#############################################################################
##
## This file is part of recog, a package for the GAP computer algebra system
## which provides a collection of methods for the constructive recognition
## of groups.
##
## This files's authors include Max Neunhöffer, Ákos Seress.
##
## Copyright of recog belongs to its developers whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-3.0-or-later
##
##
## Code to recognise (simple) groups by their two largest element orders.
## At least recognise the "natural" characteristic.
##
#############################################################################
# parses certain strings and numbers into a number
RECOG ## This file is part of recog, a package for the GAP computer algebra system
if IsInt(number) then
return number;
elif ## of groups ## This files's authors include Max Neunhöffer, Ákos Seress.
return # # to list here. Please refer to the COPYRIGHT file for details.
elif IsString(number) ## At least recognise the "natural" characteristic.
returnjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt h 0
fi;
return default;
end;
# RECOG.MakeStabChainHint := function( chain, stdgens )
# local b,bb,choice,dims,f,gens,grpnum,grps,i,j,lens,llens,m,name,names,nams,nrs,o,orblens,pts,r,size,slps;
# f := FieldOfMatrixList(stdgens);
# name := chain[1].name;
# size := chain[1].order;
# slps := [];
# names := [];
# dims := [];
# orblens := [];
# pts := [];
# gens := stdgens;
# repeat
# Print("Working on ",name,"\n");
# grps := [];
# nams := [];
# nrs := [];
# for i in [1..Length(chain)] do
# r := chain[i];
# if IsBound(r.parent) and r.parent = name then
# Add(grps,ResultOfStraightLineProgram(r.generators,gens));
# Add(nams,r.name);
# Add(nrs,i);
# fi;
# od;
# if Length(grps) = 0 then break; fi;
# Print("Considering subgroups: ",nams,"\n");
# bb := [];
# llens := [];
# grpnum := [];
# for i in [1..Length(grps)] do
# # will be left by break in case of success
# Print(" Considering ",nams[i],"\n");
# m := GModuleByMats(grps[i],f);
# if not MTX.IsIrreducible(m) then
# b := List(MTX.BasesMinimalSubmodules(m),MutableCopyMat);
# Sort(b,function(a,b) return Length(a) < Length(b); end );
# Print(" Dimensions: ",List(b,Length),"\n");
# lens := [];
# for j in [1..Length(b)] do
# TriangulizeMat(b[j]);
# if Length(b[j]) = 1 then
# o := Orb(gens,b[j][1],OnLines,rec( report := 10000,
# treehashsize := 1000, storenumbers := true ));
# else
# o := Orb(gens,b[j],OnSubspacesByCanonicalBasis,
# rec( report := 10000, treehashsize := 1000,
# storenumbers := true ));
# fi;
# Enumerate(o);
# Print(" Found orbit of length ",Length(o),"\n");
# lens[j] := Length(o);
# od;
# Append(bb,b);
# Append(llens,lens);
# Append(grpnum,ListWithIdenticalEntries(Length(b),i));
# else
# Print(" Restriction is irreducible!\n");
# fi;
# od;
# choice := 1;
# Print("Dimensions: ",List(bb,Length),"\n");
# Print("Orbit lengths: ",llens,"\n");
# Error("now decide which orbit to take, set choice");
# if choice > 0 then
# i := grpnum[choice];
# Add(names,nams[i]);
# Add(dims,Length(bb[choice]));
# name := nams[i];
# gens := grps[i];
# size := size / llens[choice];
# Add(orblens,llens[choice]);
# Add(slps,chain[nrs[i]].generators);
# Add(pts,bb[choice]);
# fi;
# until size = 1 or choice = 0;
# return rec( slps := slps, names := names, dims := dims, orblens := orblens,
# pts := pts );
# end;
java.lang.StringIndexOutOfBoundsException: Range [0, 21) out of bounds for length 15
local S,# if choice > 0 then
# Add(names,nams[i]);
if# name := nams[i];
Info( size := size / llens[choice# Add(orblens,llens[choice]);
" not java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 11
Info(InfoRecog# pts := pts );
return fail;InstallGlobalFunction( DoHintedStabChain, function(ri,G,hint)
fi;
gm := Group Sb,bra,c,cf,lmfinder,fu,gm,,mmax,,maxgens,opt,stdgens;
gm.pseudorandomfunc := [rec(
func := function(ri) return RandomElm(ri,"java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 25
args := [ri])];
(nfoRecog,2,Finding standard generators with bbox program...");
stdgens := RunBBoxProgram" not availabe!");
rec( orderfunction := RECOGnInfoInfoRecog,"heck your AtlasRep installation!");
if stdgens =fail stdgens ="timeout" then
Info(InfoRecog,2,Stdgens finder did not succeed for ",hint.name);
return fail;
fi;
gm!.seudorandomfunc : [ec
: function()return RandomElm(ri,"StdGens",true).el; end,
#SetStdGens(ri,StripMemory(stdgens));args : [i]];
if (hint.semax) then
if IsBound(hint.brauercharelm) then
elm: ResultOfStraightLineProgram(hint.brauercharelm,stdgens);
bra := BrauerCharacterValue( rec( orderfunctionrec(orderfunction := RECOG.ProjectiveOrder ) );
.usemaxFiltered[1.(.),
i->hint.brauercharvals[i] Info(nfoRecog,,Stdgens did not succeedfor"hintname)java.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
maxes := hint. if IsBound(hint.brauercha(int.brauercharelm)
fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
max in maxes do
s : :=hint.semax{(1.(hint.semax]
s = fail then
Info(InfoRecog,1,"Expected java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 12
for in java.lang.StringIndexOutOfBoundsException: Range [27, 28) out of bounds for length 27
Info(java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
(nfoRecog1,"Expected subgroup slp "n,
fi;
:= ResultOfStraightLineProgram(program,
returnfailjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
m:=GModuleByMats(maxgens,i!field);
if MTX.IsIrreducible( StripMemory()java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
Info(InfoRecog,2,"Found irreducible submodule!");
continue;
fi;
cf := List(TXCollectedFactorsm,-x[])
(,unctiona) dimension .dimension; );
for c in cf do
(nfoRecog2" irreducible submodule!)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
if Length(homs Sort(,unction(a,b) . dimension; end;
vertToMatrixRep[,!.field)java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
homs =MTX.(,mjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
break;
fi;
# Some must be in the socle, so this terminates with break!java.lang.StringIndexOutOfBoundsException: Range [44, 38) out of bounds for length 58
od;
TriangulizeMatbreak;
=function)returnRandomElm(ri""true)e;end;
opt : ( : true,RandomElmFunc =fu )
if java.lang.StringIndexOutOfBoundsException: Range [0, 21) out of bounds for length 15
opt. :rec(points: b],ops :[])
else
opt.and : rec( points : []
ops := [ ifLength()= 1then
fi;
gm := GroupWithGenerators else
opt.Size :hint.size;
Info(InfoRecog, :=[] );
java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 35
S := .Size: hint.size;
#Verify correctness sifting :
# Actually, genss does not terminate if no group of this
# size is found!
ri!.S := StabilizerChain,pt)
Setslptonice(i,SLPOfElms(())
SetSize(ri,hint.sizees terminate if no this
ForgetMemory(S);
nc)
Setslptoniceri,(StrongGenerators();
SetFilterObj(ri,IsLeaf);
if SetSizeri,hint.)java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
Setslpforelement(ri,SLPforElementFuncsProjective.StabilizerChainProj);
fi;
SetIsRecogInfoForAlmostSimpleGroup IsBound(hinti)then
: .namejava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
return ;
od;
fi;
o( InfoRecog 2 Got stab chainhint,not implemented")
return fail;
end );
InstallGlobalFunctionInfo ,2 G stabhint,not implemented!)
