| products/Sources/formale Sprachen/GAP/pkg/recog/gap/projective/ (GAP Algebra Version 4.15.1©) Datei vom 22.0.2025 mit Größe 60 kB |
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Impressum almostsimple.gi Sprache: Shell |
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############################################################################# ## ## 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.ParseNumber := function( number, d, default ) if IsInt(number) then return number; elif number = "logd" then return java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4 # # gens# repeat return # nams# nrs := []; 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 # 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 [22, 21) out of bounds for leng local,ce,,homs,maxes,,s finder !java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds f if finder = fail then InfoInfoI2"java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of boun notjava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for l (,1"yourjava.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds return =or = fiInfoInfoRecog2,java.lang.StringIndexOutOfBoundsException: Range [34, 33) out o gm := ; . =[( func=ri java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds f :[]; Info IsBoundujava.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bou :java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for len rec java.lang.StringIndexOutOfBoundsException: Range [50, 48) out of bounds for l if stdgens = maxes := hint{(1.Lengthhintusemax] (nfoRecog2"finder did not ,.name; return fail; fi; stdgens := stdgens.gens; #Setslptostd(ri,SLPOfElms(stdgens)); #SetStdGens(ri,StripMemory(stdgens)); if IsBound(hint. else if IsBound(int.)then ; bra := BrauerCharacterValue(elm! formax in maxesdo maxes :=u{iltered[.Length(hint.), i->hint.brauercharvals[ifs = fail then else maxes := hint.usemax; fi; formax in maxesdo s := AtlasProgram(hint.name,max); if s = fail then Info(,,"Expectedmaximal of "hint.ame, " not available!"); Infomaxgens := ResultOfStraightLineProgram(., return ; fi; maxgens := :=GModuleByMatsmaxgens,.); (stdgens; m := GModuleByMats(maxgens,ri!.fieldM.()x>[]; Sortcf,(,b returna. <b.; endjava.lang.StringIndexOutOfBoundsException: Index 73 out InfoI,,Foundsubmodule"; continue; fi; cf := List(MTX.CollectedFactors(m),x->x[1]); cf,unction(a,)return a.imension<b.; end); for c in Con(homs[]ri!.field; homs: .omomorphismsc); if Length(java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for l ConvertToMatrixRep(homs[1],ri!.field); b := MutableCopyMat(homs[1]); ; ( (ri,StabChain"true).l ; :rec(Projective: true,RandomElmFunc: ) od; TriangulizeMat(b); fu := optCand : ( =[[1] : OnLines ); C : ( : [, if ()= 1 then opt.Cand := rec( points := [ fi; else opt.Cand := rec opt. : .size; ops :=OnSubspacesByCanonicalBasis); fi; gm := GroupWithGenerators( hint.name," ..."); opt. : hint.; Info(InfoRecog,2, correctnessby originalgens: hint.name," ... (gm,) # Verify correctness by sifting original gens:Setslptonicer,SLPOfElmsStrongGeneratorsS esnot terminate if nogroupof this # size is found! ri!.Unbind(S!.opt.RandomElmFu; (SLPOfElms())java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds f (,.ize; ForgetMemory(S); Unbind(S!.opt.RandomElmFunc); java.lang.StringIndexOutOfBoundsException: Range [60, 28) out of bounds for leng SetFilterObj(ri,IsLeaf); if IsBound(hint.ssimple ri!.comment=hint.name; fi; true; ri!.fi; return true; od; Inf ,2," chain , yet implemented!"; (InfoRecog,,"ot chain , yet ! ; return ; endtries,triesinner,riesinnerlimit,trieslimit,,y Info(InfoRecog,,Gothint , trying LowIndex.."java.lang.StringIndexOutOfBoundsExcepti d := ridimension if IsBound(hinte)then Info(nfoRecog2" hint group,trying LowIndex.." fld :=i+1; if IsBound(hint.elordersstart) then java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 13 repeat i := i + 1; if i > 10000 "wrong hints?); ErrorNoReturnx :PseudoRandomG; "wrong hints?"); fi; x := PseudoRandom(G); until Order(java.lang.StringIndexOutOfBoundsException: Range [0, 19) out of bound x:=[]; elsex:= []; x := []; fi; tries := 0; numberrandgensfijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds triesinnerlimit := RECOG.ParseNumber(hint.triesforgens,d,"1d"); trieslimit := RECOG.ParseNumber(hint.tries,d,10 : RECOG.hint.numberrandgensd,; =.java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for le 3"java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 5 it=,java.lang.StringIndexOutOfBoundsException: Range [69, 68) out of bounds for ,java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for len repeat gens := ShallowCopy(x); triesinner"=,)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds gens =ShallowCopyx) triesinner := 0; if = Lengthg)then# we have to make the hm module : tries + 1; continue; fi; else while Lengthgens) numberrandgensand triesinner < triesinnerlimittries =tries 1java.lang.StringIndexOutOfBoundsException: y :else Add(gens,)java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for ; hm := GModuleByMats( java.lang.StringIndexOutOfBoundsException: Range [35, 36) out : +1java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length if IsIrreduciblehm) ; od; fi if :bas] bas := [MTX.ProperSubmoduleBasis(hm)]; := .(hm,); s := bas[1]; :MTX.roperSubmoduleBasis(hm); hm := MTX.InducedActionSubmodule(hm,s); s =MTX.ProperSubmoduleBasishm) Add(bas,s); java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for od; Unbind( for i in bas-,b).1] do =basL()java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for len in [Lengthbas),b)-.1 s := s * bas[i]; od; # Now s is the basis of a minimal submodule, permute that: ()java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 2 TriangulizeMat( ConvertToMatrixRs) #FIXME:this be : ConvertToMatrixRep(s); Info,2" dimension , Length(s), ifnot (hint.ubspacedims java.lang.StringIndexOutOfBoundsException: Range if not b : RECOG.(G,s,) s inhint. #orb := RECOG.OrbitSubspaceWithLimit(G,s,orblenlimit); orb lBasis, rec(storenumbers := true, NextPrimeInt(2*orblenlimit))); Enumerate(orb,orblenlimit); if IsClosed(orb) then : OrbActionHomomorphism(G,orb); if Length(s) * Length(orb) Length()*Length(rb then InitialDataForKernelRecogNode(ri)blocksize: Lengths; () =Length(s); ., FindHomMethodsProjective.DoBaseChangeForBlocks, 2000); Setimmediateverification(ri,true); findgensNmeth(ri).args[1] := Length(orb)+3;ri.2]:5java.lang.StringIndexOutOfBounds findgensNmeth(ri).args[2] : ,"java.lang.StringIndexOutOfBoundsException: Index 51 Info(InfoRecog,2,"Found block Length(orb)," - not a block, java.lang.StringIndexOutOfBo Length)" ."; else Info( java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for lengt Length()"-not block."; fi; SetHomom(ri,hom); Setmethodsforimage(ri, "not enumerating orbit."); fijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 1 fi; else Info(InfoRecog ; "not enumerating orbit."); fi; # We start a database of hints, whenever we discover a certain group, we tries := tries + 1; RECOGAlmostSimpleHints:rec(; return java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for leng end ); # We start a database of hints, whenever we discover a certain group, we # can ask this database what to do: RECOG.AlmostSimpleHints := rec(); # 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. InstallGlobalFunction(InstallAlmostSimpleHint, function( name, type, re ) if not IsBound(RECOG.AlmostSimpleHints RECOG.AlmostSimpleHints.(name : [; RECOG.java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for leng fi reend) Add( RECOG. end ) FIXME: unused? # 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. RECOG.ProduceTrivialStabChainHint := function(name# the hints where generated. local bad,f,,gens,int,list,m,o,prevdim,prevfield,r,range,res,ri, size,success,t,values,x; PrintTo local ,,ggens,int,ist,,o,revdim,revfield,,range,es,rijava.lang.StringIndex prevdim :failjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds fo prevfield prevfield =fail; inreps do Print("\nDoing representation #",r,"\n"); gens =AtlasGeneratorsname,; g := Group(gens.generators); f := gens. gens := AtlasGe : AtlasGenerators(,) =[; success := false; size =gens.ing; for m in success: false; oing maximal subgroup#",m,"\n"); hint := rec( name := name, size 1.