitsfor gen stabgensdo
 else
 if not [ ] then
 fi;

 fi;

 if part od;
 if not la=la-ength(rb)java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
(thisshouldjava.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 37
# subs.lengths := [ ];
# for k in [ 1 .. subs.sublilen ] do
# if subs.reps[ k ] = false then
# Add( subs.lengths, -SizeBlist( subs.blists[k] ) );
# else
# Add( subs.lengths, SizeBlist( subs.blists[k] ) );
# fi;
# od;
 java.lang.StringIndexOutOfBoundsException: Range [10, 1) out of bounds for length 13
 ifLength(),(orb)>100then

 # Determine the partition into unions of suborbits of equal length..[k ] =[1]
 subs .[ =Immutable(Setorb);

 fork in [1..Length( subs..engths ) ] do
 Append( cell, SuboLiBli( ran, subs.blists[ k ^ perm ] ) );
 AddSet( bylen fi;
 =Length( .engths )
 or subs. pnt:fail;
 Add( P, java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 14
 Add( subs.subs.sublilen:=Length(subs.)
 fi;
 od;
 if Length( omega ) Length(suborbits)>lthen
 Add( P, omega );
 fi;
 subs.suborbits:suborbits[+];
 fi;
 subs := [(][,subs;
 subs. (,[a,mega,ubs])
 return subs;
end );

#############################################################################
##
#F OrbitalPartition( <subs>, <k> ) . . . . . . . . . . make a nice partition
##
##
## ahulpke, added aug-2-00: If there are only one or two cells, the function
## will return just one cell (the partitions split functions can treat this
## as a special case anyhow).
InstallGlobalFunction# subs.lengths := [ ];
local dom, # operation domain for the group
 ran, # range including <dom>, for blist construction# if subs.reps[ k ] = false then
 d, # number of suborbits, estimate for diameter
 len, # current path length
 K, # set of suborbits <k> to process# od;
 Key perm :=Sortex subs.lengths ) ^ -1;
 key, # discriminating information for suborbit number <k>
 old, # farthest distance zone constructed so far
 new, # new distance zone being constructed
 img, # new endpoint of path with known predecessor
 o,i, # suborbit of predecessor resp. endpoint
 ,# pointsordered <ey , aspartition
 typ, (cell,SuboLiBli ran, subs.blists[ k ^ perm ] ) );
 sub, # suborbit as list of integers
 csiz,
 pos;

 if IsInt( k ) and IsBound( k = Length( subs.lengths )
 Info(InfoBckt,2,"Orbital partition ",k," cached or subs.[ k + 1 ]<>subslengths[ k then
 P:subs.orbitalPartitionsk];
 else
. Length( subs. )]);
 IsSSortedList(ran);
 d := subs.sublilen;
 if IsRecord( k ) fi;
 else K := [ k ]; Length omega ) <> 0 then
 : 0;
 for k in K do
 if IsList( ition : ( P);
 k := k[ 1 ;
 fijava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
 key := #############################################################################

 # Initialize the flooding algorithm for the <k>th suborbit.
 if IsInt( k##
 if subs.reps[ k ] = false then
 sub := 0;
 key[ k ] := -1;
 new := [ ];
 else
 sub :=SuboLiBli ran,subs.blists[ k ]);
 key[ k ] := 1;
 new := [ k ];
 fi;
 else
 #sub := ListBlist( ran, UnionBlist( subs.blists{ k } ) );
 if IsEmpty(k) then
 sub:[];
 else
 sub:=subs.blists[k[1] ,# set of <>toprocess
 if IsInt(sub) then
 sub:=BlistList(old # farthest distance zone constructed so far
 elif not new # new distance zone being constructed
 subjava.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 36

 subjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
 (.orbitalPartitions ])then
 foro2L(k) do
SuboUniteBlist(an,ubs.lists[k[])java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 ;
 sub:=ListBlistIsSSortedListran)java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
fi;

 key{ := 1 +0*k
: , -java.lang.StringIndexOutOfBoundsException: Range [44, 42) out of bounds for length 59
 fi;
 len =java.lang.StringIndexOutOfBoundsException: Range [39, 37) out of bounds for length 46

 if IsInt( k ) then
 >0do
 len := len + 1;
 :=java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19


 # Map the suborbit with each old representative.
 for o ;
 if #sub :=
 subsreps ]
 subs.reps[ o ] sub:=];
 SuboTruePossub:subs.blists1;
 fi;
 img inOnTuples(sub reps[o ])

 # Find the suborbit of the image. sub:java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 38
 i := subs.which[ img ;

 # If this suborbit is encountered for the first time, add
#it<> l>java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
 if key[ i ] = 0 then
 Addkey{k} : 1+0*k;
 [i ]:= len;
 fi;

 # Store the arrow which starts at suborbit <o>.
 key[o ]:= key[o +d*
 Length( sub ) ^ ( key[ i ] mod d );
 od;
 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
 Info(
 ;
 ;
 od;

 if sub <> 0 then
* (d+d*Length( + key;
 fi;
 od;

 # Partition <dom> into unions of suborbits w.r.t. the values of
 <Key>.
 if Key = 0 then

 if =.hich img]java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 subs.orbitalPartitions[ k ] := P;
 fi; # it to <new> and store its distance <len>.
 return P;
 else

#T1:=Runtime()-T1;
 typ := Set( Key );
 csiz# java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
 dom:=List(typ,i->[[],[],[]]);
 for i in [1..Length(Key)] do
 pos : (typ Keyi ;
 csiz[pos]:=csiz[pos]+AbsInt(subs.lengths[i]);
 if IsInt(subs.blistselse
 ([pos[1],ubs.lists[];
 elif IsBlistRep(subs. fi;
 Add(dom[pos][3]java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 Key ( d+ d *(sub)^ ) key;
 Add(dom[pos][2],subs.blistsfi
 fi;
 od;
 Sum(csiz)=Length(ubs.domain) Length(typ)=1 then
 P:=[];
 if IsInt( k ) then
 subs Key = 0 then
 IsInt(k )then
 return P;
 elif Sum(csiz)=Length(subs.domain fi;
 # only two cells
 # we need to indicate the first cell, the trick to take the sorted
 # one does not work
 P:=ConcatSubos(ran,dom[1]);
 java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
 subs.orbitalPartitions[ k ] := P;
 fi;
 return P;
 fi;

 P:=[];
 for pos in [1..Length(typ)] do
 sub := ConcatSubos( ran, dom[pos] );
 Add(P,sub);
 od;
#fi;
#T1:=Runtime()-T1;

 if Sum(List(P,Length)) <> Length(subs.domain) then
 # there are fixpoints missing
Add P, Difference(subs.domain,Union(P)));
 fi;

 fi;

 P := Partition( P );
 if IsInt k ) then
 subs.orbitalPartitions[ k ] := P;
 fi;

 Add([pos[3]subs.lists])
 return P;
end (dompos]2,ubs.lists[];

#############################################################################
##
#F EmptyRBase( <G>, <Omega>, ) . . . . . . . . . . . . initialize R-base
##
 ,,java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
 local rbase elif Sum(siz)=Lengthsubsdomain and Length(yp=2 then

 rbase := rec( domain := Omega,
 base := [ ],
 where := [ ],
 rfm := [ ],
 partition := StructuralCopy( P ),
 lev := [ ] );
 IsList G then
 if if IsInt ( k ) then
 . :=true;
 else
 rbase.
 rbase.lev2 := [ ];
 fi;
 G := G[ forpos [1.(typ)

 rbase.level2 := Add(s);
 fi;
# if IsSymmetricGroupQuick( G ) then
# Info( InfoBckt, 1, "Searching in symmetric group" );
# rbase.fix := [ ];
# rbase.level := NrMovedPoints( G );
# else
 .chain:= CopyStabChain ( G ))java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
 rbase.level := rbase.chain;
# fi;

 # Process all fixpoints in .
 for Fixcells(P) do
 .orbitalPartitions ] ;
 od;

 return rbase;
end );

#############################################################################
##
#F IsTrivialRBase( <rbase> ) . . . . . . . . . . . . . . is R-base trivial?
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 24
returnIsInt rbase.level )
 and rbase.level <= 1
 or IsRecord( rbase.level )
 and Length( rbase.level.genlabels =[ ],
end );

#############################################################################
##
#F AddRefinement( <rbase>, <func>, <args> ) . . . . . register R-refinement
##
( java.lang.StringIndexOutOfBoundsException: Range [24, 25) out of bounds for length 24
 if Length( args java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
 or not IsList( Last(args)
 or Length( Last(args) ) <> fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
 Addrbase=

 Info( InfoBckt, 1, "Refinement ", func, ": ",
 NumberCells( rbase.partition ), " java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 29
 fi;
end );

#############################################################################
##
#F ProcessFixpoint( <rbase>|<image>, <pnt> [, <img> ] ) . process fixpoint
##
## `ProcessFixpoint( rbase, pnt )' puts in <pnt> as new base point and steps
## down to the stabilizer, unless <pnt> is redundant, in which case `false'
## is returned.
## `ProcessFixpoint( image, pnt, img )' prescribes <img> as image for <pnt>,
## extends the permutation and steps down to the stabilizer. Returns `true'
## if this was successful and `false' otherwise.
##
InstallGlobalFunction( ProcessFixpoint, function arg )
 local rbase, image, pnt, img#############################################################################

 if Length( arg ) = 2 then
 rbase := arg[ 1 ];
 pnt := arg[ 2 ];
 if rbase.
 ChangeStabChain( rbaseand 0
 if BasePoint( #############################################################################
 rbase.#F AddRefinement( <rbase>, <func>, <args> ) . . . . . register R-refinement
 fi;
 fi;
 if IsInt( rbase.level ) or not IsList( ast(argsjava.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
 rbase.level := rbase.level - 1;
 else
 ChangeStabChain( args = args))
 BasePoint rbase. pnt
 rbase.level := (rbasep ,"cells ;
 else
 return false;
 fi;
 fi;
 else
 image := arg[ 1 ];
 pnt := arg[ 2 ];
 img := arg[ 3 ];
 if image.perm <> true ## extends the permutation and steps down to the stabilizer. Returns `true'
 if Length( arg )
 := 0 fi;
 : ExtendedT( image.perm, pnt, img, simg, image.level );
 if t = false then
 return false;
 Length arg )
 . : image.evels;
 fi;
 image.perm := t;
 fi;
2< false
 t .java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 65
 if t = false then
 return false;
 elif BasePoint( image.level2 ) =fi
 image.level2 (rbase.evel)then
 ;
 image.perm2 := t
 fi;
 fi;
 return ;
end ) rbase.: ..;