fail;
tries,triesinner,riesinnerlimit,trieslimit,x,y;
Info(InfoRecog,,Got forgroup, trying LowIndex.";
fld := ri!.field;
!.;
if IsBound(hint.lordersstart then
i : (,,Got for group LowIndex.";
repeat
i :=i 1java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
if i > 10000
";
fi;
: ();
until "wrongjava.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 44
x := [x];
else =x;
= ]java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
;
tries java.lang.StringIndexOutOfBoundsException: Range [19, 17) out of bounds for length 65
numberrandgens=ParseNumber(.,,2;
triesinnerlimit orblenlimit:= RECOG.arseNumber(hint.orblenlimit,d,"4d");
trieslimit := Info(InfoRecog,3,"Using numberrandgens=",numberrandgens,
orblenlimit := RECOG.ParseNumber(hint.orblenlimit, " triesinnerlimit=",triesinnerlimit," trieslim",rieslimit,
Info(InfoRecog "orblenlimit=",rblenlimit);
" triesinnerlimit=",triesinnerlimit," java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 0
"orblenlimit="orblenlimit;
repeat
: ()
java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 22
ifnumberrandgens = Length(ens
hm := GModuleByMats(tries=+1java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
while() <numberrandgens
: +1;
continue;
fi;
while Length(gens) Add(gensy;
triesinner < triesinner := triesinner + 1
y := PseudoRandom(G);
Add(gens,y);
triesinner =triesinner +1;
hm := GModuleByMats(gens,fld);
ifMTX.sIrreducible() then
Unbind(gens[Length(gens)]);
fi;
od;
fi;
if fi
# We hope to have the maximal subgroup!
;
s: bas[1;
while s <> # We hope to have the maximal subgroup!
hm :MTXInducedActionSubmodule,)java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
s : .java.lang.StringIndexOutOfBoundsException: Range [46, 43) out of bounds for length 48
Add( : .(hm;
od;
Unbind(bas[Length(bas)]);
s := bas[Length
[Length()1Length(as)2.1] do
s : bas[engthbas);
od;
foriin [Length()1Length(as)-.]do
s := MutableCopyMat( java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
TriangulizeMats;
# FIXME: this will be unnecessary:
ep()
Info(InfoRecog FIXME this will beunnecessary:
Length( (InfoRecog,Foundinvariantsubspaceof dimension"
if IsBoundhint.)or
Length(s) in hint.subspacedims then
b : RECOG.OrbitSubspaceWithLimit,s,rblenlimit)
orb := Length()in hint.ubspacedimsthen
rec(:= Orb(G,s,OnSubspacesByCanonica
hashlen := java.lang.StringIndexOutOfBoundsException: Range [53, 52) out of bounds for length 70
Enumerate(orb,orblenlimit);
if IsClosed(orb) then
hom := OrbActionHomomorphism(G,orb);hom =java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 54
ifLengths *()=d then
# A block system!
# A block system!
ri. = Length();
InitialDataForKernelRecogNoderi)blocksize: Length(s);
FindHomMethodsProjectiveDoBaseChangeForBlocks
2000);
Setimmediateverification(ri,true);
findgensNmeth(ri).args java.lang.StringIndexOutOfBoundsException: Range [49, 46) out of bounds for length 56
findgensNmeth(ri).rgs[2 : 5;
Info(InfoRecog,2,"Found block system with ",
Length(orb)" blocks.";
else
Info(InfoRecog,2,"Found orbit of length ",
Length(orb),"-not a block system.");
fi;
SetHomom(ri,hom);
Setmethodsforimage(ri,FindHomDbPerm (orb,blocks")
returntrue;
fi;
else
orb, a block system."java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 45
;
fi;
tries := tries + fi;
until tries > trieslimit;
return failjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
end );
# We start a database of hints, whenever we discover a certain group, we
# can ask this database what to do:
. : (;
# is called in almostsimple/hints.gi to create a database in
# RECOG.AlmostSimpleHints to store hints about almost simple groups.
# Currently just sporadic simple groups are contained.
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 0
# RECOG.AlmostSimpleHints tomple groups are java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 47
()=[
fi;
re.type := type;
Add( ;
;
# FIXME: unused?
# TODO: this was likely used to generate the hints in almostsimple/hints.gi.
# Document this, and how to replicate the hints; move the code to a separate file.
# Indeed, ideally a user should be able to trivially regenerate the list of hints
# by running a script. Note that for that, we need to also explain how the arguments
# "reps" and "maxes" are chosen...
# Perhaps a full script is not possible; but then we should still explain how
# the hints where generated.
RECOGfgh,java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 68
badf,hl,m,,revdimp,r,ranger,,
size,success,t,values,x;
prevdim: ;
prevdim := fail;
prevfield: fail;
forforr repsdo
Print("\nDoing representation : (,)java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
gens=AtlasGeneratorsname,;
g := Group(gens.generatorsvalues: ]java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
f: r;
values := [];
: false;
size := Size maximal java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
formin[..ength()
Print("Doing maximal subgroup #",m,"\n");
: rec( name := name, size := size, usemax := [m] );
ri := RecogNode((),g,java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
t :res: java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 46
res := res=then
=)-t
if res =1;
o : (,x*Length+,)o))
x := o[1];
x
Add(values,[fi
dv+,)]
fi;
Print("valuePrint(\";
Length( : truejava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
ViewObj(x);
Print("\n");
success : ;
else
java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 9
()=prevfield andLength(gensg[1)=prevdim then
fi;
od ">SAME \n;
if success java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 13
ifbad: (.java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 71
AppendTo(.,,
">>>SAME FIELD AND DIM\if v)> java.lang.StringIndexOutOfBoundsException: Range [40, 41) out of bounds for length 40
fi;
list =ShallowCopymaxes;
SortParallel(values,list);
bad := First( else
if = fail or bad >3then
if Length(values;
range : [..];
else
)];
fi;
else
range := [1..bad-1];
fijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
AppendTo(Concatenation("NEWHINTS.", ,\ : ,size,
( ",ame,\,\StabChainHint\,n,
" rec values{}"n)\")java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 0
"], \n usemax := ",list{range},
", \ local br1,br2,class ,br2classes,gjava.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 60
,atlasrepnrs := [",r,"], \n values := ",
values{range},"gens2: java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 49
=x>java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 52
l := Filtered.Length(),>r1]>br2[)java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
od;
endlens :=List(l,-Length((lps[]);
# FIXME: unused?
: function(name,rep1,
local br1,br2,classes, [br1[l[1]],br2[l[1"\";
classes := java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 0
gens1 := GeneratorsWithMemory(AtlasGenerators(name,rep1).generators);
: AtlasGenerators(name,rep2).generators;
guck1 : java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 54
guck2 I =;
=g,xBjava.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 52
br2 := PrintGenericStabChainHint =java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 49
l :java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 42
slps := List(guck1,SLPOfElm);
:=List(,>(LinesOfStraightLineProgram[]);
SortParallel(lens,l);
( := ,l1]" : ,
[br1[l[1]],br2[l[1]]],",\n");
end;
# This is for the released AtlasRep package:
not ()then
AGR_TablesOfContents := failPrint("rec(name :=\" ,"" =")
AGR_InfoForName := fail;
fi;
# FIXME: unused?
RECOG.rintGenericStabChainHint := function ( n )
local S,g,gens,nn,toc,tocs;
tocs := AGR_TablesOfContents( "all" );
end
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
gens := AtlasGenerators( n, 1 ).generators;
g := # if triesforgens = "Xd" then it will use X * # if orblenlimit = "Xd" then it will use X * d (X a number as a string)
S := # This means:
Print( "# orblenlimit := "4d" )
# BUG: The following hint # can lead to an infinite loop in DoHintedLowIndex, because
Print such elements are found.