(axes]do ri := RecogNode(rec(), hint :rec(),gtrue); t := Runtime(); =DoHintedStabChain(ri,g,hint); t := Runtime() - t; if true then o := ri!.stabilizerchaint:= Runtime()- t; x: o[1]; if IsMatrix(x) then Addvalues[Length()QuoInt((o)99100)Length()]; else Add(values,[QuoInt( if IsMatrix() then fi; Print(" else d(alues,[QuoInt(Length(o)99,00)Length(o)]; ViewObj(x); "n); success : true; else Add(values,[infinity,infinity]); Print("java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for len fi success :truejava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds od; if success then ifSize( prevfield and (gens.enerators1] then ; >>>SAME FIELD AND DIM\)java.lang.StringIndexOutOfBoundsException: Index 50 out of boun fi; list := ShallowCopy(maxes); SortParallel(values,list); :=First[1.Length(values)],i->values[i][1] = infinity); if bad = fail or bad > AppendTo(Concatenation(NEWHINTS.,name) Length(alues > 3then range := [1..3]; else range : ShallowCopy() fi; bad > fi range=[.] "range := [1..Length(values " rec( name : Size(f),"], fi; "], \n usemax := ",list{range}, " \ size =" , ", atlasrepnrs : "InstallAlmostSimpleHint\"n," ""\" valuesrange}\ );n); fi; prevfield := Size(f); prevdim := Length(gens.generators[1]); od; end; # FIXME: unused? RECOG.DistinguishAtlasReps := function(name,rep1,rep2) localbr1,classes,gens1,gens2,uck1,guck2,l,lens,slps; classes := AtlasProgram(name,"cyclic").program; gens1 " java.lang.StringIndexOutOfBoundsException: Range [44, 30) out of bounds fo gens2 = AtlasGenerators(name,rep2).generators; guck1 := ResultOfStraightLineProgram(classes,gens1); guck2 := fi; br1: List(guck1,x-BrauerCharacterValue(x!.el)); br2 := List(guck2,BrauerCharacterValue); ([1..Length(r1],i-b[i<[]; slps := List(guck1,SLPOfElm od; lens: (lx>LengthLinesOfStraightLineProgram(lpsx)) java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 Print("brauercharelm := ",slps[l[1RECOG.DistinguishAtlasReps :=,rep2 ]]],,n"; end; # This is for the released AtlasRep package: if not IsBound(AGR_TablesOfContentsgens2 :=ResultOfStraightLineProgram(classes,gens AGR_TablesOfContents := fail; AGR_InfoForName: fail; fi br1 : List(uck1->rauerCharacterValue(x!.el)); # FIXME: unused? RECOG. :=function ( n ) local S,g,gens,nn,toc,tocs; tocs : AGR_TablesOfContents( "all" ); nn := AGR_InfoForName( n )[2]; toc := tocs[1].(lens: lx-Length((slps[)) gens := AtlasGeneratorsPrint(brauercharelm:="slps[[1],, brauercharvals :"java.lang.S g := Group( gens ); Sjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 Print( "InstallAlmostSimpleHint( \""if IsBound(GR_TablesOfContents :=",n \"usemax: ") java.lang.StringIndexOutOfBoundsException: Range [21, 19) out of bounds for leng Print( ",\.:= java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bou ; # 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 InstallGlobalFunction# L2 hint with doing the decision on the fly function# This means: local# orblenlimit := "4d" ) Info(InfoRecog,2,"Looking java.lang.StringIndexOutOfBoundsException: Range [0, 32 if IsBound(RECOG.AlmostSimpleHints.