#############################################################################
##
#F RegisterRBasePoint( , <rbase>, <pnt> ) . . . . . register R-base point
##
InstallGlobalFunction( RegisterRBasePoint else
localO k lev;

 if
 Add lev2 rbase.evel2)
 fi;
 Add else java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 62
 Add( rbaset java.lang.StringIndexOutOfBoundsException: Range [26, 24) out of bounds for length 30
latePoint ,pnt)
 Info( InfoBckt, 1, image.level : image..java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 P.lengths[ k ] + 1,
 if not ProcessFixpoint( rbase, pnt ) then
fixed" );
 fi;
Add .here, ;
 Add( rbase.rfm, [ ] );
 if P.lengths[ k ] = 1 then
 pnt := elif BasePoint( imageBasePoint( image.evel2 ) = pnt then
 ProcessFixpoint( rbase, pnt );
AddRefinement rbase,STBBCKT_STRING_PROCESSFIX, [ pnt, k ] );
 fi;
 if rbase.level2 <> false then
 if rbase. p =;
 else
 end)
 O := #############################################################################
 strat := StratMeetPartition#F RegisterRBasePoint( , <rbase>, <pnt> ) . . . . . register R-base point
 AddRefinement(##
 fi;
 fi;
end );

#############################################################################
##
#F NextRBasePoint( , <rbase> [, <order> ] ) . . . find next R-base point
##
nstallGlobalFunction(NextRBasePoint, ( arg)
 local Add(rbase.,rbase. ;
 P, # partition of <Omega> to be refinedAdd .lev,.evel)
 order, # order in which to try the cells of <Omega>
 lensInfo ,1," , ( rbase.ase :" ,,,
 p, # the next point chosen
 k, l; # loop variables

 # Get the arguments.
 P := arg[ 1 ];
 ];
 if Length( arg ) > 2 java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 7
 else order := false; fi;

 # When this is called, there is a point that is neither fixed by

 lens := P.lengths;
 =fail;
 if order <> false then
 if IsInt( rbase.level ) then
 p := PositionProperty( order if rbase.evel2 > false then
 lens[ CellNoPoint(P,p ) ] <> 1 );
 else
 p := PositionProperty( else : rbase.level2;fi
 lens[CellNoPoint(P,p) < 1
 and not IsFixedStabilizer( rbase.level, p : OrbitsPartition(lev,rbase. );
 fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
 fi;

 if p <> fail then
 p := order[ p ];
 else
 lens := ShallowCopy( lens );
 order := [ 1 .. NumberCells( P ) ];
NextRBasePoint,(arg )
 k := local rbase, #-base be extended
 l := fail;
 whileorder order in which to try the cells of <Omega>whichtotrythecells >
(level
 l :=k ;# loop variables
 java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
 : PositionProperty
( Pfirsts[ order[k] ]-1 +[1..lens[k ] ]java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
i -> not IsFixedStabilizer( rbase.level,
 P.points[ i ] ) );
 fi;
 k
 od;
 p := P.points[ P.firsts <rbase.level> nor in .
 fi;

 RegisterRBasePoint( P, rbase if order < falsethen
end );

#############################################################################
##
#F RRefine( <rbase>, <image>, <uscore> ) . . . . . . . . . apply refinements
##
InstallGlobalFunction( >1)java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
local Rf, t;

 if not uscore then
 for Rf in rbase.rfm[ and not IsFixedStabili( rbase.evel,p))
 t := java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 11
 ( [ rbasejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 if java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 elif t <> true then return =1 . ;
 ;
 ;
 java.lang.StringIndexOutOfBoundsException: Range [8, 4) out of bounds for length 18
 for Rf in rbase (l then
 if Rf.func[ 1 ] = '_' then
 t := CallFuncList( Refinements.( Rf.func ), (P.irsts[ rder ] - 1+[1. lens[ k]]
 ([rbase,image] . ) );
 if t = false then return fail;
 elif t <> true then return t; java.lang.StringIndexOutOfBoundsException: Range [12, 46) out of bounds for length 15
 ;

 returnjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
 ;

 #old code
 for #############################################################################
 if not uscore or Rf.func[ 1 ] = '#F RRefine( <rbase>, <image>, <uscore> ) . . . . . . . . . apply refinements
 t := CallFuncList( Refinements.Rf t;
 ( [ not then
 if t = false then return t := CallFuncList( Refinements.( Rf.fujava.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
 elif t < true t fi
 ;
 ;
 return true;

end );

#############################################################################
##
#F PBIsMinimal( <range>, <a>, , <S> ) . . . . . . . . . . minimality test
##
InstallGlobalFunction( PBIsMinimal if Rf.[ 1 ]='' then
 local , , , l, ;

 IsInBasicOrbit(S, then
 return ForAll( S.if t=false then ;
 elif b < a then return false;
 elif IsFixedStabilizer( S, java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 old := Rf in rbase.fm . do
 for pnt in orb do
 for l in Sgenlabelsdo
 img := pnt ^ S.labels[ l ];
 if not old[ img ] then
 img <a
 return false;
 fi;
 old img]: true;
 Add( orb, img );
 fi;
 od; ;
 od;
 return true;
);

#############################################################################
##
#F SubtractBlistOrbitStabChain( <blist>, <R>, <pnt> ) remove orbit as blist
##
InstallGlobalFunction SubtractBlistOrbitStabChain(blist,R,pnt )
 local orb, gen, img;

 orb := [ pnt ];
 blist[ pnt ] := false;
 for pnt in orb do
 java.lang.StringIndexOutOfBoundsException: Range [20, 15) out of bounds for length 36
 img := pnt ^ gen;
 [ img
 java.lang.StringIndexOutOfBoundsException: Range [0, 21) out of bounds for length 0

 fi;
 od;
 od;
end );

#############################################################################
##
#F PartitionBacktrack( <G>, <Pr>, <repr>, <rbase>, <data>, <L>, <R> ) . . .
##
InstallGlobalFunction( PartitionBacktrack,
 function( G, Pr, repr ( orb,img)
 local PBEnumerate,od;
 blen, # length of R-base
 rep, # representative or `false', the result
 branch, # level where $Lstab\ne Rstab$ starts
 image, # image information running through the tree
 , # old value of <image.partition.cellno>
 # intersected (mapped) basic orbits of <G>

 # range for construction of <orb>
 fix, fixP, # fixpoints of partitions at root of search tree
 prm,#
 nrback, # backtrack counter
 bail, # do we want to bail out quickly?if blist[img]
 i, dd, p; # loop variables

#############################################################################
##
#F PBEnumerate( ... ) . . . . . . . recursive enumeration of a subgroup
##
 PBEnumerate := function( d, wasTriv )
 local undoto, # number of cells of wanted after undoing
 oldprm, #\
 ,Pr ,,data ,R)
 a R-ase point
 m,blen,
 maxrep, representative`false,
 b, # image of base point currently being considered
 t; # group element constructed, to be handed upwards

 if,#
 return
 fi;
 image.depth := d;

 i, dd, p; # loop variables
 undoto := NumberCells( image.##
 if image.perm = java.lang.StringIndexOutOfBoundsException: Range [0, 28) out of bounds for length 2
 oldcel := image.partition;
 else
 oldcel := image.partition a base
 if IsSlicedPerm( image.perm ) , # maximal number of candidates
 else oldprm := image;# group element constructed, to be handed upwards
 java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 fi;
 if image.level2 <> false then oldprm2 := image.perm2;
 else oldprm2 := false; fi;

 # Recursion comes to an end if all base points have been prescribed
 # images.
 if d >(image.erm then oldprm: image..ength
if( rbase then
 blen := Length( rbase.base );

 # Do not add the identity element in the subgroup
 # construction.
 if wasTriv then

 # In the subgroup case, assign to <L> and <R> stabilizer
 # chains when the R-base is complete.
 L := ListStabChain( CopyStabChain( StabChainOp( L,
 rec( rec( base
 reduced # construction.
 R := ShallowCopyjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

 if image.perm <> true then
 Info( InfoBckt, 1, "Stabilizerrec( base =rbase
 DepthSchreierTrees( rbase.chain ) );
 fi;
 Info( InfoBckt, 1, "Indices: ",
 IndicesStabChain( L[ 1 ] ) );
 return fail;

 else
 = true then
 prm := MappingPermListList
 ( rbase.fix[ Length( rbase.base ) ],
 fail
 else
 prm := image.perm;
 fijava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
 image.level2 < false then
 prm := UnslicedPerm@( prm ) Fixcells( image.partition )
 if SiftedPermutation( image prm : image.perm;
 prm / UnslicedPerm@( image.perm2 ) )
 = image.level2.identity then
 return prm;
 fijava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
 elif Pr( prm ) then
 return UnslicedPerm@( prm );
 fi;
 return fail;
 fi;

 # Construct the next refinement level. This also initializes
 # <image.partition> for the case ``image = base point''.
 else
 if not repr then
 oldcel := # <image.partition> for
 fi;
 rbase.nextLevel( rbase. oldcel := StructuralCopy( ol
 image.erm then
 Addrbase.ix ( rbase.artition))java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
 fi;
 Add( org, ListWithIdenticalEntries( Length( range ), 0 ) );
 Length( ,0));

 # In the representative case, change the stabilizer

 ChangeStabChain( L[ d ], [ rbase.base[ d ] ], false );
 L[ d + 1 ] := L[ d ].stabilizer;
 ChangeStabChain( [ ,[rbase.ase[]] ;
 R[ d [ d+ 1 ]: L d .stabilizer;

 fi;
 fi;

 fi;
 a := rbase.base[ d ];
 fijava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15

 # Intersect the current cell of with the mapped basic orbit of
 # <G> (and also with the one of <H> in the intersection case).
 ifimage.perm =true then
 orb[ d ] := BlistList( range, Cell( oldcel, rbase.where[ d ] ) );
 if java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 0
 b := Position( java.lang.StringIndexOutOfBoundsException: Range [70, 36) out of bounds for length 70
 [d ]: BlistList range,Cell oldcel,rbasewhere d ] ));
 IsInBasicOrbit rbase.lev2[ d ], b/image.perm2 )
 then
 orb[ d >
 fi;
 b := Position( orb[ d orb[ d][b ]:=false;
 od;
 fi;
 else
 orb[ ;
 for p in rbase.lev[ d ].orbit do
 b := p ^ orb[ d ] := BlistList d] := BlistList(range, [ ] );
 if oldcel[ b ] = rbase.where[ d ]
 (imagelevel2 false
 orb :p^image.erm
 orb[ if oldcel[b ]=.where[d]
 org[ d ][ b ] := p;
 fi
 od;
 fi;
 if d=1 and org[d ][ b ] := p;
 orb[d][a]:=true; # ensure a is a possible image (can happen if
 # acting on permutations with more points)
 od;

 orB[ d ] := StructuralCopy( fi

 # Loop over the candidate images for the current base point. First[]a]=;# ensure a is a possible image (can happen if
 # the special case ``image = base'' up to current level.
 if wasTriv
 image.bimg ]:;

 # Refinements that start with '_' must be executed even when base
 # = image since they modify `image.data' etc.
 RRefine( rbase, image, true );