Print# See also https://github.com/gap-system/recog/issues/6
end;
# dimensions optionally
# subspacedims there or not
# elordersstart unbound ==> start with empty generator list
# if numberrandgens = "logd" then it will use LogInt(d,2)
# if triesforgens = "Xd" then it will use X * d (X a number as a string)
# if orblenlimit = "Xd" then it will use X * d (X a number as a string)
# L2 hint with doing the decision on the fly
# depending on the ppd-Properties of L2(p)
# This means:
# rec( numberrandgens := "logd", tries := 10, triesforgens := "1d",
# orblenlimit := "4d" )
# is the standard low index.
# BUG: The following hint was added a long time ago, but it
# can lead to an infinite loop in DoHintedLowIndex, because
# elordersstart suggests searching for elements of order 31,
# but no such elements are found.
# See also https://github.com/gap-system/recog/issues/6
# InstallAlmostSimpleHint( "L2(31)", "LowIndexHint",
# rec( characteristics := [31], dimensions := [1,2,3],
# elordersstart := [31], numberrandgens := 2, tries := 1,
# triesforgens := 100, orblenlimit := 32, issimple := true ) );
# if hint in AlmostSimpleHints exists appropriate function is executed
if hi]java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 53
name
,,q
ForAnyj.java.lang.StringIndexOutOfBoundsException: Range [44, 42) out of bounds for length 65
if IsBound(RECOG. dim in hijava.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 45
j := 1;
hi := RECOG.AlmostSimpleHints.( return DoHintedLowIndex,[]java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
f := ri!.field return (ri,G,i[]);
p: (f;
q := Size(f);
dim := ri!.dimension;
while j <= Length(hi) do
ifnot ([j]characteristicsor
p in hi[j].characteristics) andod
(not IsBound Info(InfoRecog,,Nohint worked up.)java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
q in hi[.)and
(java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
ForAny(hi[j].dimensiondivs,d->dim mod d = RECOG. : functionvec,g,bound)
n IsBound(hi[j]dimensions
=java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 29
#
if hi[j] 1.]java.lang.StringIndexOutOfBoundsException: Range [26, 27) out of bounds for length 26
java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 18
elif java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 13
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
# Put other hint types here!
fi;
fi;
j := j + 1;
od;
fi;
Info(# uniformlydistributed random elements in G togetherwith its
return fail;
end );
# checks whether the orbit of <vec> under g is not longer than bound
RECOG.shortorbit := function(vec,g,bound)
v,i, pos;
v := StructuralCopy(vec randelfunc =function()
pos := PositionNonZeroel= (r;
:= vec / vec[pos];
for i in [1..bound] do
v := v * g;
if v = v[pos] * vec then
break;
fi;
odjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
return i;
;
# Under the assumption that G is an almost simple group,
# attempt to guess the "natural" characteristic of the
# group based on the two or three maximal orders of group elements.
#
# Used by FindHomMethodsProjective.ThreeLargeElOrders.
fi
# randelfunc must be a function taking ri as one argument and returning
# uniformly distributed random elements in G together with its
# projective order (as for example below), or fail.
t,,vecbound,count,m1,m2,m3,order,,last,,,d,pr;
if randelfunc =
m3=0;
randelfunc := function(ri)
local el;
el repeat
rec( el ,order :ProjectiveOrdere)1 ;
end;
fi;
p := Characteristic(ri!.field);
: ri!.dimension;
mat:=One(G);
vs:=VectorSpace(GF(p),mat);
repeat
vec:=Random(vs) :=.rderjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
until not IsZero()
(,Product(GeneratorsOfGroup(),3*)=3*dthen
return p;
fi;
find three largest elementorders ,m3
bound:=32*(LogInt(d
=0;
m1:=0;
m2 m3=m2;
m3:=0;
last:=0;
repeat
:count+1;
m3:order;
g := r.el;
order:=r.order;
if last:count;
return p;
eliforder > m1 then
m3:=m2;
m2:=m1;
:order;
last:=count;
elif order [137 "B2,8]]java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
m3:=2;
m2:=order;
last: elif [1m2, =[,7,6]then
order<2 order>3 then
=;
last:=count [13,,"",]]
;
until count=bound java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 34
#handle ambiguous cases
if [m1,m2,m3 [,,m3 1296
[[,,[2"8];
elif [m1,m2] = [13,8] then
[138 [l,3,]];
[,,""4,];
[13,7,[l"2,13]]
elif [ return [[ 5,3,["l",2,4]]];
[1,2]= [,4] then
java.lang.StringIndexOutOfBoundsException: Range [12, 8) out of bounds for length 36
return [[13,12 elif [m1,m2] = [7,4] then
elif [m1,m2,m3] = [12,java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 33
returnelif m,2] =[,]then
return [,,"",4];
return[129[u,4,];
elif [m1,m2] = [5,3] then
return [,3[,,];
elif [m1,m2] = [5,4] then
elif [m1elif [1m]= [30,4 then
[m1,2]then
return [[7,4,[" [1m]=[,]then
[6360[u",4,5]]];
return [[15,13,[",3,]]java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
elifm1,] 30,0]then
return [[30,20,["s" fi;
elif :(., x>[1=1andx[2]m2);
return [[30,24,["s",8,2]]];
elif [m1,m2] = [63,60] then
return [[63,60,[u,,5];
elif [m1,m2] = [91,85] then
return [[91, list2[][,]=""2 list[]3[]"2)
fi;
list:FilteredRECOGg, x-x[]m x[2]=2;
#one more ambiguous case
if Length(return l,x>[]1=l";
(list[1][3]{[1,2]}=["l",2] and list[2][3][1]="G2") or
fi
if m3>m1/2 then else
return Filtered(list,x->[3][]="2";
else
return Filtered(list,x->
fi;
else
return list;
fi;
end;
# just called for PSL (in FindHomMethodsProjective.ThreeLargeElOrders),
# gives hints
RECOG.MakePSL2Hint := function local d,defchar,f,p,q;
local d,defchar,f,p,q;
f : DefaultFieldOfMatrixGroup(G);
q := Size(f);
p:=java.lang.StringIndexOutOfBoundsException: Range [25, 21) out of bounds for length 25
d := java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 25
defchar := Factors(ame[])1;
if p = defchar then
;
fi;
,2,Making hint forgroup "name,..";
#we are in cross java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 35
# to be made better...
return# we arein
triesforgens # to be made better...
=3*(ame3]1))java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
orblenlimit=3([+1 ;
# is used in FindHomMethodsProjective.ComputeSimpleSocle
# it computes the non-abelian simple socle randomly (it might
# underestimates it)
# if called for an abelian group (even a group with nilpotence class smaller
# than 3?) it runs in an infinite loop
RECOG.simplesocle := function(ri,g)
local x,y,comm,comm2,comm3,gensH;
repeat
x:=RandomElm(ri,"simplesocle",trueRECOG. =functionri,g)
until not ri!.isone(x) local x,y,java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 35
y: ri!i(x;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
until not ri!. y:RandomElm(ri,"simplesocle",true).el;
repeat
y=RandomElm(ri,"simplesocle",true)java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
comm2:=Commjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
until not ri!.isone(comm2);
lm(,,.;
comm3:=Comm(comm2,comm2^yjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 29
gensH:=FastNormalClosure(g,[comm3],20);
return gensH:=FastNormalClosure(g,[comm3],20);
end;
#! @BeginChunk ComputeSimpleSocle
#! This method randomly computes the non-abelian simple socle and
#! stores it along with additional information if it is called for
#! an almost simple group. Once the non-abelian simple socle is
#! computed the function does not need to be called again for this
#! node and therefore returns <K>NeverApplicable</K>.
#! @EndChunk
BindRecogMethod(FindHomMethodsProjective#! computed the function does not need to be called again for this
"compute simple socle #! @EndChunk
function(ri,G)
local x;
RECOGS,";
ri!.simplesocle := Group(RECOG.function(ri,)
ri!.simplesoclepr :RECOG.(,"
.:=(100)java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
Append(ri ri!.implesoclerand := EmptyPlist(100);
ri!.simplesoclerando := EmptyPlist( Append(ri!.simplesoclerand,GeneratorsOfGroup(ri!.simplesocle));
for x in ri!.simplesoclerand do
Add simplesoclerando : EmptyPlist(100)java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
od;
ri!.simplesoclerandp := 0;
ri!.simplesocle!.pseudorandomfunc :=
[rec( func := ;
return ri!.simplesoclerandp := 0;
end);
# computes a random element in the non-abelian simple socle
# and its projective order
# first uses the random generator and afterwards generate
# a new random element
: java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 43
# computes a random element in the non-abelian simple java.lang.StringIndexOutOfBoundsException: Range [0, 59) out of bounds for length 26
ri!.RECOGR: ri)
not (i.r!]then
el := Next( ri!s: .+ ;
ri if not IsBoundr!simplesoclerand[i.] then
ord =ProjectiveOrder()[];
!.implesoclerando[i!simplesoclerandp]: ord;
else
el : !simplesoclerando[!. :ord;
ord := ri!.simplesoclerando[ri el :=ri.simplesoclerandr!.simplesoclerandp];
fi;
return rec( el := el, order := ord );
end;rec : , =ord ;
#! @BeginChunk ThreeLargeElOrders
#! In the case when the input group <A>G</A><M> \le PGL(d,p^e)</M> is
#! suspected to be
#! simple but not alternating, this method takes the three
#! largest element orders from a sample of pseudorandom elements of
#! <A>G</A>. From these element orders, it tries to determine whether <A>G</A>
#! is of Lie type and the characteristic of <A>G</A> if it is of
#! Lie type. In the case when <A>G</A> is of Lie type of characteristic
#! different from <M>p</M>, the method also provides
#! a short list of the possible isomorphism types of <A>G</A>.