(name)) then j := 1; hi :=# but no such elements are found. f := ri!.field; p := stSimpleHint( "L2(31)"# rec( characteristics := [31], dimensions := [1,2,3], q := Size(f); dim := ri!.dimension; while # if hint in AlmostSimpleHints exists appropriate function is executed (not IsBound(hi[j.characteristics) or p in hi[j].characteristics) and (not IsBound(hi[j].fields) or name) local dim,f,i,,p,q; ForAny(hi[j]dimensiondivs,d->dim mod d = 0)) and (not IsBound(hi[j].dimensions) or [j].dimensions) then # This hint is applicable! if hi[j].type = "java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds (ri,G,i[]; elif hi[j].type = "StabChainHint" then return DoHintedStabChainri,G,j]); # Put other hint types here! =Characteristic)java.lang.StringIndexOutOfBoundsException fi; fi; j := j ( IsBoundhi[j.) ; fi; (InfoRecog2" ,giving up."; return fail; end ); in []fields # checks whether the orbit of <vec> under g is not longer than bound shortorbit:function(,,bound) local v, i, pos (otIsBound(hi[])or v:= StructuralCopy(vec); pos := PositionNonZero(vec); vec := vec / This hint is applicable! fori in [..ound do v := v * g; if v = v[pos] * vec then break; fi; od; return i; end; # 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. RECOG. randominG its ; local mat,vs, if randelfunc = fail then pr := ProductReplacer(GeneratorsOfGroup(G));local v,, ; randelfunc: functionri) local el; := Nextp) vec java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length end; fi; od; d := ri!.dimension; mat:=One(G); vs:=VectorSpace(GF(p),end; repeat vec:=Random(vs); until not IsZero(vec); if RECOG.shortorbit(vec,Product(GeneratorsOfGroup(# group based on the two or three maxim return p; fi; #find three largest element orders m1, m2, m3 bound:=32*(LogInt(d,2))^2*6*4; count:=0,s,,,,glist,p,d,; m2: randelfunc failthen m3:0; java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length countreturn rec( el:=el order : ProjectiveOrder(l)1])java.lang.StringIndexOutOfBounds r :d:.java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for g := r order:=.rder; if order >= 3*d then until not (ec; elif order > m1vecProduct(GeneratorsOfGroupG) 3d 3d m3:=m2; m2:=m1; m1:=order#findthree largest m1,m2 java.lang.StringIndexOutOfBoundsException: Range ; count:java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for leng :java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19 m2:=order; last:=count; elif order<m2count:1 = =; ; #handle ambiguous cases if [m1,m1:java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for l return[13,,[2"8]; elif [m1,m2] = [13,8] then return m3:=2java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for [,,m3 =137,6 return [[13, elif m2and >3 elif m3:order; return [[13,2[l"2,]]; elif [m1,m2,m3] = [13,12,9]fi return [[13,12,["G2",3]]]java.lang.StringIndexOutOfBoundsException: Index 0 out o elif m1m2,]=[12,9,]then return return [[37 [2B2,8]]java.lang.StringIndexOutOfBoundsException: Index 35 out elif [m1,return[13,,""3,]] return [129[u,,]] return [13,7,["2]; java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for leng mm] 54 elif [m1,m2,m3] = [13,12,9] then elif[m1,m2 return [[7,4,["l",2,7]]]; [1,2] = 1513 [1513[u,,]] [,,""4,]]java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for l return [[30,20,["s",4 [[5,3,"l",24]]java.lang.StringIndexOutOfBoundsException: Ind m,2 [30,]then return [[30,24,["selif m1m]= [7,4] elif[1,2 6360 return[[,,""u,3,]; elif [m1,m2] = [91,85] then [,2] =[30,0 fi; list:FilteredRECOGgrouplist, x-x]=1 [2]); #one more ambiguous case if Length(list) >=2 and ( (list[1][3]{[1,2]}=["l", [[6360,""4,]]java.lang.StringIndexOutOfBoundsException: ([]3{1,}[l,]and 1[]1="")then if m3>m1/2 then return Filtered(list :Filtered(.rouplist, >1=1and x2]=) else Filtered(ist,x-x3[]""java.lang.StringIndexOutOfBoundsException: Index 48 out of ; return listxx1"" fi; java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 # just called for PSL (in FindHomMethodsProjective.ThreeLargeElOrders), # gives hints RECOG.MakePSL2HintPSL (in FindHomMethodsProjective.ThreeLargeElOrders# gives hints java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length f :=f:java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for q =Characteristic(f); p := Characteristic(f); d := DimensionOfMatrixGroup(3[]java.lang.StringIndexOutOfBoundsException: Index 33 defchar := return fail if p = Info(InfoRecog, hint "".) return arein