 # Recursion.
 PBEnumerate( d + 1, true );
 image RRefine(rbase,image,true ;

 # Now we can remove the entire <R>-orbit of <a> from the
 # candidate list.
 SubtractBlist( orb[ d

 fi;

# Only the early points of the orbit have to be considered.
 m := SizeBlist( orB[ d ] fi
 if m < Length( L[ d ].orbit
 return fail;
 fi;
max:PositionNthTrueBlist( orB[ d ],
 m - Length( L[ d ].orbit ) + 1 );
 if wasTriv and a > max then
 m:=m -1;
 if m < Length( L[ d ].orbit ) then
 return fail;
 fi;
 java.lang.StringIndexOutOfBoundsException: Range [47, 39) out of bounds for length 50
 m if <Length [d.orbit)then
 fi;

 # Now the other possible images.
 b := Position( orb[ d ], true );
 if b <> fail and b > max max := PositionNthTrueBlist( [ d ],
 b := fail;
 ;
 while b <> fail do

 # Try to prune the node with prop 8(ii) of Leon's paper.
ifnot andIsBound [d ].rbit ) then
 dd: branch;
 while dd < b : failjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
 if IsInBasicOrbit( L[ java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
(range R[dd ]orbit 1] ,R[d then
 Info( InfoBckt, 3, d, ": point ", b,
 " pruned by (L[dd] a not PBIsMinimal
 dd:=d+1
 else
 dd := dd + 1;
 fijava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
 odjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
 else
 dd := d;
 fi;

 if dd = d then

 # Undo the changes made to <image.partition>, <image.level>
 # and <image.perm>.
 for i in [ java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
 UndoRefinement( image.java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 0
 od;
 . < true then
 image.level := rbase.lev[ d . )
 if IsSlicedPerm( image.perm ) ifimage.erm<
 p!l : oldprmjava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
the code rgtObj used avoidmultiplication
 # of permutations. It has been commented out for a long time, but accidentally remained
 # documented in `doc/ref/stbchain.xml` until its withdrawal in 2018.
# image.perm!.rgtObj := oldrgt;
 else
 image.perm := oldprm;
 fi;
 fi;
 if image.level2 <> false then
 image.level2 := rbase.lev2[ d ];
 image.perm2 := oldprm2;
 fi ;

 If<> java.lang.StringIndexOutOfBoundsException: Range [58, 57) out of bounds for length 77
 # refinement was impossible, give up for this image.
 []:java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 (. )java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51

 if ProcessFixpointjava.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 51
#Error(a," ",b," ",Cells(rbase.partition),Cells(image.partition));
 t =( ,)java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
 else
 t := fail;
 fi;

 if t <> fail then

 # Subgroup case, base <> image at current level: <R>,
 # without affecting <L>, so take a copy.
 # without affecting <L>, so take a copy.
 if wasTriv and IsIdenticalObj( L[ d ], R[ d ] ) then
 R{ [ d .. Length( rbase.base ) ] } := List {[d. Length(rbase. )]}: Listjava.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
 L{ [ d .. Length( rbase.base ) ;
 if 2* then
 ;

 if 2 * d <= [d+1 ]: [d]java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
 ChangeStabChain( R[ d ], [ b ], false );
 R[ d + 1 ] := R[ d ].stabilizer;
 else
 if IsBound( R[ d ].stabilizer ) then
 R[ d + 1 ] := ( R[ d + 1 ], gen -> b ^ gen
 (, ," java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 56
fi

 R[ d + 1 ] := rec( generators if
(R d 1] ;
 fi;

 else
 Info( InfoBckt, 5, d, ": point ", b,
 " prunedfi;
 fi;

 # Recursion.
 if t = true then
 t := PBEnumerate( d + 1, false );
 nrback:=nrback+1;
 if bail and nrback>500 then
 return infinity; # bail out, this will bail out
 # recursively
 fi;
 image.depth := d;
 fi;

 # If <t> = `fail', either the recursive call was # know the stabilizer of <L> at an earlier level.
 # unsuccessful, or all new elements have been added to
 # levels below the current one (this happens if base =
 # image up to current level).
 if t <> fail then

 # Representative case, element found: Return it.
 # Subgroup case, base <> image before current level: We
 # need only find a representative because we already
 # know the stabilizer of <L> at an earlier level.
 if repr or not wasTriv then
 return t;

 # Subgroup case, base <> image at current level: Enlarge
e <max> accordingto
 # enlarged <L>. Reset <R> to the enlarged <L>.
 else
 ;
 ( [dd] ])
 od;
 (InfoBckt, 1"Level ", d
 ": ", IndicesStabChain( L[ 1 ] ) );
]orbit ) then
 return fail;
 fi return fail;
 max := PositionNthTrueBlist( orB[ d ],
 m - Length( L[ d ].orbit ) + 1 m - Length(L d].orbit ) +1)java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
R[d .Length(rbasebase)]}: List(
 L{ [ d .. Length( rbase.base ) ] }, CopyStabChain );
 fi;

 fi;

 # Now we can remove the entire <R>-orbit of from the
 # candidate list.
 if IsBound( R[ d ].translabels )
 and IsBound( R[ d ].translabels[ b ] ) then
 SubtractBlist( orb[ d ],
 BlistList( range, R[ d ].orbit ) );
 else
 SubtractBlistOrbitStabChain( orb[ d ], R[ d ], b );
 fi;

 fi;

 b := java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 0
 if b <> fail and b > max then
 b := fail;
 fi;
 od;

 return fail;
 end;

##
#F main function . . . . . . . . . . . . . . . . . . . . . . . . . . . .
##

 nrback:=0; # count the number of times we jumped up
 bail:=repr and ValueOption("bailout")=true;

 If necessary, convert <Pr> from a list to a function.
 if IsList( bail:=repr and Valu:reprand ("")true
 and ( IsTrivial( G )
 #or IsSymmetricGroupQuick( G )
 ) then
 obj := rec( lftObj := Pr[ 1 ],
# rgtObj := Pr[ 2 ],
 opr := Pr[ 3 ],
 =Pr[4 ];
 Pr := gen -> obj.prop
 ( rec( lftObj := obj.lftObj
# ,
# rgtObj := obj.opr( obj.rgtObj, gen ^ -1 )
 ) ) rec(lftObj : lftObj
 )

 # Trivial cases first.
 if IsTrivial( G ) then
 IsTrivial( G ) then
 elif Pr( One( G ) ) then return One( G );
 else return fail; fi;
 fi;

 # Construct the <image>.
 image := rec( data := data,
 bimg := [ ],
 depth :
 if repr then # Construct the <image>.
 else image. : rbase.partition ;
if ( rbase. )then
 image.level2 := false;

 image.level2 := rbase.level2;
 image.perm2 := rbase.level2.identity;
 fi;

 # If <Pr> is function, multiply permutations. Otherwise, keep them
 # factorized.
# if IsSymmetricGroupQuick( G ) then
# image.perm := true;
# else
 if IsList( Pr ) then
 image.perm := Objectify
 ( NewType( PermutationsFamily, IsSlicedPerm ),
 rec( length IsList(Pr)then
: Pr[1]java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
# image.perm!.rgtObj := Pr[ 2 ];
 image.perm!. rec( ength :=0,word:= [ ]) )java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
 Pr =Pr 4];
 else
 image.perm := One( G );
 fi;
 image.level := rbase.chain;
# fi;

 if repr then

 # In the representative case, map the fixpoints of the partitions atimage.level:=rbase.;
 # fi;
 if rbase.partition.lengths <> image.partition.lengths if repr then
 image.perm := false;
 else
fix: Fixcells( rbase.partition );
 fixP := Fixcells( image.partition );
 for i in [ 1 .. Length( fix ) image.perm : false;
 ProcessFixpoint( image, fix[ i ], fixP[
 java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
 fi

#java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
 # chains.
 L := ListStabChain;
 R := ListStabChain( CopyStabChain(

 fi;

 org : [] orb :[] : ;
 range := [ 1 .. Last(rbase.domain) ];
 L:=ListStabChain( CopyStabChain( StabChainImmutable( L ) ) );
 rep := PBEnumerate( =(( );
 if fi;
 ReduceStabChain( L org: ; =[] =[ ;
L[ , ;
 else
 return rep;
 fi;
end );

#############################################################################
##
#F Refinements.ProcessFixpoint( <pnt>, <cellnum> ) . . . process a fixpoint
##
InstallGlobalFunctionend )java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
function( rbase, image, pnt, cellnum )
 local img;

 img := FixpointCellNo(InstallGlobalFunction(Refinements_ProcessFixpoint,
 return ProcessFixpoint( image, pnt, img );
end);
Refinements.(STBBCKT_STRING_PROCESSFIX): Refinements_ProcessFixpoint;

#############################################################################
##
#F Refinements.Intersection( <O>, <strat> ) . . . . . . . . . . second type
##
InstallGlobalFunction(Refinements_Intersection
function( ProcessFixpointimage img)
local t;

 if image.level2 = false then t := image.perm;
 else): ;
 if IsSlicedPerm( t ) then
 t := ShallowCopy( t );
 SET_TYPE_COMOBJ( t, NewType( PermutationsFamily, IsSlicedPermInv )#
 else
 t := t ^ -1;
 i
 return local t tjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14

Refinements.(STBBCKT_STRING_INTERSECTION) := else t := image.perm2t =image.erm2 ;

#############################################################################
##
#F Refinements.Centralizer(<no>,<g>,<pnt>,<strat>) . P meet Pz for one point
##
InstallGlobalFunction(Refinements_Centralizer,
( ,,pnt )
 local P, img;

 : image.artition
 img := FixpointCellNo java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 59
 IsolatePoint ,
 and#############################################################################
end)#F Refinements.Centralizer(<no>,<g>,<pnt>,<strat>) . P meet Pz for one point
Refinements): ;

#############################################################################
##
#F Refinements._MakeBlox( <rbase>, <image>, <len> ) . . . . . . . make blox
##

function( rbase, image, len )
 local F;

 F := image.data[ 2 ];
 image.data[ 4 ] := Partition( java.lang.StringIndexOutOfBoundsException: Range [0, 40) out of bounds for length 5
 image.bimg{ [ 1, len ] } ) );
 return Collected( rbase.blox.lengths ) =
 Collected( image.data[ 4 ].lengths );
end);
Refinements.(STBBCKT_STRING_MAKEBLOX) := Refinements__MakeBlox;

#############################################################################
##
#F Refinements.SplitOffBlock( <k>, <strat> ) . . . . . . . . split off block
##
InstallGlobalFunction(rbase, image len )
(, k )
 local B, a,

 B := image.data[ 4 ];
 a := FixpointCellNo( image.partition, k );
 orb =Cell B, CellNoPointBa )
 if Length( orb ) = Length( rbase.domain ) then
 return false;
 else
 return MeetPartitionStrat( rbase, image, orb, (),strat );
 fi;
end)#############################################################################
Refinements.(STBBCKT_STRING_SPLITOFF) := #F Refinements.SplitOffBlock( <k>, <strat> ) . . . . . . . . split off block