#!
#! This method assumes that its input is neither alternating nor sporadic and
#! that <Ref Func="ComputeSimpleSocle"/> has already been called.
#!
#! This recognition method is based on the paper <Cite Key="KS09"/>.
#! @EndChunk
BindRecogMethod(FindHomMethodsProjective, "ThreeLargeElOrders",
"recognise Lie its"
G
,,pjava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
RECOG !: ;
ri!.simplesoclerandp := 0;
p=java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 70
if p = Characteristic(ri!Info2java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 75
Info(InfoRecog,2,"ThreeLargeElOrders: defining characteristic p=",p) fi;
return false; # FIXME: false = NeverApplicable here really correct?InfoRecog2":found ,)java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
fi;
# Try all possibilities:
Info(nfoRecog2,ThreeLargeElOrders "p)
name1] l then# Handle PSL specially
name[] =2then
namehint : .akePSL2Hint(ameG;
if name[1] = "l" then # Handle PSL specially
if name[2] = 2 then
hint FindHom,,,3;
if hint < fijava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
res := DoHintedLowIndex(ri,G,hint);
else # we use Pete Brooksbank's methods
return :name1)
;
else
return F(i,,name[2]name[];
fi;
else
if Length(name) = 3 then
namecat := Concatenation(UppercaseString(name[1]namecat : name[1];
String(name[2]),
"(",String(name[3])," res : LookupHintForSimple(ri,G,namecat);
else
namecat := name[1];
fi;
LookupHintForSimple(ri,G,namecat);
fi;
if res = true then
return
fi;
od;
Info(InfoRecog
return fail; # FIXME: fail = TemporaryFailure here really correct?
# degs := [];
# RECOG.DegreeAlternating := function (orders)
# local degs, prims, m, f, n;
# degs := [];
# prims := [];
# for m in orders do
# if m > 1 then
# f := Collected(Factors(m));
# fi;
# n := Sum(f, x->x[1]^x[2]);
# if f[1][1] = 2 then n := n+2; fi;
# AddSet(degs,n);
# UniteSet(prims,Set(f,x->x[1]));
# fi;
# od;
# return [degs, prims];
# end;
#
# RECOG.RecognizeAlternating := function (orders)
# local tmp, degs, prims, mindeg, p1, p2, i;
# tmp := RECOG.DegreeAlternating (orders);
# degs := tmp[1];
# prims := tmp[2];
# if Length(degs) = 0 then
# return "Unknown";
# fi;
# mindeg := Maximum (degs); # minimal possible degree
#
# p1 := PrevPrimeInt (mindeg + 1);
# p2 := PrevPrimeInt (p1);
# if not p1 in prims or not p2 in prims then
# return 0;
# fi;
# if mindeg mod 2 = 1 then
# if not (mindeg in orders and mindeg - 2 in orders) then
# return 0;
# fi;
# else
# if not mindeg - 1 in orders then
# return 0;
# fi;
# fi;
#
# for i in [3..Minimum (QuoInt(mindeg,2) - 1, 6)] do
# if IsPrime (i) and IsPrime (mindeg - i) then
# if not i * (mindeg - i) in orders then
# return 0;
# fi;
# elif IsPrime (i) and IsPrime (mindeg - i -1) then
# if not i * (mindeg - i - 1) in orders then
# return 0;
# fi;
# fi;
# od;
# return mindeg;
# end;
#
# SLPforElementFuncsProjective.Alternating := function(ri,x)
# local y,slp;
# RecSnAnIsOne := IsOneProjective;
# RecSnAnEq := IsEqualProjective;
# y := FindImageAn(ri!.recogSnAnDeg,x,
# ri!.recogSnAnRec[2][1], ri!.recogSnAnRec[2][2],
# ri!.recogSnAnRec[3][1], ri!.recogSnAnRec[3][2]);
# RecSnAnIsOne := IsOne;
# RecSnAnEq := EQ;
# if y = fail then return fail; fi;
# slp := SLPforAn(ri!.recogSnAnDeg,y);
# return slp;
# end;
#
# SLPforElementFuncsProjective.Symmetric := function(ri,x)
# local y,slp;
# RecSnAnIsOne := IsOneProjective;
# RecSnAnEq := IsEqualProjective;
# y := FindImageSn(ri!.recogSnAnDeg,x,
# ri!.recogSnAnRec[2][1], ri!.recogSnAnRec[2][2],
# ri!.recogSnAnRec[3][1], ri!.recogSnAnRec[3][2]);
# RecSnAnIsOne := IsOne;
# RecSnAnEq := EQ;
# if y = fail then return fail; fi;
# slp := SLPforSn(ri!.recogSnAnDeg,y);
# return slp;
# end;
#
# FindHomMethodsProjective.AlternatingBBByOrders := function(ri,G)
# local Gm,RecSnAnEq,RecSnAnIsOne,deg,limit,ordersseen,r;
# if IsBound(ri!.projordersseen) then
# ordersseen := ri!.projordersseen;
# else
# ordersseen := [];
# fi;
# limit := QuoInt(3*ri!.dimension,2);
# while Length(ordersseen) <= limit do
# Add(ordersseen,RECOG.ProjectiveOrder(PseudoRandom(G)));
# if Length(ordersseen) mod 20 = 0 or
# Length(ordersseen) = limit then
# deg := RECOG.RecognizeAlternating(ordersseen);
# Info(InfoRecog,2,ordersseen);
# if deg > 0 then # we strongly suspect Alt(deg):
# # Switch blackbox recognition to projective:
# Info(InfoRecog,2,"Suspect alternating or symmetric group of ",
# "degree ",deg,"...");
# RecSnAnIsOne := IsOneProjective;
# RecSnAnEq := IsEqualProjective;
# Gm := GroupWithMemory(G);
# r := RecogniseSnAn(deg,Gm,1/100);
# RecSnAnIsOne := IsOne;
# RecSnAnEq := EQ;
# if r = fail or r[1] <> "An" then
# Info(InfoRecog,2,"AltByOrders: Did not find generators.");
# continue;
# fi;
# Info(InfoRecog,2,"Found Alt(",deg,")!");
# ri!.recogSnAnRec := r;
# ri!.recogSnAnDeg := deg;
# SetSize(ri,Factorial(deg)/2);
# Setslpforelement(ri,SLPforElementFuncsProjective.Alternating);
# Setslptonice(ri,SLPOfElms(Reversed(r[2])));
# ForgetMemory(r[2]);
# ForgetMemory(r[3][1]);
# SetFilterObj(ri,IsLeaf);
# SetIsRecogInfoForSimpleGroup(ri,true);
# return Success;
# fi;
# fi;
# od;
# return fail; # FIXME: fail = TemporaryFailure here really correct?
# end;
# abbreviation stands for "homomorphism fully deleted permutation module";
# returns a permutation
RECOG# abbreviation stands for "homomorphism fully deleted permutation module";
local r
r : RECOG.FindPermutation(ata.obxdata.cobi,ata.fdpm)java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
if
java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 18
fi;
return r#! This method is a black box constructive (?) recognition of#! and symmetric groups.
end;
#! @BeginChunk AltSymBBByDegree
#! This method is a black box constructive (?) recognition of alternating
#! and symmetric groups.
#!
#! This algorithm is probably based on the paper <Cite Key="BLGN+05"/>.
#! @EndChunk
# subroutines are in AnSnOnFDPM.gi and also paper reference
BindRecogMethod("try BB recognition fordim+ and/ dim2 if sensible",
" recognition for dim+1 and/or dim+2 if sensible",
function(ri,G)
,RecSnAnIsOned,,ffact,,newgens,o,orders,p,primes,
r,totry;
RECOG.SetPseudoRandomStamp(G,"AltSymBBByDegree");
d := RECOG.S(G,AltSymBBByDegree)java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 34
if Length(orders) = 0 then
= [andomElmOrd(,AltSym"false).order];
fi;
primes := Filtered(Primes,x-> fi;
for o in orders do
fact := FactorsTD(o =ri.java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
if(2)>0then
Info( I,.);
return NeverApplicable;
fi;
;
f=.