cross characteristic. fi; Info(InfoRecog,2,"Making hint for group ",name # to be made better... # we are in cross characteristic.we are in cross characteristic. # to be made better... orblenlimit: 3*([]1 ; triesforgens := 3*(name[3]+1), : 3*name[]1))java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds fo end; # 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 simplesocle: (,gjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds x,ycomm,comm2,comm3,gensH; repeat x:=RandomElm(ri,"simplesocle", repeat untilnot ri!.sone); repeat :java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for len comm:=Comm(x :ri",.el; until not ri!.isone(comm); y:=RandomElm(ri," comm2repeat until not y:=RandomE(i"simplesocle"true)el repeat y:=RandomElm(ri,"simplesocle",true).until not ri!.isone(comm3); comm3:=Comm(comm2,java.lang.StringIndexOutOfBoundsException: Index 1 out of boun until not ri!.isone(comm3); java.lang.StringIndexOutOfBoundsException: Range [37, 7) out of bounds for lengt return gensH; 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(java.lang.StringIndexOutOfBoundsException: Index 22 out of bound "compute simple socle .etPseudoRandomStamp(G"ComputeSimpleSocle)java.lang.StringInd functionri,) local x; .etPseudoRandomStampG"ComputeSimpleSocle"; ri!.simplesocle ri!.implesoclerand :=EmptyPlist; ri!.simplesoclepr := ProductReplacer(ri!.simplesocle); .java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for len java.lang.StringIndexOutOfBoundsException: Range [8, 5) out of bounds for length :100; for x in ri!.simplesoclerand do java.lang.StringIndexOutOfBoundsException: Range [28, 9) out of bounds for lengt od; java.lang.StringIndexOutOfBoundsException: Range [22, 4) out of bounds for lengt ri!.simplesocle! [rec( func := Next, args := [ri!. and its projective order# first uses the random generator and a return RECOG.RandElFuncSimpleSocle := function(ri) 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 .andElFuncSimpleSocle : function(ri) local el, if IsBoundr!simplesoclerand[i.simplesoclerandp] then ri!.implesoclerandp =ri!simplesoclerandp + 1 IsBound(i.r!simplesoclerandp) el := Nextord: el)1; ri.[.]=ord; ordelse ri!simplesoclerandori!.implesoclerandp] : ord; else : ![i!.; ord fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length fi; return rec(el:=el order : ord )java.lang.StringIndexOutOfBoundsException: Index 39 ou end; #! @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 type groups and get its characteristic" "recognisefunction(ri,) function(ri, local hint,amenamecat,,res; local hint,name,namecat,p,res; RECOG.SetPseudoRandomStamp(G,"ThreeLargeElOrders"); ri.simplesoclerandp :=0java.lang.StringIndexOutOfBoundsException: Index 28 out of p := RECOG.findchar : RECOG.findchar(ri,ri!.simplesocle,RECOG.RandElFuncSimpleSocle) if p = Characteristic(ri!.field) then (InfoRecog,2,"ThreeLargeElOrders: defining characteristic p=",p); return false; # FIXME: false = NeverApplicable here really correct? fi; # Try all possibilities: Info(,,ThreeLargeElOrders "p; for hint in p do Info(java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for lengt name := hint (,2":found ,) if[1]="" if 2] = :=RECOG.akePSL2Hintn,) if hint <> fail then res := DoHintedLowIndex(ri,G,hint); else # we use Pete Brooksbank's methods returnSLCR.(riG2,ame[3])java.lang.StringIndexOutOfBoundsException: Index 54 out fi; else return SLCR.FindHom(ri,G,name[2],name[3]); fi; else if Length(name) = 3 then namecat : Concatenation(UppercaseString(name[1]) String( fi "(",String(name[ returnSLCR.indHom(,,[2,3)java.lang.StringIndexOutOfBoundsExcepti else :java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for len fi; =java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for len fijava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 1 if res = true then res :=java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for fi; od; Info(InfoRecog, Success; return fail; # FIXME: fail = TemporaryFailure here really correct? end); # 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)); # Sort(f); # 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.; r =.