#############################################################################
##
#F Refinements._RegularOrbit1( <d>, <len> ) . . . . . . extend mapped orbit
##
## Computes orbit and transversal `bF' for group <F> = `data[6]' regular on
## that orbit.
##
InstallGlobalFunction(Refinements__RegularOrbit1,
function( rbase, image, d, len )
 F, treesjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22

 trees := image
 if d = 1 then
 F := image.data[ 6 ];##
 image.regorb := EmptyStabChain( [ ], One( F ), image## that orbit.
 AddGeneratorsExtendSchreierTree( image.regorb,
 GeneratorsOfGroup( F ) );
Length(image.)< (rbaseregorb.rbit) then
 returnfunction ,java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 32
 fi;
 trees[ d ] := EmptyStabChain( [ ], One( F if =1 then
 .regorborbit[1 ]);
 else
 trees[ d ] := StructuralCopy( trees[ d - 1 ] );
 AddGeneratorsExtendSchreierTree( trees[ d ],
 [ QuickInverseRepresentative
 .egorb .img[d] )^- ;
 if GeneratorsOfGroup(F) ;
 return false;
 fi;
 fi;
 return true;
end);
() = Refinements__RegularOrbit1java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67

#############################################################################
##
#F Refinements.RegularOrbit2( <d>, <orb>, <strat> ) . . . meet mapped orbit
##
## Compute images `bhg' of `bh' under $g$ in `trees[<d>].orbit = bE$ ($h\in
## E$).
## Entries in <strat> have the following meaning:
## [i,j] means that the image `bhg\in P[j]' of `bh = orb[]' can be
## calculated from `bg'.
## [-p,j] means that fixpoint was mapped to fixpoint in `P[j]',
## i.e., `P[j]' has become a one-point cell.
##
InstallGlobalFunction(Refinements_RegularOrbit2,
function( rbase, image, d, orbit##
 local P, trees, orb, i;

 P := image.partition;
 trees := ## Entries in <strat> have the following meaning:
 orb := trees[ d ].orbit;
 for i in strat do
 if ( i[ 1 ] < 0
 and not ProcessFixpoint( image, -InstallGlobalFunction(,
 or ( i[ 1 ] > 0
 and ( IsolatePoint( P, orb[ i[ 1 ] ] ) <> i[ 2 ]
 or not ProcessFixpoint( image, orbit[i[1]], orb[i[1]] ) ) :image.ata 5 ];
 then return false;
 fi;
 od;
 return true;
end);
=Refinements_RegularOrbit2;

#############################################################################
##
#F Refinements.RegularOrbit3( <f>, <strat> ) . . . . . find images of orbit
##
## Register images `yhg' of `yh' under $g$ in an arbitrary orbit `yE' ($h\in
## E$). `yg\in P[f]' is a one-point cell.
## Entries in <strat> have the following meaning:
## [yh,i,j] means that the image `yhg\in P[j]' of `yh' can be calculated
## from `yg' and `bhg\in P[i]' (a one-point cell).
## [-p,j] means that fixpoint was mapped to fixpoint in `P[j]',
## i.e., `P[j]' has become a one-point cell.
##
InstallGlobalFunction(Refinements_RegularOrbit3,
function( rbase, image, f, strat )
 local P, yg, bhg, hg, yhg, i;

 P := image.partition;
 yg := FixpointCellNo( P, f );
 for i in strat do
 if i[ 1 ] < 0 then
 if not ProcessFixpoint( image, -i[1], FixpointCellNo## [yh,i,j] means that the image `yhg\in P[j]' of `yh' can be calculated
 then
 return false;
 fi;
 else
 bhg := FixpointCellNo( P, i[ 2 ] );
 java.lang.StringIndexOutOfBoundsException: Range [51, 44) out of bounds for length 66
 yhg := PreImageWord( yg, :,java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
 i[1 0 then
notProcessFixpoint( image, i[ 1 ], yhg ) then
 return false;
 fi;
 fi;
 od;
 return true;
end);
.): Refinements_RegularOrbit3

#############################################################################
##
#F Refinements.Suborbits0( <tra>, <f>, <lens>, <byLen>, <strat> ) subdegrees
##
## Computes suborbits of the stabilizer in <F> = `image.data[2]' of the
## fixpoint in cell no. <f>. (If <F> is multiply transitive, replace it by
## the stabilizer of the first <tra>-1 images of R-base points.)
##
## Returns `true' if (1)~the list of suborbit lengths (subdegrees) equals
## <lens>, (2)~the list of subdegree frequencies equals <byLen> and (3)~the
## meet with the partition into unions of suborbits of equal length
## succeeds.
##
InstallGlobalFunction(Refinements_Suborbits0,
function( rbase, image, tra, f, lens, byLen, java.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 2
 Fjava.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 27

 F :, pntjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
 pnt := FixpointCellNo( image.partition
 subs : Suborbits( , imagebimg{[1.tra -1]} ,
 rbase.domain );
 if subs.lengths.;
 or List( subs.byLengths, Lengthif .engths<>
 ;
 else
 return MeetPartitionStrat( rbase, image, subs.partition, MeetPartitionStrat rbase, .partition,c
 strat );
 fi;
endend));
Refinements.(Refinements.(STBBCKT_STRING_SUBORBITS0.STBBCKT_STRING_SUBORBITS0):=Refinements_Suborbits0;

#############################################################################
##
#F Refinements.Suborbits1( <rbase>, <image>, <tra>, <f>, <k>, <strat> ) . .
##
## Meets the image partition with the orbital partition of the union of
## orbital graphs of suborbits of length `subs.byLengths[ <k> ]'. (<tra> and
## <f> as in `Suborbits0'.)
##
InstallGlobalFunction(Refinements_Suborbits1##
function( rbase, image, tra, f,,tra , java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
localF , subs, Qjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31

 F := image.data[ 2 ];
 pnt := FixpointCellNo( image.partition, f );
 subs := Suborbits( F, image.bimg{ [ 1 .. tra - 1 ] }, pnt,
 rbase. Q := OrbitalPartition( subs,[ ] );
Q=OrbitalPartitionsubs [k ] ;
 return MeetPartitionStrat( rbase, image, Q, subs.conj, strat );
end);
Refinements.(STBBCKT_STRING_SUBORBITS1) := Refinements_Suborbits1;

#############################################################################
##
#F Refinements.Suborbits2( <rbase>, <image>, <tra>, <f>, <start>, <coll> ) .
##
## Computes for each suborbit the intersection sizes with cells <start> or
## more in the image partition. Stores the result in `data[3]' (needed only
## on this level, hence no '_'). Returns `true' if the collected result
## equals <coll>.
##
 F ,,subs ,k
function( rbase, image, tra, f, start, coll )
 local .[2 ;

 F := image =Fb{ . ,pntjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
 pnt := FixpointCellNo( image. image.data[ 3 ] := List( subs- ;
 subs := Suborbits( F, image .java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 61
 .domain );
 if start = 1 then
 image.data[ 3 ] := List( subs.blists, o -> [ -SuboSiBli( o ) ] AddSet( [ k],i )java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
 fi;
 types := image.data[ 3 ];
 Refinements() : Refinements_Suborbits2
 for k in Set( subs.which
 { OnTuples( Cell( image.partition, i ), subs.##
 AddSet( types[ k ], i );
 od;
 od;
 return Collected( types ) = coll;
end);
Refinements.(STBBCKT_STRING_SUBORBITS2) := Refinements_Suborbits2InstallGlobalFunction(Refinements_Suborbits3,

#############################################################################
##
#F Refinements.Suborbits3( <rbase>, <image>, <tra>, <f>, <typ>, <strat> ) .
##
## Meets the image partition with the orbital partition of the union of
## orbital graphs of suborbits of type <typ>. Returns `false' if there are
## not <many> of them. (<tra> and <f> as in `Suborbits0'.)
##
Length > java.lang.StringIndexOutOfBoundsException: Range [32, 33) out of bounds for length 32
function( rbase, Q := OrbitalPartition,k;
 ,types k java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43

 F := image.data[ 2 ];
 types := image.data[ 3 ];
 pnt := FixpointCellNo( #############################################################################
 subs := Suborbits( F, <G>, <Q>, <d>, <strat> ) . . . . . . two-closure
 rbase.domain );
 k := Filtered( [ 1 .. subs.sublilen ], k -> types[ k ] = typ );
 if Length( k ) <> many then
 return java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 0
 =InverseRepresentative rbase.uborbits.stabChainTop,pnt ;
 Q := OrbitalPartition( subs, k mage,Q, , strat );
 return MeetPartitionStrat( rbase, image, Q, subs.conj, strat );
 fi;
end).STBBCKT_STRING_TWOCLOSURE=efinements_TwoClosure;
Refinements.(STBBCKT_STRING_SUBORBITS3) := Refinements_Suborbits3;

#############################################################################
##
#F Refinements.TwoClosure( <G>, <Q>, <d>, <strat> ) . . . . . . two-closure
##
 ,,yh ,bh, ;
function( rbase =
 local pnt, #java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77

 pnt := FixpointCellNo( image if 1then
t=InverseRepresentative( ..stabChainTop,pnt)java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
 return MeetPartitionStrat( rbase, image, Q, t , java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
end
Refinements.(STBBCKT_STRING_TWOCLOSURE):=Refinements_TwoClosure;

#############################################################################
##
#F NextLevelRegularGroups( , <rbase> ) . . . . . . . . . . . . . . local
##
InstallGlobalFunction( NextLevelRegularGroups, java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 45
local , b , tree strat,i,j,p
 S, f, y, =QuickInverseRepresentative .egorb, ^-1;

 d := LengthAddGeneratorsExtendSchreierTree( tree, [ gen ] );
 p := fail;