#
if d >= 6 x-java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 49
Info(,3,"ryingdeleted permutation module method...");
r := RECOG.RecogniseFDPM(G,f,1/10);
if r <> fail and IsRecord(r) then
# Now make a homomorphism object:
newgens := List(GeneratorsOfGroup(G),
SetHomomrihom)
fail then
GG
hom := GroupHomByFuncWithData(G,GG,RECOG.HomFDPM java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 29
(," ";
Setmethodsforimage(ri,FindHomDbPerm);
ri!.comment := "FDPM";
return
fi;
fi;
Info(java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 1
fi;
return# totry := EmptyPlist(2);
# TODO: try out an example that should need this;
# e.g. start with A_n on k-subsets, k >= 2, then go to perm mats...
#
# FIXME: there is dead code below...
# p := Characteristic(f);
# totry := EmptyPlist(2);
# if (d+1) mod p <> 0 and d+1 > 10 then
# Add(totry,d+1);
# fi;
# if (d+2) mod p = 0 and d+2 > 10 then
# Add(totry,d+2);
# fi;
#
# for deg in totry do
# Info(InfoRecog,3,"Looking for Alt/Sym(",deg,")...");
# RecSnAnIsOne := IsOneProjective;
# RecSnAnEq := IsEqualProjective;
# Gm := GroupWithMemory(G);
# r := RecogniseSnAn(deg,Gm,1/100);
# RecSnAnIsOne := IsOne;
# RecSnAnEq := EQ;
# if r = fail then
# Info(InfoRecog,2,"AltSym: deg=",deg,": did not find generators.");
# continue;
# fi;
# if r[1] = "An" then
# Info(InfoRecog,2,"Found Alt(",deg,")!");
# ri!.recogSnAnRec := r;
# ri!.recogSnAnDeg := deg;
# SetSize(ri,Factorial(deg)/2);
# Setslpforelement(ri,SLPforElementFuncsProjective.Alternating);
# Setslptonice(ri,SLPOfElms(Reversed(r[2])));
# ForgetMemory(r[2]);
# ForgetMemory(r[3][1]);
# SetFilterObj(ri,IsLeaf);
# SetIsRecogInfoForSimpleGroup(ri,true);
# ri!.comment := "Alt";
# return Success;
# else # r[1] = "Sn"
# Info(InfoRecog,2,"Found Sym(",deg,")!");
# ri!.recogSnAnRec := r;
# ri!.recogSnAnDeg := deg;
# SetSize(ri,Factorial(deg));
# Setslpforelement(ri,SLPforElementFuncsProjective.Symmetric);
# Setslptonice(ri,SLPOfElms(Reversed(r[2])));
# ForgetMemory(r[2]);
# ForgetMemory(r[3][1]);
# SetFilterObj(ri,IsLeaf);
# SetIsRecogInfoForAlmostSimpleGroup(ri,true);
# ri!.comment := "Sym";
# return Success;
# fi;
# od;
# return TemporaryFailure;
end# RECOG.SporadicsSizes[i] is the size of the sporadic simple group
# Looking at element orders to determine which sporadic it could be:
# The following may have been generated by RECOG.MakeSporadicsInfo.
# RECOG.SporadicsElementOrders[i] contains all appearing element orders
# in the sporadic simple group RECOG.SporadicsNames[i].
# RECOG.SporadicsElementOrders[i][j] contains an element order of the
# sporadic simple group RECOG.SporadicsNames[i] with
# probability RECOG.SporadicsProbabilities[i][j].
# RECOG.SporadicsSizes[i] is the size of the sporadic simple group
# RECOG.SporadicsNames[i].
# RECOG.SporadicsKillers contain orders that appear relatively often.
RECOG.SporadicsElementOrders :=
[ [ 1,2,3, [12,34,,6,,8,0,2,4,1721,28 ,
[ ,,345,,11]java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
[ 1,2,3,4,5,6,8,9,10,12,15,17,19 ],
[ 1,2,3,4,5,6,7,8,11,14,15,23 ],[ 1, 1,34567810111214151620,21,2,,,28,
[ 1,2,3,4,5,6,7,8,10,12,15 ],
[1234567810,12,,,,,8]
[ 1,2,3,4,5,6,7 ,,1,, ]
[12,45,,,,0,11121520]
[ 1,2,3,4,5,6,7,8,10,11,12,14,15,21,23 ],
[1,,3,4,,6,7,8,,,12,14,15,16,0,,22,23,4,28,
29,30,31,33,35,37,40,42,43,44,66 ],
[ 1,2,3,4,5,6,7,8,10,11,12,14,15,16,19,20,28,31 ],
[ 1,2,3,4,5,6,7,8,9,10,12,13,14,15,18,19,20,21,24,27,
2830,3136, ,
[ 1,[12345678910111214151820212223,2430
[ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,19,20,21,22,25,30, 35,40 ],
[ 1, [12,45678910111213,4,15,16,18,20,2122,24,0 ]
28,30,31,33,37,40,42,67 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,20,21,22,23,24,30
],[ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,20,23,24,28,30 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,20,21,24 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,30 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,
23,24,26,28,30,33,35,36,39,40,42,60 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,
,,4,26,27,,,,,,, ,
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,
22,23,24,26,27,28,29,30,33,35,36,39,42,45,60 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,30,31,32,33,34,35,36,38,39,40,
42,,46,7,8,2,5,6,6066,0 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,38,39 , ,234568,0,, ,
404142444546474850515254,,5657,,,,
66,68,69,70,71,78,84,87,88,92,93,94,95,104,105,110,119 ]
, ,2,34,,6,8,10,,12 ],
[ 1,2,3,4,5,6,7,8,10,11,12,14 ],
[ 1,2,3,4,5,6,7,8,10,11,12,14,15,20,30 ],
[ 1,2,3,4,5,6,7,8,10,12,14,15,24 ],
[ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,20,22,24,30 ],
[12,3,45,6,78,,0,1,1213,14,5,16,18,20,1,2224,28,30,40]java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
,6,7810,2,41516,720,,,, ,
[ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,19,20,21,22,24,
25,28,30,35,40,42,44,60 ],
[,2345678,,,11,,13,,15,,20,21,,2430,, ,
[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,
22,23,24,26,27,28,29,30,33,34,35,36,39,40,42,45,46,54,60,66,70,78,84 ],
[ 1,2,3,4,5,6,7,8,10,11,12,14,15,16,19,20,22,24,28,30,
31, 31,856 ][ 1,2,,,,,8,9,10,121517,18,924,34 java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
,[ ,345681012,,16,0]]java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
2,56,,,12,,,6,20]]
RECOG.SporadicsProbabilities :=
[ [ 1/175560,1/120,1/30,1/15,1/6,1/7,1/5,1/11,2/15,3/19 ],
[ 1/7920,1/48,1/18,1/8,1/5,1/6,1/4,2/11 ],
[ 1/95040,3/320,5/108,1/16,1/10,1/4,1/4,1/10,2/11 ],
[ 1/50232960,1/1920,49/9720,1/96,1/15,1/24,1/8,1/9,1/5,1/ 2/17,219]
2/17,2/19 ],
[ 1/10200960,1/2688,1/180,1/32,1/15,1/12,1/7,1/8,2/11,1/7 /23][ 1443520138413633215112,/18211]
2/23 ],[ 1/443520,1/384,1/36,3/32,1/5,1/12,2/7,1/8 [ 14030387200,73225602945,1/84,1300,/18,/4116,/16,/20java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
[ 1/604800,3/640,31/1080,1/96,7/150,1/8,1/7,1/8,3/10,1/12 11/,/40,/8,/52,/28,1/15,8,3/,/12,352,229]java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
[403038720017322560,9451/,/,/,/116,/,/20,
1/6,5/28,1/15,2/17,4/21,1/14 ],
[/,/,/,/,/000148,1/,
11/192,3/40,1/8,1/52,3/28,1/15,1/8,3/20,1/12,3/52,2/29 ],
44352000/,1360,/,17375,5/72173161/,211java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
1/12,1/15,1/10 ],
[ 1/244823040,19/107520,11/3780,1/48,1/60,1/12,1/21,1/16,1/20,