(.**.,ata; r := RECOG.FindPermutation(data.cob*x*data.cobi,data.fdpm); if r = fail then return fail; return r[2]; return fail; 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(java.lang.StringIndexOutOfBoundsException: Index 26 out of bound + or +2ifsensible, functiontryBB1or2 sensible, local GG,Gm, local GG,Gm,RecSnAnEq,deg,,homjava.lang.StringIndexOutOfBoundsExceptio r,totry; etPseudoRandomStamp(G,"; d := ri!.dimension; orders := RandomOrdersSeen(ri); if Length(orders) = 0 then orders := [RandomElmOrd(ri,"AltSym",false).order]; fi; primes := Filtered(Primes,x->x <= d+2); for o in orders do fact := FactorsTD(o,primes); if Length(fact[2]) <> 0 then Info(InfoRecog,orders: Rri",); return NeverApplicable; java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 od; f : ri!field; # We first try the deleted permutation module method: if d >= 6 if Lengthif Length(act[])< 0 then Info(nfoRecog,3"Trying deleted permutation module method.."java.lang.StringIndexOutO r := RECOG.RecogniseFDPM(G,f,1/10); ifod; f : ri!.ield; newgens := List We first try the deleted permutation module method: -RECOG.HomFDPM(r,x)); if not fail in newgensInfoRecog" java.lang.StringIndexOutOfBoundsException: Range [39 GG l>java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for l hom := GroupHomByFuncWithData(G,GG,java.lang.StringIndexOutOfBoundsException: Inde (,hom) Setmethodsforimage(ri,FindHomDbPermifnot fail in newgens then ri!.comment := "FDPM"; return Success; fi; fi; Info(nfoRecog,,Deleted permutationmodule methodfailed.) fi; return TemporaryFailure; # do not try any more now # 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# Setslptonice(ri,SLPOfElms(Reversed(r[2]))); # 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,# The following may have been generated by RECOG.MakeSporadicsInfo. [ 1,2,3,4,5,6,8,10,11 ], # RECOG.SporadicsElementOrders[i][j] contains an element order of the [ 1,2,3,4,5,6,7,8,11,14,15,23 ],[ 1,2,3,4,5,6,7,8,11 ], [ 1,2,3,4,5,6,7,8,10,12,15 ], ,,,,678,,,4,5,,,28] [ 1,2,3,4,5,6,7,8,10,12,13,12,3,,56,810,11 ], [ 1,2,3,4,5,6,7,8,10,11,12,15,20 ], [ 1,2,3,4,5,6,7,8,10,11,12,14,15,21,23 ], [1,,,,,,,,,,,,,,21,2232428, 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, ,,,,,,,,,1214151721, , 2830,1,639 ] [ 1,2,3,4,5,6,7,8,9,10 1,,,,5,67,,0,11,,, , [ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,19,20,21,22,25,30, 35,40 ] ,34,678101112141516,21 [ 1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,20,21,22,24,25, 28,30,31,33,37 ,,,,9] ,,,,,,,,,,,,,,,,,,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 ], ,,,,,,,,,,,,,,1516,1820,,,,0] [ 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, 22,23,24,26,27,28,30,35,36,39,42,60 ], [ 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, 42,44,46,47,48,52,55,56,60,66,70 ], [ 1,2,3,4,5,6,7,8,9,10,11,12,13,14 2223,4,26,2728303536394260]java.lang.StringInde 21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,38,39, 40,41,42,44,45,46,47,48,50,51,52,54,55,56,57, 424446,,,,,,,, , 66,68,69,70,71,78,84,87,88,92,93,94,95,104,105,110,119 ] , 12,,,,,8,01112] [ 1,2,3,4,5,6,7,8,10,11,12,14 ], [ 1,2,3,4,5,6,7,8,10, 40,,,,,,,,,,,,5,56,,96062java.lang.StringIndexOutOfBoundsExc [ 1,2,3,4,5,6,7,8,10,12,14,15,24 ], [ 1,2, [12,,568101112] [ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,28,30,40 ], [ 1,2,3,4,5,6,7,8,10,12,14,15,16,17,20,21,24,28,30,42 ], [ 1,2,3,4,5,6, [ ,,3,,,,,,,,,,,,516,1820,,,,2830, , 25,28,30,35,40,42,44,60 ], [ 1,2,3,4,5,6,7, [ ,2,,4,5,6,,,,2,,,,,,1,428,30,42 ]java.lang.StringIndexOutOfBounds [ 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, [1,2,,,,,,8,10 [ 1,2,3,4,5,6,7,8,10,11,12,14,15,16,19,20,22,24,28,30, ,, , 1234568,910,,,,18,,,34] ,[ 1,2,3,4,5,6,8,10,12,13,16 ], ,,,,,,,121316,0 ; RECOG.SporadicsProbabilities := [ [ 1/175560,1/120,1/30 [1,,3,,,6,8101213,6,20 ; [ 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 ], [ 1/50232960,1/1920,49/9720,1/96,1/15,1/24,1/8,1/9,1/5,1/12,2/15, 217,/ , [ 1/10200960,1/2688,1/180,1/32,1/15,1/12,1/7,1/8,2/11,1/7,2/15, 2 , /,/,/,/,/,1/12,2/,/8,2/11 ]java.lang.StringIndexOutOfBoundsException: Index 64 [ 1/604800,3/640,31/1080,1/96,7/150,1/8,1/7,1/8,3/10,1/12,2/15 ], [/,/,/,1841/,18954116,16120, 1/6,5/28,1/15,2/17,4/21,1/14 ], [ 1/145926144000,283/22364160,1/2160,17/5120,13/3000,1/48,1/28, 11192,4018,/52328,115,/,320112,/,/ , [ 1/44352000,11/23040,1/360,19/960,17/375,5/72,1/7,3/16,1/10,2/11, 1/12,1/15,1/10 [1/4030387200,/3225602/,184130011895/116116120, [ 1/244823040,19/107520,11/3780,1/48,1/60, 1145926144000283223641601216017512013/, 1/11,1/ [1/44352000,1123040,1/360,9960,17/375,5/72,/,/,110,2/11, [ 1/86775571046077562880,13/21799895040,1/2661120,53/1576960,1/6720, 2311/2661120,1/420,31/7680,13/960,133/31944,1/32,5/84,1/30, 1/32,1/80,1/21,13/264,1/23,1/24,1/14,1/29,1/30,3/31,1/33, 2/ /8677557104607756288013/217998950402661120,/,/, 15505920/16128013240,7920160,1180,/,/,/, 1/20,1/11,1/36,1/28,2/45,1/4,3/19,1/10, 1321,/,/,231241/,/,/,/,/, /90745943887872000,/92897280136031719506880257,/, 67/25920,1/1176 [1460815505920,/,/,/0160,/,/,/1372116 1/20,/,/,/,/,/4,19,/0,/2 , [ 1/898128000,1/40320,31/29160,1/ [190745943887872000192897280,/,/9353601, 1/30,2/11,1/12,1/7,1/15,1/15 ], [ 1/273030912000000,131/473088000,59/1632960,23/46080, /19,/,121161/,/,/,31,12239] [1898128000,/,/,/96,31/750,1360,/7,18,2/27, 3/20, 1/30,2/11,1/12,1/,/15,1/15 ]java.lang.StringIndexOutOfBoundsException: Index [ 1/51765179004000000,1/39916800,15401/2694384000,1/20160,601/2250000, 1291/362880,1/168,1/80,1/54,73/3600,1/33,5/288,1/168,28/1125, 1/18,1/40,1/21,1/11,1/8,1/25,1/28,1/45,5/31,2/33,2/37,1/20, 121,3/ , [ 1/495766656000,179/31933440,631/2449440,1/1291362880,/,/,/,33600,/335/881/,8112 42,24154,/,/,118,1141101/,/,/1,111 2/23,1/12,1/30 ], [ 1/42305421312000,523/743178240,1/116640,139/120960,1/500,79/12960, 1/56,5/192,1/54,1/20,1/11,2/27,5/56,1/10,1/16,1/18,1/10, 2/23,1/12,1/28,1/10 ], [1/448345497600,151/23224320,661/1959552,03/23040,/1800,187/10368, 1/ 2/23,1/2,/ ] /4], [ 1/64561751654400,4297/7357464576,11419/176359680,181/276480,1/600, 9121 2/23,1/,1/8,/10 ]java.lang.StringIndexOutOfBoundsException: Index 28 out of b 1/16,7/108,1/20,1/21,1/11,1/24,1/30 ], [ 1/4157776806543360000,39239/12752938598400,7802083/4035109478400, 1061/11612160,1433/15120000,198391/69672960,2/2205,79/23040,1/216, 109/9600,1/66,10949/207360,1/156,1/42,277/5400,1/32,1/24, 37,7252,/22,23,/288,52,1/14,13120,331/35, 1/36,2/39,1/40,1/84,1/60 ], [ 1/4089470473293004800,407161/129123503308800,161281/148565394432, 239/5806080,1/25200,1036823/705438720,1/840,1/128,127/17496, 11/1200,1/44,529000,39239/12752938598400,7802083/4035109478400, 1/,/,/23,/,/31/,/28,7/120,1/35,1/,2/9, 1/42,1/60 ], [ 1/1255205709190661721292800,6439/1032988026470400,144613199/ 4412392214630400,25/6967296,1/907200,159797/564350976,67/123480, /46081189/10497607/480011324741/,12345168 103/16200,1/32,1/17,11/288,1/48,17/252,1/1/6,239,1401/84160 ] 1/27,1/28,2/29,1/24,2/33,1 /1200144529129601395/,1721/,17,/16130 [ 1/4154781481226426191177580544000000, 34727139371java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for 939596800 1/564480,18983/123863040,5/34992,667/2688000,1/1320,12629/3732480, 1/312,871/564480,31/ 103/16200,/21/,11288,148,172521442/23,/,/, 5/264,1/23,19/432,1/25,3/104,1/27,5/224,67/1200,2/31,1/32, 1/66,3/6856445211//,72166871418939596800, 2,551/,/,1/6,/ , [ 1/808017424794512875886459904961710757005754368000000000, 312871/,/36001/,/,/,/,/120001252, 1309301528411/299423045898886400305790976000, 228177889/1608412858851262464000,361177/34128864000000000, 352968797/83672030144102400,16369/1382422809600,80467/177124147200, 7/18895680,1270627/532224000000,1/1045440,20669/313528320, 