 All images of a regular orbit are known if $s$ are known (where the
 # regular group has $s$ generators). See sec. 3.7 of my thesis, read `b'
 # for `\omega'.
 if d = 1 then
 p := rbase.regorb.orbit[ 1 ];
, ;
 rbase.trees := [ EmptyStabChain( [ ], rbase.regorb.identity, p ) ];
 AddRefinement( rbase, STBBCKT_STRING_REGORB1, [ d, 1 ] );
 else
 tree := Last(rbase.trees);
 if Length( tree.orbit ) < Length( rbase.regorb.orbit ) then
 p := =1then
 P.lengths[ CellNoPoint(rbase java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
 ( IsInt rbase.level )
 or not IsFixedStabilizer( rbase.level, q ) ) );
 java.lang.StringIndexOutOfBoundsException: Range [30, 31) out of bounds for length 30
 b := rbase.regorb.orbit Add(rbase., tree)java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
 RegisterRBasePoint( P, ,strat ] );
 gen := QuickInverseRepresentative( rbase.regorb, b ) ^ -1;
 tree := StructuralCopy( tree );
 AddGeneratorsExtendSchreierTree( tree, [ gen ] );
 AddRefinement( rbase, STBBCKT_STRING_REGORB1,
 [ d, java.lang.StringIndexOutOfBoundsException: Range [0, 35) out of bounds for length 11
java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 30
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 j := IsolatePoint( P, tree.orbit[ i ] );
 if j <> false then
 ProcessFixpoint( rbase, tree.orbit[ i ] );
 Add( strat, [ i, j ] );
 if P.lengths[ j ] = 1 then
 : ,)
 ProcessFixpoint( rbase, p );
 Add( strat, [ -p, j ] );
 fi;
 fi;
 od;
 Add((S .;
 AddRefinement( rbase, STBBCKT_STRING_REGORB2 strat :=[ ;
 [ d, tree.orbit, strat ] );
 fi;
 fi;
 fi;
 if p = fail then
 i := CellNoPoint,h;
 fi;

image<java.lang.StringIndexOutOfBoundsException: Range [67, 66) out of bounds for length 76
 # See sec. 3.7 of my thesis, read `y' for `\gamma'.
 fix := Set( CellNoPoints(P,rbase.regorb.orbit ProcessFixpoint( rbase, yh );
 f : ( strat, [yh i j]);
 while < do
 y := FixpointCellNo : FixpointCellNo , )
 S := EmptyStabChain( [ ], rbase.regorb.java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
 # ^ rbase.regorb.labels

 UniteSet(fix,CellNoPoints(P,S.orbit));
 strat := [ ];
 for in .orbit
 h := InverseRepresentativeWord( S, yh );
 bh := PreImageWord( rbase.regorb.orbitodjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
 i := CellNoPoint(P,bh);
 if :GOmegajava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
 j := IsolatePoint( P, yh );
 if j <> false then
 , java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
 Add( strat, [ yh, i, j ] )#############################################################################
 if P.lengths[ j ] = 1 then
 p Ijava.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 86
 ( ;
 Add( strat, [ -p, j ] );
 java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
 fi;
 fi;

 AddRefinement ,#degree java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 54
 len ;
 od;

end );

BindGlobal("STBCTEARNS",function(G,Omega)
 G=(,Omega);
 if Length(G)=0 then return fail;
 elif Length(G)=1 then return G[1];
 else Error("more than one Earns");fi;
end);

#############################################################################
##
#F RBaseGroupsBloxPermGroup( ... ) . . . . . opr. on groups respecting blox
##
InstallGlobalFunction# Find the order in which to process the points in the base choice.
 local NumberCells( ) 1
 order,max,L,# order in which to process the base pointsorder :=false;
 min,l,#
 n, # degree of <G>
 reg, orbs, # regular subgroup of <E> or `false'
 doneblox, # blox already considered
rootsof graphs alreadyconsidered
 tra, # degree of transitivity of <E>
 cp,
 len, i;

 # If <E> is a multiply transitive subgroup of <G>, consider orbital
 # graphs of the first non 2-transitive stabilizer.
 tra := Transitivityorder =( E) ;
 if tra = 0 then
 tra := 1;
eliftra 1
 Info( t an -. Startwiththepartitioninto<>orbits
 fi;

 # Find the order in which to process the points in the base choice.
 if NumberCells( B ) = 1 then
 order := false;
 else
 =(;
inityi=0java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
 while i : ,Omega;
 reg := Po(orbs, - ( orb ) Size( E ))java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
 len >max :=len; L: i; fi
 if len < min then min := (InfoBckt ," ")
 od;
 order := rbase.regorb ( ,(E,
 if 2 * order < n then order := Cell( B, l );
else =Cell(B ) ;
 fi;

 # Construct an R-base. Start with the partition into <G>-orbits on the
 # cells of . In the normalizer case, only the factor group $N_G(E)/E$
 # acts on the cells.
 rbase: EmptyRBase( G Omega,CollectedPartition(B div))
 rbase. . = ( ,One(reg)java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61

( B)=1 rbase. : ;
 else rbase.blox := B; fi GeneratorsOfGroup(reg ) );

java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
 ( Omega;
 reg
 < failthen
Info ,1 Subgroup regularorbit )
 rbase.reggrp := function( E, Omega ) return E; start oldstart types, typ, coll,pnt,done;
 ([ )
 [ [1 );
 AddGeneratorsExtendSchreierTree( rbase.regorb,
 GeneratorsOfGroup( E ) );
 elif IsPrimitive( E,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 reg := STBCTEARNS( E, Omega );
 if reg <> fail then
 Info( InfoBckt, 1, "Subgroup is affine" );
 =(E .ase . -1}
 rbase fpt, Omega);
 Omega[ 1 ] );
 AddGeneratorsExtendSchreierTree( rbase.regorb,
 GeneratorsOfGroup( reg ) );
 fi;
 fi;

 doneblox := [ ];
 doneroot := [ ];

 rbase.nextLevel := function( P, rbase )
 local Q,strat, , f ,subs k, i,
 start, oldstart, types, typ, coll, pnt, done;

 if reg <> fail then NextLevelRegularGroups( P, rbase );
 else NextRBasePoint( P, rbase, order ); fi;
 len := Length( rbase.base );
 if len >= tra then

 # For each fixpoint in , consider the orbits of its

 f :=fork [1..)]do
 while f <> false do
 fpt: (, java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
 subs := Suborbits( E, rbase.base{ [ 1 : StratMeetPartition( rbase, P,
 fpt, Omega );

 # `Suborbits0' computes and meets the partition into unions of ;
 # suborbits of equal length.
 strat := returnjava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
 subs.conj
 AddRefinement( rbase, STBBCKT_STRING_SUBORBITS0
 [tra f,subs.engths,
java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64

#
 # `OrbitalPartition' of the union of orbital graphs for the
 # suborbits of that length (only if there are less than = byLengthsjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
 # sqrt(subdegree) many and if they are in the component of the
 # root).
 for k in [ 1 .. Length( subs.byLengths ) ] do
 (
 < subs.sublilen
 and subs.reps[ subs.byLengths[ k ][ 1 ] ] <> false then
 strat := StratMeetPartition( rbase, P,
 OrbitalPartition( subs, subs.byLengths[ k ] ),
 subs.conj );
 AddRefinement( rbase, STBBCKT_STRING_SUBORBITS1,
 [ tra, f, k, strat ] );
 if IsTrivialRBase( rbase ) then
 return;
 fi;
 fi;
 od;

 # Find the types of the suborbits, i.e., the sizes of their
 # intersections with the cells of .
 if LARGE_TASK then start := NumberCells( P ) + 1
 else start := 1; oldstart := 1; fi;
 types := List( subs.blists, o -> [ -SuboSiBli( o ) ] );
 AddSet done, k)java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
 while start <= NumberCells( P ) do

 # Do not consider a cell number in twice (consider only
 # cell numbers between <oldstart> and <start>).
 for i in [ start .. NumberCells( P ) ] do
 for k in Set( subs.which
 { OnTuples( Cell( P, i ), subs.conj ) } ) do
 AddSet( types[ k ], i );
 od;
 od;
 coll := Collected( StructuralCopy( types ) );
 start := NumberCells( P ) + 1;

 # For each type, consider the `OrbitalPartition' of the union
 # of orbital graphs of that type.
 for typ in coll do
 k := Filtered( [ 1 .. subs.sublilen ],
 k -> types[ k ] = typ[ 1 ] ) fi;
 if not k in done then
 AddSet( done, k );
 strat := StratMeetPartition( rbase, P,
 OrbitalPartition ;
 subs.onj )
 if Length( strat ) <> 0 (doneroot cp;

 fi
 # in `data[3]') and compares them with <coll> (only for
 # new cells between <oldstart> and <start>).
 if oldstart < start then
 AddRefinement( rbase, STBBCKT_STRING_SUBORBITS2,
 [ tra, f, oldstart, coll ] );
 oldstart := start;
 fi;

# Suborbits3 computes andmeetsthe orbital java.lang.StringIndexOutOfBoundsException: Range [77, 78) out of bounds for length 77
 # for the image.
 AddRefinement( rbase, STBBCKT_STRING_SUBORBITS3,
 [ tra, f, typ[ 1 ], Length fi;
 # Split off blocks whose images are known.
 return;
 fi;
 fi;
 fi;
 od;

 od;

# at java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
# to yield no extra progress.
 pnt inOrbit(E fpt do
 cp:=CellNoPoint(P,pnt);
 if P.lengths[cp] = 1 then
 AddSet doneroot, cp);
 fi;
 od;

 f := FixcellPoint( P, doneroot );
 od;
 fi;

 # Construct a block system for <E>.
 if len > 1 and rbase.java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 6
 Q := Blocks( E, rbase.domain, rbase.base{ [ 1, len ] } );
 if Length( Q ) <> 1 then
 rbase.blox := Partition( Q );
 AddRefinement( rbase, STBBCKT_STRING_MAKEBLOX, [ len ] );
 fi;
 fi;

 # Split off blocks whose images are known.
 if Lengtharg)>2 IsList(arg 3]
 k := java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 15
 while k <> false do
 for i in [ 1 .. Length(
 orb := Cell( rbase.blox, k[ 1 ][ i ] );
 Length( orb )<>Length( Omega ) then
 strat := StratMeetPartition( rbase, P, orb );
 AddRefinement( rbase, STBBCKT_STRING_SPLITOFF,
 [Omega= ;
 repr (Phi)< Length then

 fi;
 fi;
 od;
 k := FixcellsCell( P, rbase.blox, doneblox );
 od;
 fi;

 end;

 return rbase;
end );

#############################################################################
##
#F RepOpSetsPermGroup( <arg> ) . . . . . . . . . . . . . . operation on sets
##
InstallGlobalFunction( RepOpSetsPermGroup, function( arg )
 local G, Phi, Psi, repr, Omega, rbase, L, R, P, Q, p, Pr ( Psi Omega p- inPsi
 i,phitail;

 G := arg[ 1 ];
 Phi := Set( arg[ 2 ] );
 if Length( arg ) > 2 and IsList( arg[ 3 ] ) then
 p := 3;
 Psi := Set( arg[ 3 ] );
 repr := true;
 else
 p := 2;
 Psi := Phi;
 repr := false;
 fi;

 Omega := MovedPoints( G );
 if repr and Length( Phi ) <> Length( Psi ) then
 return fail;
 fi;

 Psi:=java.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 12

 # Special case if <Omega> is entirely inside or outside <Phi>.
 if IsSubset(else
 if repr then
 DifferencePhi >(Psi,Omegajava.lang.StringIndexOutOfBoundsException: Range [73, 74) out of bounds for length 73
 return fail;
 else
 return One( G );
 fi;
 else
 return G;
 fi;
 R =L
 ( IsSubsetjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 return fail;
 fi;