1/11,1/6,1/7,2/15,2/21,2/23 ],
[186775571046077562880,,13/21799895040,1/2661120,531576960,/720,
231115505920,1/161280,1/3240,79/20160,1/180,172291372116,
/,/80121,13264,/23,/24,1/141/291/03/1,133,
2/35,3/37,1/20 [1907459438878720001,/,/193536013000
[/46081550592011612801324079/0160118017229/1372,/,
111136,28,451/4,/191/0,1/4,2/31 ]
[ /90745943887872000,/92897280,36031719506880257/935360,/3000,
67/25920,1/1176,5/384,5/648,1/120,25/432,1/39,1/56,1/15,5/72,
1,201/,/,1/9,128,/5,/31,/12,2/ java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
[/89812800014032031291601/96,1/360,7,/,227,
1,/111/115,115 ,
[ 1/273030912000000,131/473088000,59/1632960,23/46080,16913/31500000,
1/192,1/420,9/320,1/27,431/12000,1/22,17/144,1/28,13/180,2/19,
3/20,1/21,1/22,2/25,1/12,2/35,1/20 ],
[ 1/51765179004000000,1/39916800,15401/2694384000 1/,67]
/362880,/168,/0,/4,3/3600,1/33,5/88,1/68,8/1125,
1/18,1/40,1/21,1/11,1/8,1/25,1/28,1/45,5/31,2/331/42,/24,/54,/5111,1/18,1/,1/,1/81/01/1,1/,
1/21,3/67 ],
[ 1/495766656000,179/31933440,631/2449440,1/1440,1/250,373/12960,
1/42,1/24,1/54,1/15,1/11,1/18,1/14,1/10,1/18,223112128110]
231/130]
[ 1/42305421312000,523/743178240,1/116640,139/120960,1/500,79/12960,
1/56,5/192,1/54,1/20,1/11,2/27,5/56,1/10,1 1/4 ],
2231121/110 ,
[ 1/448345497600,151/23224320,661/1959552,103/23040,7/1800,187/10368,
1/84,5/96,1/27,3/40,1/11,31/288,2/13,1/28,1/9,1/9,1/20,2/21,
1/24 ],
[ 1/64561751654400,4297/7357464576,11419/176359680,181/276480,1/600,
9121/933120,1/42,17/384,5/108,1/24,1/11,79/864,2/13,1/14 37/480,/252,22,/25288,/,1/14,/,/,/35,
1/16,7/108,1/20,1/21,1/11,1/24,1/30 ],
00039239/12752938598400,7802083/4035109478400,
1061/11612160,1433/15120000,198391/69672960,2/2205,79/23040,1/ 1/42344223,/61/,/7128,7/120,1/35,1182/9,
109/9600,1/66,10949/207360,1/156,1/42,277/5400,1/32,1/24,
37/480,17/252,1/114608,11891049760,74800,/,47413110401/,/,
/6,2/39,1/,1/84,/60 ,
[ 1/4089470473293004800,407161/129123503308800,161281/148565394432,
239/5806080,1/25200,1036823/705438720,1/840,1/128,127/17496,
11/1200,1/44,529/12960,/39,5/68,1/72,1/6,/17,13/16,/30,
1/42,3/44,2/23,1/16,1/13,1/27,1/28,7/120,1/35,1/18,2/39,
,
[ 1/1255205709190661721292800,6439/1032988026470400,144613199/
4412392214630400,25/6967296,1/907200,159797/564350976939596800,
11/4608,1189/1049760,7/4800,1/132,4741/311040,1/234,5/168,
103/162001/,1/1711/288,1/48,17/,/,2/23,7721/26java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
1/27,1/28,2/29,1/24,2/33,1/35,1/24,4/117,5/84,2/45,1/60 ],
[ 1/4154781481226426191177580544000000,
34727139371/281639525236291462496256000,160187/10459003768012800,
/060705263616000,1873110880000007216687/1418939596800
1/5644802,/,156,30,1/6170]java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
/312,871/64480,313600,,1/6,1/68,7432,/8323/12000,1/252,
5/264,1/23,19/432,1/25,3/104,1/27,5/224,67/1200,2/31,1/32,
1/66,3/68,1/70,5/108,1/38,1/39,1/20,1/36,1/44,1/23,2/47,
1/48,1/52,1/55,1/56,1/30,1/66,1/70 ],
[ 1/808017424794512875886459904961710757005754368000000000,
1162,392,87529/43200,93,/4,51188113631/,
1309301528411/299423045898886400305790976000,
228177889/60841285885126246400036117734128864000000000,
352968797/83672030144102400,16369/1382422809600,80467/177124147200,
7/18895680,1270627/532224000000,1/1045440,20669/313528320,
1/44,1/68,2/69,3140271,1/61/8,/71/,/6293
2323/1152000,907/370440,3/3520,1/276,167/13824,1/250,1/208,
1/162,3/392,1/87,529/43200,1/93,1/64,5/1188,1/136,31/2100,
1/48,1/76,25/702,49/1600,1/41,1/56,1/176,1/135,3/92,1/47,
1/96,1/50,1/51,3/104,1/54,1/110,5/112,1/57,2/59,41/720,1/31,
1/44,1/68,2/69,3/140,2/71,1/26,1/28,2/87,1/44,1/46,2/93,
1/47,2/95,1/52,1/105,1/110,2/119 ],
[ 1/190080,17/1920,5/216,3/32,1/20,5/24,1/8,3/20,1/11,1/4 ],
[ 1/887040,29/8960,1/72,71/277601/,,/14130110111,/,1/ ,
],[ 1/88704000,11/21504,1/720,7/240,17/750,17/240,1/14,1/8,1/6,
1/11,1/12,1/14,1/30,1/5,1/30 ],
[ 1/1209600,103/26880,31/2160,11/192,7/300,7/48,1/14,5/48,3/20,
5/24,1/14,1/15,1/12 ],
/,/887040,3158320172880,/,/720114,/48,
1/27,7/60,1/11,7/72,1/14,1/30,1/10,1/11,1/12,1/30 ],
[896690995200,6081/554675200,661/3919104,031/22560,7/600java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
2879/103680,1/168,53/1440,1/54,89/1200,1/22,65/576,1/13,3/56,
1/18,1/16,1/18,1/40,1/21,1/22,19/144,1/28,1/30,1/20 ]12871201/351101421221/0]
[ 1/8060774400,23/387072,1/945,9/1120,1/600,473/7560,95/8232,7/96,
1/24,1/8,19/168,1/30,1/8,1/ 1/51041141838132344258560035214985765431527572688076800java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
,[ 1/546061824000000,7057/25546752000,59/3265920,119351/177408000,
16913/63000000,2497/362880,1/840,21/640,1/54,691/24000,1/44,
101/1440,5/168,13/360,1/4153139968,/,/72641237965156,/,2
1/28,7/120,1/35,1/10,1/42,1/22,1/60 ],
1129123503308800,10781/1751777280011419352719360,329/414720,
1/1200,46757/4354560,1/84,1/32,5/216, 1/921631011840,40167415040,1648079/40320,1/601772029/,
1/12,1/60,1/16,29/216,1/20,1 /81151/313/381/ ,
[ 1/2510411418381323442585600,352149857/65431527572688076800,
144613199/8824784429260800,12091/4180377600,1/1814400,
20115929623//5368773550080,7/46960,/76801189/2099520,767200,
1/264,282547/13063680,1/468,31/1680,103/32400,1/32,1/34,
4153/139968,41/2400,17/504,7/264,1/23,7/96,5/156,1/54,2/21,
1/29,11/240,1/33,1/34,1/70,31/432,2/117,1/40,11/168,1/45,
1/23,1/54,1/60,1/33,1/70,1/39,1/84 ],
[ 1/921631011840,401/67415040,1/6480,79/40320,1/360,17/720,29/2744,
3/672,7/120,/22,1/2,556,145,1/8,3/38,/20,/22,/12,
1/28,1/15,1/31,3/38,1/14 ],
[ 1/100465920,91/195840,49/19440,1/64,1/30,11/144,5/48,1/18,1/10 '"""M"M122,M22.2""S.java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
1/8,1/15,1/17,1/6,1/19,1/12,1/17 ],[175560,920,,50232960,02009604435206048004030387200,
[ 1/17971200,23/30720,1/108,11/384,1/50,1/12,3/16,1/10,1/6,2/13,
1/4 ],
[ 1/35942400,23/61440,1/216,37/1280,1/100,1/24,3/16,1/20,
1/4,1/13,1/4,1/10 ] ]; 808017424794512875886459904961710757005754368000000000,190080,887040,
RECOG.SporadicsNames :=
[ "J1","M11","M12","J3","M23","M22"," 88704000,1209600,1796256000,8966909951209600,796256000,896690995200,8060774400,546061824000000,
" 129123503308800,2510411418381323442585600,21631011840,00465920,,
"Fi23","Fi24'","B","M","M12.2","M22.2","HS.2","J2.2","McL.2","Suz.2",
"He.2","HN.2","Fi22.2","Fi24'.2","ON.2","J3.2","2F4(2)'","2F4(2)'.2"];