 P := Partition( [ Intersection( Omega, Phi ),
 Difference( Omega, Phi ) ] );
 if repr then Q := Partitionjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 Difference( Omega, Psi ) ] );
 else :Phi[..Length()}java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35

# # Special treatment for the symmetric group.
# if IsSymmetricGroupQuick( G ) then
# if repr then
# return MappingPermListList( Phi, Psi );
# else
# gens := [ ];
# for i in [ 1 .. NumberCells( P ) ] do
# cell := Cell( P, i );
# if Length( cell ) > 1 then
# Add( gens, ( cell[ 1 ], cell[ 2 ] ) );
# if Length( cell ) > 2 then
# Add( gens, MappingPermListList( cell,
# cell{ Concatenation( [ 2 .. Length( cell ) ],
# [ 1 ] ) } ) );
# fi;
# fi;
# od;
# return GroupByGenerators( gens, () );
# fi;
# fi;

 if( repr,,e ,L
 L: arg[p+1 ]
 else
 L:=SubgroupNC(G,
 Filtered(StrongGeneratorsStabChain(StabChainMutable
 gen -> OnSets ,# the R-base for the backtrack algorithm
 fi;
 if repr then
 if Length( arg ) > p + 1 java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 12
 R := arg[ p + 2 ];
 else
 R:=ifForAll( GeneratorsOfGroup( G ), gen -> OnTuples( e, gen ) = e ) then
 Filtered(StrongGeneratorsStabChain(StabChainMutable(G)),
 gen->OnSets(Psi,gen)=Psi));
 fi;
 else
 R := L;
 fi;

 # Construct an R-base.
 rbase := EmptyRBase( [ G, G ], Omega, PCycleStructurePerm(f[])))then
 rbase.nextLevel := NextRBasePoint;

 #Pr := gen -> IsSubsetSet( OnTuples( Phi, gen ), Psi );

 phitail:=Phi{[2..Length(Phi)]};
 Pr:=function(gen)
 local i;
 ^gen in Psithen
 return false;
 fi;
 for i in phitail do
 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 5
 false
 fi;
 od;
 return ;
 end;

 # Pr := [ Phi, Psi, OnTuples, gen ->
 # IsSubsetSet( gen!.lftObj, gen!.rgtObj ) ];
 return java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 11
end );

#############################################################################
##
#F RepOpElmTuplesPermGroup( <repr>, <G>, <e>, <f>, <L>, <R> ) on elm tuples
##
InstallGlobalFunction( RepOpElmTuplesPermGroup,
function( repr, G, e, f, L, R )
local Omega, # a common operation domain for <G>, <E> and <F>
 order, # orders of elements in <e>
 cycles, # cycles of <e> on <Omega>
 P, Q, # partition refined during construction of <rbase>
 java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
 Pr, # property
 baspts, # base for group
 eran, # range
 map,
 bailout,
 i,j, size; # loop/auxiliary variables

 # Central elements and trivial subgroups.
 if ForAll( GeneratorsOfGroup( G ), gen -> OnTuples( e, # To avoid particular configurations falling repeatedly into,
 if not repr then return G;
 elif e = f then return One( G ("java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 38
 else return fail; nneTwister,
 fi;

 if SortPar(-ci
 ( Lengthrepeat
 i -> CycleStructurePerm( e[ i ] ) <>
 CycleStructurePerm( f[ i ] ) ) ) then
 return fail;
 fi;

 rbasenextLevel: function( P rbase )
 if IsTrivial(L) then
 L:=SubgroupNC(G, , pnt , , strat;
 Filtered(e,gen->gen in G),
 StrongGeneratorsStabChain(StabChainMutable(G))),
 gen->OnTuples(e,gen)=e));
 else
 bailout:=false;
 fi;

 if IsTrivial(R) then
 if repr then
 R:=SubgroupNC(G,Filtered( Concatenation(
 Filtered(f,gen->gen in G),
 StrongGeneratorsStabChain(StabChainMutable(G))),
 gen->OnTuples ,g , )java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68

 else
 R:=L;
 fi;
 fi;

 Omega := MovedPoints( Concatenation( GeneratorsOfGroup( G ), e, f ) );

 P := TrivialPartition
 if repr then size := 1;
 else size := Size( G ); fi;
 for if repr java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 cycles := Partition( Cycles( e[ i ], Omega ) );
 StratMeetPartition( P, CollectedPartition( cycles, size ) );
 od;

 # Find the order in which to process the points in the base choice.
 #SortParallel( ShallowCopy( -cycles.lengths ), order );

 # The criterion for selection of base points is to select them according
 # to (descending) cycle length of the permutation to be conjugated. At the
 # moment no other criterion is used (though experiments can observe a
 Pr:=gen -> gen!.lftObj = gen!.rgtObj;
# Beyond this choice, the base point order is determined as a side effect
 # of the sorting algorithm.
badjava.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74

 # criterion used. This can be turned off through an option for debugging
 # purposes.
 if ValueOption("norandom")=true then
 i:=[1.local ,;
 else
 i:=FLOYDS_ALGORITHM(RandomSource(IsMersenneTwister
 c.irsts)false;
 fi;
 order := cycles.points if (j/gen)ei)gen=^[]then
 SortParallel( -(cycles.lengths{i}), order );

 repeat

 # Construct an R-base.
 rbase := EmptyRBase(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

 # Loop over the stabilizer chain of <G>.
 rbase.nextLevel := function( P, rbase )
 local fix, pnt, img, g, strat;

 NextRBasePoint( P, rbase, order );

 # Centralizer refinement.
 fix := Fixcells( P ) L:=G;
 for pnt in fix do
 for g ;
 img := pnt ^ e[ g ];
 strat := IsolatePoint( P, img );
 if strat <> false java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 Add( fix, img );
 ProcessFixpoint( rbase, img );
 AddRefinement( rbase,#F ConjugatorPermGroup( <arg> ) . . . . isomorphism / conjugating element
 [ CellNoPointp( ,function)
 if P.lengths[ strat ] = 1 then
 pnt := FixpointCellNo( P, strat );
 ProcessFixpoint( rbase, pnt );
 AddRefinement ,",
 [ pnt E :=arg 2 ]java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
 ;
 fielif IsTrivial )thenreturn(;
 od;
 od
 end;

 if repr then
 Q := TrivialPartition( Omega );
 for i in [ 1 .. Length( f ) ;
StratMeetPartition( Q, CollectedPartition( Partition
 ( Cycles( f[ i ], Omega ) ), 1 ) );
 od;
 else
 Q := P;
 fi;

 #Pr:=gen -> gen!.lftObj = gen!.rgtObj;
 baspts:=BaseStabChain(StabChainMutable(G));
 if not (ForAll(e,i- IsCyclic()then returnfail;fi;
 baspts:=Union(baspts,MovedPoints(Concatenation(e,f)));
 fi;

 eran:=[1..Length(e)];
 Pr:=function(gen)
 local i,j;

 for i
 for j in baspts do
 if not ((j/gen)^e[i])^gen=j^f[i] java.lang.StringIndexOutOfBoundsException: Range [0, 51) out of bounds for length 36
returnfalse;
 fi;

 odiffailreturn;
 return true;
 end;

 map:=PartitionBacktrack( G, [ e, f, OnTuples,Pr],
 repr, rbase, Concatenation( [ Q ], f ),
 L, R:bailout:=bailout );
 if not (bailout and map=infinity) then
 return map;
 fi;
 Info(InfoBckt,1,"\n#I ------\n#I First compute new L");

=
 :(G,
 (E,GeneratorsOfGroupF));
 od;
t=alse
 # go back as we need to build the base anew
 until false;

end );

#############################################################################
##
#F ConjugatorPermGroup( <arg> ) . . . . isomorphism / conjugating element
##
InstallGlobalFunction( ConjugatorPermGroup, function( arg )
local G, E, F, L, R, mpG, mpE, :=[..engthorb])
et ,Pr ,BF,;

 ;
 E := arg[ 2 ];
 F := arg[ 3 ];
 if Size( E ) <> Size( F ) then return fail found:false;
 elif IsTrivial(java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 elif Size( E ) = 2 then
 if Length( arg ) > 3 then
 L := arg[ 4 ]; R := arg[ 5 ] if([pos]<
 else
 L := if Size(Stabilizer(P,dOnTuples)=
 fi;
 E := First( GeneratorsOfGroup( E ), gen -> Order( gen ) <> 1 );
 F := First( GeneratorsOfGroup( F ), gen -> Order( gen ) fi;
 return RepOpElmTuplesPermGroup( true, G, [ E ], [ F ], L, R );
(E
 # special case of cyclic groups
 if not IsCyclic(F) then return (,rue);
 if Length( arg ) > 3 then
 L := arg[ 4 ]; R := arg[ 5 ];
 else
 L := TrivialSubgroup( G ); R := L;
 fi;
 E:=MinimalGeneratingSet(E)[1];
 F:=MinimalGeneratingSet(F)[1];
 Q:=Order(E);
 for pos in Filtered([1..Q],x->Gcd(x,Q)=1) do
 found:=RepOpElmTuplesPermGroup( true, G, [ E ], [ F^pos ], L, R );
 if found<>fail then return found;fi;
 od;
 return fail;
 fi;
 # `Suborbits' uses all points. (AH, 7/17/02)
 mpG:=MovedPoints(GeneratorsOfGroup(G));
 mpE:=MovedPoints(GeneratorsOfGroup(E));
 :IsTransitive(E,Omega);

 map:=false;
 Omega := [1..Maximum(Maximum(mpG) java.lang.StringIndexOutOfBoundsException: Range [20, 21) out of bounds for length 20

 ifIsSubset(pG,pE and IsSubset(,mpF)andnot (,)then
 # is there a chance to use only some orbits?
 if not (IsSubset(G,E) and IsSubset(G,F)) then
 P:=Group(Concatenation(GeneratorsOfGroup(java.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 7
 GeneratorsOfGroup(E),GeneratorsOfGroup(F)));
 else
 P:=G;
 fi;
 orb:=Orbits(P,mpG : arg[Length( arg )-1 ;
then
 # join orbits to make only a few
 java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 9
 SortBy(orb, Length);
 comb:=Union(orb{[7..Length(orb)]});
 orb=Concatenation{[.6},]);
 fi;
 comb:=Combinations(orb);
 SortBy(comb,a->Sum(a,Length)else
 found : TrivialSubgroup )java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
 pos:=0; # pos1 is empty
 lc:=Length(mpG)*2/3;
 while pos<Length(comb) and not found and pos<=Length(comb) do
 pos:pos+1;
 if Sum(comb[pos],Length)<lc then
 :=(comb[pos];
 if Size(Stabilizer(P,dom,OnTuples))=1 then
 # found faithful
 :truejava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 fi;
 fi
 od;
 if found then
 map:=ActionHomomorphism(P,dom,"surjective");
 SetIsInjective(map,true);
 G:=Image(map,G);
 E:=Image(map,E);
 F:=Image(map,F);
 Omega:=[1..Length(dom)];
 ;
 fi;