RECOG.poradicsSizes:=
[ 175560,7920,95040,50232960, [[ 11,4],[1415],[10,8 ],[[ 1211],[29202623],
145926144000,4352000244823040,86775571046077562880,460815505920,
90745943887872000,898128000,273030912000000,51765179004000000,
495766656000,42305421312000,448345497600,64561751654400,
4157776806543360000,4089470473293004800,1255205709190661721292800,
4154781481226426191177580544000000,
[[26 .. 32 ], 25 . 32 ]], 28 . 32 ], 27 ..32 ] ],
88704000,1209600,1796256000,896690995200,8060774400,546061824000000,
129123503308800,2510411418381323442585600,921631011840,100465920,
17971200,35942400 ];
RECOG.SporadicsKillers :=
[5, ],[ 5, ],[67],[,],[ , ][ ,7][ ,9]]
[[ 11,14 ]],[[ 14,15 ]],[[ 10,8 ]],[[ 12,11 ]],[[ 29,20,26,23 ]],
[[ 15,14 ]],[[ 20,19 ]],[[ 13,11 ]],[[ 12,16 ]],[[ 19,23 ]],[[ 11,14,16 ]],
[[ 17,14,21 ]],[[ 15,13 ]],[ [ 18 .. 22 ] ] [35,,2336,37,8,0,1,42,43],#
[ [ 26 .. 32 ],[ 25 .. 32 ] ],[ [ 28 .. 32 ],[ 27 .. 32 ] ],
[ [ 27 .. 35 ],[ 29 .. 35 ],[ 27,29,34 ] ], # the latter is for Fi23
[ [ 31 .. 49 ],[ 40,41,42,43,44,45,46,48,49 ] ], # the latter is agains Fi23
[ [ 32 .. 73 ],[ 61 .. 73 ] ],[[ 6,10 ]],[[ 7,12 ]],[[ 9,14 ]],[[ 9,10 ]],
[[ 15,8,10 ]],[[ 13,12,21 ]],[[ 11,13,10 ]],[[ 25,17,20 ]],
[is to distinguish Fi22.2 and Fi22
[[ 35,32,23,26 ],[ 36,37,38,40,41,42,43 ]], # the latter is for Fi23
[18,2,4 ]][ 10,13],[ 7,11 ],[9,1 ]]
java.lang.StringIndexOutOfBoundsException: Range [22, 5) out of bounds for length 29
# Removed to avoid dependency on unpublished package gensift:
#RECOG.SporadicsWorkers[2] := SporadicsWorkerGenSift; # # for o in orders do
# and same for: M12, M22, J2, HS, Ly, Co3, Co2
#RECOG.MakeSporadicsInfo :=function(name)
# local ct,i,index,killers,o,orders,p,pos,prob,probs,probscopy,sum;
# ct := CharacterTable(name# : + 1SizesCentralizers(ct)p]java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
java.lang.StringIndexOutOfBoundsException: Range [13, 10) out of bounds for length 50
# probs := [];
# for o in orders do
# prob := 0;
# pos := Positions(OrdersClassRepresentatives(ct# sum =probscopy[Length(orders)];
# for p in pos do
# prob := prob + 1/SizesCentralizers(ct)[p];
# =i - 1;
# Add(probs,prob);
# od;
# index := [1..Length(orders)];
# probscopy := ShallowCopy(probs);
# SortParallel(probscopy,index);
];
# i := Length(#end;
# repeat
# i := i - 1;
# sum := sum + probscopy[i]java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
# until sum > 1/4;
# killers := index{[i..Lengthlocal ov;
# return rec( if IsPerm()then
# probabilitieso :=Order)
# end;
# returns a number (the projective order of <m>?) if the order is smaller than
# 120 otherwise fail
RECOG.RuleOutSmallProjOrder := function(RECOG.RuleOutSmallProjOrder := function(m
local l,o,v;
if IsPerm(m) then
o := Order(m);
if o > 119 then
return fail;
fi;
return o;
fi;
v := ShallowCopy(m[l : Length(;
Randomize(v);
ORB_NormalizeVector(v);
o := Orb([,,OnLinesrec( =300, report: 0);
Enumerate(o,121);
if not IsClosed(o) then
return fail;
fi;
l := Length(o);
Randomize(v);
ORB_NormalizeVector(v);
o := Orb([m],v,OnLines,rec( hashlen := 300, report := 0 ));
Enumerate(o,121);
if not IsClosed(o) then
return fail;
fi;
l : Lcm(l,Length(o));
if l > 119 then
return fail;
fi;
return l;
end;
#! @BeginChunk SporadicsByOrders
#! This #!groups and otherwise checks whether the most common ("killer") orders
#! possibly could be# of the sporadic groups appear.
#! <A>G</A> has elements of orders that do not appear in sporadic
#! groups and otherwise checks whether the most common ("killer") orders
#! of the sporadic groups appear.
#! Afterwards it creates hints that come out of a table for the sporadic
#! simple groups.
#! @EndChunk
BindRecogMethod(FindHomMethodsProjective, "SporadicsByOrders",
"generate a few random elements and compute the proj. orders",
function(ri,G)
local count,gens,i,j,jj,k,killers,l,limit,o,ordersseen, RECOG.SetPseudoRandomStamp(,"SporadicsByOrders);
l =[.Length(RECOG.SporadicsNames]
l := [1..Length(RECOG.SporadicsNames)];
pp := 0count : 0;
[];
count := 0;
gens := GeneratorsOfGroup(G);
limit := 120+Length(gens);
or in [1..limit] do
if i <= Length(gens) then
r := rec( el := gens[i] );
else
r := RandomElm(ri,"SporadicsByOrders",false);
fi;
o := RECOG.RuleOutSmallProjOrder(r.el);
if o = fail then
Info(InfoRecog,2,"Ruled outInfo(nfoRecog,2,"Ruled out all sporadic groups.");
return NeverApplicable;
elif i <= Length(gens) then
r.order := OrderFunc(ri)(r.el);
else
GetElmOrd(ri,r);
fi;
o := r.order;
x := r.el;
AddSet(java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 27
Info(l := Filtered,-o in RECOG.poradicsElementOrders[i])java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
l := Filtered(l,i->o in RECOG.SporadicsElementOrders[i]);
if l = [] then
Info(InfoRecog NeverApplicablejava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
return NeverApplicable;
fi;
# Throw out improbable ones:
j: 1java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
while j <= Length(l) do
if Length() =1then
java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 30
else
jj:l[]java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
fi;
jj := l[j];
raus := false;
# check whether orders appear in killers
for k in [1..Length(RECOG.(1-RECOG.SporadicsProbabilities[]^i<limit then
if not RECOG. Info(InfoRecog,3,"Have thrown out ",RECOG.SporadicsNames[jj],
(1-RECOG.SporadicsProbabilities[jj][k])^i < (id not see order ",
Info(InfoRecog,3,"Have thrown out ",RECOG.SporadicsNames[jj],
" (did not see order ",
RECOG.SporadicsElementOrders[jj][k],")");
raus := true;
break;
fi;
od;
if not raus and IsBound(RECOG ;
for killers in RECOG.SporadicsKillers[jj] do
if Intersection(ordersseen,
RECOG.SporadicsElementOrders[jj]{killers})=[]
and (1-Sum(RECOG.and (1-Sum(RECOG.SporadicsProbabilitiesjava.lang.StringIndexOutOfBoundsException: Range [69, 68) out of bounds for length 73
< 10^-3 then
raus := true;
break;
.SporadicsNames[jj]java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
" (did not see orders in ",
RECOG.SporadicsElementOrders[jj] RECOG.SporadicsElementOrders[jj]{killers},")");
fi;
od;
fi;
if raus thenfijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 26
else
j := j + 1;
fi;
od;
if l = [] then
(InfoRecog,,"uled out all sporadic groups.");
return NeverApplicable;
elif Length(l) = 1 then
count := count + 1;
if count >= 9 then
Info(InfoRecog,2,"I guess that this is the sporadic simple group ",
RECOG.SporadicsNames[l[1]],".");
break;
fi;
fi;
if Length(l) < 6 then
Info(InfoRecog,2,"Possible java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 11
RECOG.SporadicsNames{l}," i=",i);
else
Info(InfoRecog,,"Possible sporadics left: ",Length(l)," i=",i);
fi;
od;
if ValueOption("DEBUGRECOGSPORADICS") <> fail then
return RECOG.SporadicsNames{l};
fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
for i in [1..Length(l)] do
Info(InfoRecog,2,"Trying hint for ",RECOG.SporadicsNames ifValueOption("EBUGRECOGSPORADICS") < fail then
=LookupHintForSimple(ri,,RECOG.SporadicsNames[l[i]]);
if res = true then
return Success;
fi;
if IsBound(RECOG.SporadicsWorkers[l[i]]) then
nfo(nfoRecog,,"alling its installed worker...");
res := RECOG.SporadicsWorkers[l[1]](RECOG.SporadicsNames[l[i]],
RECOG.res := LookupHintForSimple(ri,G,RECOG.SporadicsNames
if res = true then
return Success;
;
fi;
Info(InfoRecog,2,"Calling its installed worker...");
od;
java.lang.StringIndexOutOfBoundsException: Range [53, 8) out of bounds for length 69
endRECOG.SporadicsSizes[l[],ri,G);
# Data for the function NameSporadic
RECOG.return Success
rec( fi;
maximalOrdersOverset := [5, 6, 8, 11],
maximalOrdersSubset := [],
length := 4),
rec(name := "M12",
maximalOrdersOverset := [6, 8, 10, 11],
maximalOrdersSubset := [],
length := 4),
java.lang.StringIndexOutOfBoundsException: Range [22, 23) out of bounds for length 22
maximalOrdersOverset := [5, 6, 7, 8, 11],
:= [,
length := 5)maximalOrdersSubset := [],
rec(name := "M23",
java.lang.StringIndexOutOfBoundsException: Range [0, 28) out of bounds for length 21
maximalOrdersSubsetrec(name := "M12",
rec(name := "M24",
maximalOrdersOverset=[8,10,11 12 ,15,21 ]java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
maximalOrdersSubset := [11, 21, 23]),
rec(name := "J1",
maximalOrdersOverset := [6, 7, 10, 11, 15, 19],
maximalOrdersSubset := [11, 15, 19]),
rec(name := "J2",
maximalOrdersOverset := [7, 8, 10, 12, 15],
maximalOrdersSubset := [7, 12, 15]),
rec(name := "J3",
maximalOrdersOverset := [8, 9, 10, 12, 15, 17, 19],
maximalOrdersSubset := [15, 17, 19]),
rec(name := "HS",
maximalOrdersOverset := [7, 8, 10, 11, 12, 15, 20],
maximalOrdersSubset := [11, 20]),
rec(name := "McL",
maximalOrdersOverset := [8, 9, 11, 12, 14, 30],
maximalOrdersSubset := [11, 14, 30]),
rec(name := "Suz",
maximalOrdersOverset := [11, 13, 14, 15, 18, 20, 21, 24],
maximalOrdersSubset := [11, 13]),
rec(name := "Ru",
maximalOrdersOverset := [14, 15, 16, 20, 24, 26, 29],
:= [26,29),
rec(name := "Co3",
maximalOrdersOverset := [14, 18, 20, 21, 22, 23, 24, 30],
maximalOrdersSubset := [22, 23, 24, 30]),
rec(name := "Co2",
maximalOrdersOverset := [11, 16, 18, 20, 23, 24, 28, 30],
java.lang.StringIndexOutOfBoundsException: Range [35, 27) out of bounds for length 49
rec(name := "Co1",
rec(name := "McL",
maximalOrdersSubset := [33, 42]),
rec(name := "ON",
maximalOrdersOverset := [11, 12, 15, 16, 19, 20, 28, 31],
maximalOrdersSubset := [19, 28, 31]),
rec(name maximalOrdersOverset := [11, 13, 14, 15, 18, 20, 21, 24],
maximalOrdersOverset := [13, 14, 16, 18, 20, 21, 22, 24, 30],
maximalOrdersSubset : maximalOrdersSubset := [11, 13]),
rec(name := "He",
:[,10,12 , 17,21 28],
maximalOrdersSubset := [17, 28]),
rec(name := "Ly",
maximalOrdersSubset: [26,29])
maximalOrdersSubset := [31, 67]),
maximalOrdersOverset :=[14,18 ,21 22,23 24,30,
maximalOrdersOverset := [16, 23, 24, 28, 29, 30, 31, 33, 35, 37, 40, 42, 43, 44, 66],
maximalOrdersOverset := [11, 16, 18, 20, 23, 24, 28, 30],
recname :"i23"
maximalOrdersOverset(java.lang.StringIndexOutOfBoundsException: Range [14, 12) out of bounds for length 22
maximalOrdersSubset := [17, 23]),
rec(name := "Fi24'",
maximalOrdersOverset := [6,17, 22,23,24 26 ,28 ,33,,36, 39,42 45,60],
aximalOrdersSubset : [7 29])
rec(name := "Th",
maximalOrdersOverset := [19, 20, 21, 24, 27, 28, 30, 31, 36, 39],
maximalOrdersSubset := [19, 31, 39]),
]);
#! @BeginChunk NameSporadic
#! This =[,24 ],
#! underlying <A>ri</A> could be. It does not recognise extensions of sporadic
#! simple groups nor the Monster and the rec(name := "He",
#! Magma v2.24.10 function <C>RecognizeSporadic</C>.
#! @EndChunk
# TODO G is unused
BindRecogMethod(indHomMethodsProjective, "NameSporadic",
"generate maximal orders",
function(ri, G)
local orders, setOfOrders, maximalOrders, isMaximal maximalOrdersOverset := [18, 22, 24, 25, 28, 30, 31, 33, 37, 40, 42, 67],
namesOfPossibleSporadics, res, i, j, data, name;
orders := [];
#do we need SetPseudoRandomStamp?
for i in [1 .. 500] do
Add(orders, RandomElmOrd( maximalOrdersSubset := [37, 43]),
od;
# Compute maximal orders. Maximal in the sense that it does not divide the
order of another group element.
setOfOrders := AsSet(orders);
# All orders we look for are <= 66.
if setOfOrders[Length(setOfOrders)] > 67 then
return NeverApplicable;
fi;
maximalOrders := [];
for i in [1..Length(setOfOrders)] do
isMaximal := true;
for j =[9 ,21 ,27,28,30 ]
ifsetOfOrders[] odsetOfOrders[i] = 0 then
isMaximal := false;
;
fi;
;
if ! underlying <A>ri>could .It doesnot extensionsof sporadic
maximalOrders,setOfOrdersi];
fi;
;
namesOfPossibleSporadics := [];
for data in RECOG.NameSporadicData do
IsBound(data.length) and not Length(maximalOrders) = data.length then
continue;
fi;
IsSubset(aximalOrders,data.maximalOrdersSubset)
and IsSubset(data.maximalOrdersOverset, maximalOrders) then
Add(namesOfPossibleSporadics, data.name);
fi;
od;
# HN works a bit differently
if IsSubset([9, 12, 14, 19, 21, 22, 25, 30, 35, 40], maximalOrders)
and (IsSubset(maximalOrders, [19]) or IsSubset(maximalOrders, [21]))
then
Add( # Compute orders.Maximal the sensethat it doesnot divide the
fi;
if ValueOption(" setOfOrders := AsSet(orders): AsSet(rders);
return # All orders we look for are 66.
java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
for name in java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 7
Info(InfoRecog, 2, "Trying hint for ", name,
"...[+1.java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 46
res := LookupHintForSimple(ri, Grp(ri), name);
if res = true then return Success; ;
Info(InfoRecog, 2, "This did not work.");
od;
return NeverApplicable;
end);
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