 # test whether we have a chance mapping the groups (as their orbits fit
 # together)
 if )
 Collected(List(OrbitsDomain(F,Omega),Length)) then
 return fail;
 fi;

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 BindGlobal("DoNormalizerPermGroup",function(G,E,L,Omega)
 if not IsIdenticalObj(E,F) then
et=sTransitiveEOmega;
 ft:=IsTransitive(F,Omega);
 if et<ft java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
 return fail;
elifandIsPrimitiveEOmega)>sPrimitiveF,Omega)then
 java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 8
 fi;
 fi;

 Pr := (,
 Length 3then
 L := arg[ Length( arg ) - 1 ];
 R := arg[ Length( arg ) ];
 if map<>false then
 =(map,)java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 R:=Image(map,R);
 fi;
 elif IsSubset( G, E ) then
 L := E;
 if IsSubset( G, F ) then R := F;
 else return fail; fi;
 else
 L := TrivialSubgroup( G );
 R := TrivialSubgroup( G );
 fi;

 rbase := RBaseGroupsBloxPermGroup( true, G, Omega,
 E, 1, OrbitsPartition( E, Omega ) );
 BF := OrbitsPartition( F, Omega );
 Q := CollectedPartition( BF, 1 );
 ,F ,BF []]java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 if IsBound( rbase.reggrp ) then
 P:=rbase.reggrp( F, Omega );
 if P=fail then
 # the first group has an EARNS, the second not.
 return
 fi;
 Add( data, P );
 fi;
E.suborbits:=[;
 found:=PartitionBacktrack( G, Pr, true, rbase, data, L, R );
 if IsPerm(found) and map<>false then
 found:=PreImagesRepresentative( (E ) 2then
 fi;
 return found;
)

#############################################################################
##
#F NormalizerPermGroup( <arg> ) . . . automorphism group / normalizer
##

# the backtrack call
BindGlobal("DoNormalizerPermGroup",function(G ifLength( )= 3then
local Pr, div, B, rbase, data, N;

 Pr := gen -> ForAll( GeneratorsOfGroup( E ), g -> g elifIsSubset ,E)then
 if not (IsTrivial( G ) or IsTrivial(E)) then
if (G )then
 div := SmallestPrimeDivisor( Index( G, E ) );
 else
 div := SmallestPrimeDivisor( Size( G ) );
 fi;
if (MovedPoints())>G andLength((G)>00then
 SubgroupProperty(G,
 i->ForAll(GeneratorsOfGroup(E),j->java.lang.StringIndexOutOfBoundsException: Range [0, 43) out of bounds for length 5
;
 B := OrbitsPartition( E, Omega );
 rbase := java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 11
 data := [ true, E, [ ], B, [ ] ];
 if IsBound( rbase.reggrp ) then
 Add( data, rbase.reggrp( E, Omega ) );
 fi ifissubthen
 N := PartitionBacktrack( G, Pr, false, rbase, data, L, L );
 else
 N := java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 8
 fi;
 # remove cached information
 G.:=[;
 E!.suborbits:=[];

 # bring the stabilizer chains back into a decent form
 ReduceStabChain(StabChainMutable(G
 ReduceStabChain(StabChainMutable(E));
 ReduceStabChain(StabChainMutable(N));

 return N;
end );

InstallGlobalFunction( NormalizerPermGroup, function( arg )
local G,i=1
Eh, Lh, Nh,G0;

 G := arg[ 1 ];
 E := arg[ 2 ];
 G!.suborbits:=[]; # in case any remained from interruption
 E!.suborbits:=[];
 if IsTrivial( E ) or while i<=Length(orb+do
 return G;
 elif Size( E ) = 2 then
 if Length( arg ) > 2 then L := arg[ 3 ];
 else L := TrivialSubgroup( G ); fi;
 E := [ First( Omega := [1..Maximum(mpG,Maximum(mpE));
 gen -> Order( gen ) <> 1 ) ];
 return RepOpElmTuplesPermGroup( false, G, E, E, so:=nionorb{start.-]);
 fi;

 if Length( arg ) = 3 then
 L := arg[ 3 ];
 issub:=fail;
 elif IsSubset( G, E ) then
 Nh=java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 60
 return G;
 fi;
 L := E;
 issub:=true;
 else
 L := TrivialSubgroup( G );
 issub:=false;;
 fi;

 if issub and HasFittingFreeLiftSetup(G) and NrMovedPoints()1000
| --
 and Size(java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 11
return (GE;
 fi;

 mpG:=MovedPoints(GeneratorsOfGroup(G));
 mpE:=MovedPoints(GeneratorsOfGroup(E));
 if IsSubset(mpG,mpE) and not IsTransitive(G,mpG) then

 if issub=false then
 issub:=IsSubset(G,E);
 fi;
 G0:=G;
if
 P:=G;
 else
 :Group((GeneratorsOfGroupG) (E))java.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
 fi;
=java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 28

 while Length(Omega)>0
 # it is not unlikely that some orbits suffice. Thus we can just stop
 # then
 and not IsNormal(G,E) do

 orb:=ShallowCopy(Orbits(P,Omega));
 SortBy(orb,Length);
 i:=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 while i<=Length(orb) and Length(orb[i])=1 do[IsPermGroup ,0,
 Omega:=Difference(Omega,orb[i]);
 i:=i+1;
 od;
 if i<=Length(orb) then
 start:=i;
 :([i;
 i:=i+1;[,java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 46
 # don't bother with very short orbits -- they will give little
 # improvement.
 while i<=Length(orb) and cnt+Length(orb[i])<10 do
 cnt:=java.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 2
 i:=i+1;
 od;
 if cnt=Length(mpG # Get the arguments.
 # no orbits...
 Omega := [1..Maximum(Maximum(mpG),Maximum(mpE))];
 return DoNormalizerPermGroup(G,E,L,Omega);
 fi;
 so:=Union(orb{[start..i-1]});

 hom:=ActionHomomorphism(P,so,"surjective");
 Gh:=Image(hom,G);
 Eh:=Image(hom,E);
 Lh:=Image(hom,L);
 Nh:=DoNormalizerPermGroup(Gh,Eh,Lh,[1..Length(so)]);
 if Size(Nh)<Size(Gh) then
 else R := TrivialSubgroup( G ); fi;
 java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
 P: # Treat the trivial case.
 fi;
 G:=PreImage(hom,Nh);
 Info(InfoGroup,1,"Orbit ",Length(so)," reduces by ",Size(Gh)/Size(Nh));
 fi;
 Omega::=Difference(Omega,o);
 fi;
 od;

 if not issub then
 G=Intersection(G,G0)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 fi;

 if Length(Omega)=0 and not IsNormal(G,E) then
 # we ran through all orbits and did not stop early because everything
 # normalized. We thus have to test the normalization on all orbits
 Nh:=DoNormalizerPermGroup(G,E,L, # Construct an R-base.
 Info(InfoGroup,1,"Union reduces by ",Size(G)/Size(Nh));
 else
 Nh:=G; # we know that G normalizes
 fi;
 ,Nh=DoNormalizerPermGroup(G,E,L,
 [1..Maximum(Maximum(mpG),Maximum(mpE))]));
 return Nh;

 else
 # `Suborbits' uses all points. (AH, 7/17/02)
 Omega := [1..Maximum(Maximum(mpG),Maximum(mpE))];
 return DoNormalizerPermGroup(G,E,L,Omega);
 fi;
end);

",IsIdenticalObj,
 [ IsPermGroup, IsPermGroup ], 0,
NormalizerPermGroup;

# this circumvents the FOA mechanism which got changed and does not permit
# three arguments any longer.
,,java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
 [ IsPermGroup, #Treat trivial .
 NormalizerPermGroup );

#############################################################################
##
#F ElementProperty( <G>, <Pr> [, <L> [, <R> ] ] ) one element with property
##
InstallGlobalFunction( ElementProperty, function( arg )
 local G, Pr, L

 # Get the arguments.
 G := arg[ 1 ];
 Pr := arg[ 2 ];
 if Length( >2 =3;
else =TrivialSubgroup );fi;
 if Length( arg ) > 3 then R := arg[ 4 ];
 else R := TrivialSubgroup( G ); fi;

 # Treat the trivial case.
 if IsTrivial( G ) then
 if Pr( One( G ) ) then []=(artj>j=l[])
 else return fail; fi;
 fi;

 # Construct an R-base.
 Omega iindo
 G=GiOnSets)java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
 rbase := EmptyRBase( G, Omega, P );
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

 return PartitionBacktrack( G, Pr, true, rbase,
;

#############################################################################
##
#F SubgroupProperty( <G>, <Pr> [, <L> ] ) . . . . . . . fulfilling subgroup
##
InstallGlobalFunction( SubgroupProperty, function( arg )
 local G, Pr, L, Omega, rbase, P;

# Get the arguments.
 G := arg[ 1 ];
=[2]
 if Length( arg ) > 2 then L := arg[ 3 ];
 else L := TrivialSubgroup( G ); fi;

 # Treat the trivial case.
 if IsTrivial( G ) then
 return G;
 fi;

 # Construct an R-base.
 Omega := MovedPoints( G );
 P := TrivialPartition( Omega );
 rbase := EmptyRBase( G, Omega, P );
 rbase.nextLevel := NextRBasePoint;

 return PartitionBacktrack( G, Pr, false, rbase, [ P ], L, L );
end );

#############################################################################
##
#M PartitionStabilizerPermGroup(<G>,<part>)
##
## This really should be a backtrack on its own
InstallGlobalFunction( PartitionStabilizerPermGroup, function
local pl,single,i,p,W,op,S;

 # first separate the sets of different lengths
 pl:=Set(part,Length);
 single:=[];
 for i in [1..Length(pl)] do
 pl[i]:=Filtered(part,j->Length(j)=pl[i]);
 Add(java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 42
 od;
 SortBy(single,Length);
 for i return;
 G:=Stabilizerfi;
 od;

 # now pl is a list of lists of sets of the same length, sorted in
 # ascending size.

 # stabilize the partitioning among sets of the same length
 for p in pl do
 # the trivial partitions are always stabilized.
 if Length(p)>1 andod;
 # the stabilizer is the set of all elements that map every set from p into
 # another set from p.
 # as a subgroup of the stabilizer compute the stabilizer on set tuples;
 S:=G;
 for i in p do
 if ForAny(GeneratorsOfGroup(S),j->OnSets(i,j)<##
 S:=Stabilizer(S,i,OnSets);
 #Info(InfoPermGroup,1,i," ",Size(S),"\n");
 fi;
 od;
 G:=Normalizer(G,S);

java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
 if not " , perm ,IsIdenticalObj,
 # the stabilizer of p in S_n is a wreath product of symmetric groups
 # (It seems that computing the intersection is better than the
 # `SubgroupProperty' call commented out below, as `Intersection' usesjava.lang.StringIndexOutOfBoundsException: Range [36, 34) out of bounds for length 45
# internally
 op:=ActionHomomorphism(G,end;
 W:=WreathProduct(SymmetricGroup(Length(p[1])),
 SymmetricGroup(Length(p)));
 if Size(W)<10^50 then
 W:=Intersection[, ,java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
 G:=PreImage(java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 59
 else

 # because we want to keep the set property, we make p immutable
 p:=Immutable(Set(p));
 # the stabilizer is the set of all elements that map every set from
 # p into another set from p. as a subgroup of the stabilizer
 # compute the stabilizer on set tuples
 S:=java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 61
 for in p
 S:Si,)java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
 od;

 G:=SubgroupProperty(G,function(gen)
 local i;
 for i in p do
 if not OnSets(i,gen) in p then

 fi;
 od;
 true;
 end,
 S);
 fi;
 fi;
 fi;
 od;
 return G;

end );

#############################################################################
##
#M Centralizer( <G>, <e> ) . . . . . . . . . . . . . . in permutation groups
##
InstallMethod( continue
 [ IsPermGroup;
 function( G, e )
 e := [ e ];
 return RepOpElmTuplesPermGroup( false, G, e, e,
 TrivialSubgroup( G ), TrivialSubgroup( G ) );
end );

(CentralizerOp perm group,perm ,IsIdenticalObj,
 [ IsPermGroup, fi;
 function( G, E )
 return RepOpElmTuplesPermGroup( false, G,
# # the intersection must stabilize the other groups orbits.
 TrivialSubgroup( Gstep
end );

# this circumvents the FOA mechanism which got changed and does not permit
# three arguments any longer.
InstallOtherMethod( Centralizer, "with given subgroup", true,
 [ IsPermGroup, IsPerm, IsPermGroup ], 0,
 function( # od;
 e := [ e ];
 return RepOpElmTuplesPermGroup( false, G, e, e, U, U );
end );

#############################################################################
##
#M Intersection( <G>, <H> ) . . . . . . . . . . . . . of permutation groups
##
(java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 60
 [ IsPermGroup, IsPermGroup ], 0,
function( G, H )
local omega, P, rbase, L, mg, mh, L=PartitionBacktrack,H,false, ,L,L)java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61

 if IsIdenticalObj#############################################################################
 return G;
 fi;

 # iterate taking stabilizer until G and H have the same set of moved points
 while true do
 # align the acting domains G ran Omega, Agemo,opr,
 mg:=MovedPoints(G);
 java.lang.StringIndexOutOfBoundsException: Range [21, 8) out of bounds for length 25
 omega := Intersection(mg,mh);

 # no two points moved in common?
 if Length(omega)<=1 then
 return TrivialGroup(IsPermGroup);
 fi;

 mg_minus_mh:=Difference(mg,mh);
 if Length(mg_minus_mh)
 G:=Stabilizer(G,mg_minus_mh, Error( "2-closure: <G> must be transit
 continue;
 fi;
 mh_minus_mg:=Difference(mh,mg);
 if Length(mh_minus_mg) > 0 then
 H P :TrivialPartitionOmega )
 continue;
 fi;
 break;
 od;

if , then
 return H;
 elif (G
 return G;
 fi;

# # the intersection must stabilize the other groups orbits.
# # go through the orbits step by step
# mg:=MovedPoints(G);
# mg:=ShallowCopy(Orbits(H,mg));
# SortBy(mg, Length);
# for i in mg do
# if Length(i)<5 then
# G:=Stabilizer(G,Set(i),OnSets);
# fi;
# od;
# mh:=MovedPoints(H);
# mh:=ShallowCopy(Orbits(G,mh));
# SortBy(mh, Length);
# for i in mh do
# if Length(i)<5 then
# H:=Stabilizer(H,Set(i),OnSets);
# fi;
# od;

 P: ,omega )java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 rbase := EmptyRBase( [ G, H ], omega, P );
 java.lang.StringIndexOutOfBoundsException: Range [12, 8) out of bounds for length 15

 # L := SubgroupNC( G, Concatenation
 # ( Filtered( GeneratorsOfGroup( G ), gen -> gen in H ),
 # Filtered( GeneratorsOfGroup( H ), gen -> gen in G ) ) );
 L := TrivialSubgroup( G );
 L:=PartitionBacktrack( G, H, false, rbase, [ P ], L, L );
 return L;
end );

#############################################################################
##
#F TwoClosure( <G> [, <merge> ] ) . . . . . . . . . two-closure
##
BindGlobal( "TwoClosurePermGroup", function( arg )
local G, merge, n, ran, Omega# if IsInt( k ) and
 adj, tot, k, kk, pnt, orb, o, new, gen# elif IsList( k ) and ForAny( k, i -> not
 tra, Q, rbase, java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 24

 G := arg[ 1 ];
 if IsTrivialjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 return G;

 Omega := MovedPoints( G ) =-1java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
 n := Length( Omega );
 S := SymmetricGroup( Omega );
,)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
 if tra = 0odjava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
 Error( "2-closure: <G> must be transitive" );
 elif tra >= 2 then
 return S;
 fi;

 P := TrivialPartition( Omega );
 rbase := EmptyRBase( S, Omega, P );
 if Length( arg ) > 1 then
 rbase.suborbits := arg[ 2 ];
 merge := arg[ 3 ];
 Append( merge, Difference( [ 1 .. rbase.suborbits.sublilen ],
 Concatenation( merge ) ) );
 else
 rbase.suborbits := Suborbits( G, [ ], 0, Omega );
 if rbase.suborbits <> false then
 merge := [ 1 .. rbase.suborbits.sublilen ];
 fi;
 fi;
 Q := OrbitalPartition( rbase.suborbits, rec( several := merge ) );

 doneroot := [ ];
 rbase.nextLevel := function( P, rbase )
 local f, fpt, rep, strat;

 ,rbase,Omega)
 if rbase.suborbits = false then f := false;
 else f := FixcellPoint( P, doneroot );
 fi;
 while f <> false do
 AddSet( doneroot, f );
 genin GeneratorsOfGroup djava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 rep := InverseRepresentative( rbase.suborbits.stabChainTop, fpt );
 strat =StratMeetPartition(rbase ,Q ;
 AddRefinement( rbase, STBBCKT_STRING_TWOCLOSURE,
 [ G, f, Q, strat ] );
 if IsTrivialRBase
 else f := FixcellPointjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 fi;
 kk : k;
 end;

 Pr := false;
# # If <G> is primitive and simple, often $G^[2] \le N(G)$.
# if IsPrimitive( G, Omega )
# and IsSimpleGroup( G ) then
# type := IsomorphismTypeInfoFiniteSimpleGroup( G );
# param := IsoTypeParam( type );
# if param = false and not [ type, n ] in
# [ [ "M(11)", 55 ], [ "M(12)", 66 ], [ "M(23)", 253 ],
# [ "M(24)", 276 ], [ "A(9)", 120 ] ]
# or param <> false and not
# ( param.type = "G(2" and param.q >= 3 and
# n = param.q ^ 3 * ( param.q ^ 3 - 1 ) / 2
# or param.type = "O(7" and n = param.q ^ 3 * ( param.q ^ 4 - 1 )
# / GcdInt( 2, param.q - 1 ) ) then
# Pr := function( gen )
# local k;
#
# if not ForAll( GeneratorsOfGroup( G ),
# g -> g ^ gen in G ) then
# return false;
# fi;
# for k in merge do
# if IsInt( k ) and
# OnSuborbits( k, gen, rbase.suborbits ) <> k then
# return false;
# elif IsList( k ) and ForAny( k, i -> not
# OnSuborbits( i, gen, rbase.suborbits ) in k ) then
# return false;
# fi;
# od;
# return true;
# end;
# fi;
# fi;

 if Pr =
 = 1. 2 ]java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30

 if Omega = [ 1 .. n ] then
 opr := function( p, g )
 p := p - 1;
 return ( p mod n + 1 ) ^ g
 + n * ( QuoInt( p, n ) + 1 ) ^ g - n;
 end;
 else
 Agemo := [ ];
 for i in [ 1 .. n ] do
 Agemo[ Omega[ i ] ] := i - 1;
 od;
 opr := function( p, g )
 p := p - 1;
 return 1 + Agemo[ Omega[ p mod n + 1 ] ^ g ]
 + n * Agemo[ Omega[ QuoInt( p, n ) + 1 ] ^ g ];
 end;
 fi;

 adj := List( [ 0 .. LogInt(rbase.suborbits.sublilen-1,2) ],
 i -> BlistList( ran, [ ] ) );
 tot := BlistList( ran, [ ] );
 k := 0;
 pnt := Position( tot, false );
 while pnt <> fail do

 # start with the singleton orbit
 orb := [ pnt ];
 p := PositionProperty( merge, m -> IsList( m )
 and rbase.suborbits.which[ pnt ] in m );
 if p <> fail then
 for i in merge[ p ] do
 Add( orb, SuboTruePos(ran, rbase.suborbits.blists[ i ] ) );
 od;
 fi;
 orb := BlistList( ran, orb );
 o := StructuralCopy( orb );
 new := BlistList( ran, ran );
 new[ pnt ] := false;

 # loop over all points found
 p := Position( o, true );
 while p <> fail do
 o[ p ] := false;

 # apply all generators <gen>
 for gen in GeneratorsOfGroup( G ) do
 i := opr( p, gen );

 # add the image <img> to the orbit if it is new
 if new[ i ] then
 orb[ i ] := true;
 o [ i ] := true;
 new[ i ] := false;
 fi;

 od;

 p := Position( o, true );
 od;

 kk := k;
 i := 0;
 while kk <> 0 do
 i := i + 1;
 if kk mod 2 = 1 then
 UniteBlist( adj[ i ], orb );
 fi;
 kk := QuoInt( kk, 2 );
 od;
 UniteBlist( tot, orb );
 k := k + 1;
 pnt := Position( tot, false, pnt );
 od;
 Pr := function( gen )
 local p, i;

 gen := UnslicedPerm@( gen );
 for p in ran do
 i := opr( p, gen );
 if not ForAll( adj, bit -> bit[ i ] = bit[ p ] ) then
 return false;
 fi;
 od;
 return true;
 end;
 fi;
 return PartitionBacktrack( S, Pr, false, rbase, [ true ], G, G );
end );

InstallMethod(TwoClosure,"permutation group",true,[IsPermGroup],0,
 TwoClosurePermGroup);

Messung V0.5 in Prozent

¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.128Angebot (Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können 2026-10-13) ¤

*Eine klare Vorstellung vom Zielzustand

Wurzel

Suchen

PVS Prover

Isabelle Prover

NIST Cobol Testsuite

Cephes Mathematical Library

Vienna Development Method

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.