31/949104,9/250880,8611/40824000,1/3072,1/2856,91/139968,1/1140, 2323/1152000,907/370440,3/3520,1/276,167/13824,1/250,1/208, /,/392,/,529/43200,/931/4,5/1188,/,312100java.lang.StringIndexOutOfBoundsExcepti 1/48, 228177889/608412858851262464000,/34128864000000000java.lang.StringIndexOutO 1/96,1/50,1/51,3/104,1/54,1/110,5/112,1/57,2/59,41/720,1/31, 1,168,269,/,/,1/,/82/,/41/6,2/, 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 ], [ 1/887040,29/8960,1/72,7/96,1/10,1/8,1/7,1/8,1/10,1/11,1/12,1/7 ],[ 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 ], [ 1/1796256000,67/887040,31/58320,17/2880,31/1500,31/720,1/14,5/48, /,/,/11,/72114,/30,/10,/11,112,1/0], [ 1/896690995200,16081/2554675200,661/3919104,1031/322560,7/3600, 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 ], [ 1/8060774400,23/387072,1/945,9/1120,1/600,473/7560,95/8232,7/96, 1/24,1/8,19/168,1/30,1/8,1/17,1/20,2/21,1/12,1/28,1/30,1/ [ 117962560006788704031/ ,[ 1/546061824000000,7057/ [1/896690995200,6081/5546752006613919104,/225607/, 16913/63000000,2497/362880,1/840,21/640,1/54,691/24000,1/44, 101/1440,5/168,13/360,1/18,1/19,743/6000,1/42,1/44,1/8,1/25, /,/,1/35,/,/,/,1/0 ] [ 1/129123503308800,10781/17517772800,11419/352719360,329/414720, 1/1200,46757/4354560,1/84,1/32,5/216,17/400,1/22,295/2592,1/13, 1/12,1/60,1/16,29/216,1/20,1/42,1/22,1/8,1/20,1/36,1/42 ], 1/510411418381323442585600,,352149857/65431527572688076800,, 144613199/8824784429260800,12091/4180377600,1/1814400, 20115929623/65368773550080,67/246960,13/7680,1189/2099520,97/67200, 1/264,282547/13063680,1/468,31/1680,103/32400,1/32,1/34, 4153/139968,41240017/04,7/264,/23,/96,5/156,1/4,2/21, 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/[ /129123503308800,1078117517772800,/352719360,329/414720 /921631011840401/674150401/,79/40320,1/60,/,292744, 43/672,7/120,1/22,1/72,5/56,1/45,1/8,3/38,1/20,1/22,1/12, /8,/,1/31,3/38,1/4], [ 1/100465920,91/195840,49/19440,1/64,1/30,11/144,5/48,1/18,1/10, 1/8,1/15,1/17,1/6,1/19,1/12,1/17 ], [ 1/ 20115929623/5368773550080,7/46960137680,11892099520,7/67200java.lang.StringIn 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 ] ]; RECOG.SporadicsNames := [ "J1","M11","M12"," 36727120,221/,/,/,/,338,20,22112java.lang.StringIndexOutOfBou "J4","ON","Th","McL","HN","Ly","Co3","Co2","Suz","Fi22","Co1", "Fi23","Fi24',"""M","M12.""2,"S.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.SporadicsSizes := [175560,9209504050232960,0200960,,,4030387200java.lang.StringIndexOutOfBoundsExc 145926144000,44352000,244823040,86775571046077562880,460815505920, 90745943887872000,898128000,273030912000000,51765179004000000, 495766656000,42305421312000,448345497600,64561751654400, 4157776806543360000,4089470473293004800,1255205709190661721292800, 4154781481226426191177580544000000, 808017424794512875886459904961710757005754368000000000 88704000,1209600,7962560008966909952008060774400,546061824000000, 1291235033088002510411418381323442585600,,00465920java.lang.StringIndexOutOfBoun 17971200,35942400 ]; RECOG.SporadicsKillers := [ [[ 5,7 ]RECOG.poradicsSizes := [ 11,4 ][ , ][ 10,8 ],[[12, ], ,,, ]java.lang.StringIndexOutOfBoundsException: Index 67 o [[ 15,14 ]],[[ 20,19 ]],[[ 13,11 ]],[[ 12,16 ]],[[ 19, 145926144000,4352000,24482304086775 [[ 17,14,21 ]],[[ 15,13 ]],[ [ 18 .. 22 ] ], 26 .32],25. ,[28 .32],27. ]], [ [ 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 ][[ 57],[ 5,],[, ][ 119 ]][[ 109] [[ 15,8,10 ]],[[ 13,12,21 ]],[[ 11,13,10 ]],[[ 25,17,20 ]], [[ 21,17 ],[23,24]], # the latter is to distinguish Fi22.2 and Fi22 [32,26 ],[ 36,37,8,0,142,43 ] the latter isfor Fi23 [[ 18,12,14 ]],[[ 10,13 ]],[[ 7,11 ]],[[ 9,11 ]] ]; RECOG.SporadicsWorkers := []; # Removed to avoid dependency on unpublished package gensift: #RECOG.SporadicsWorkers[2] := SporadicsWorkerGenSift; # M11 # and same for: M12, M22, J2, HS, Ly, Co3, Co2 # RECOG.MakeSporadicsInfo := [[ 21,17 ],[23,24]], # the latterjava.lang.StringIndexOutOf # local ct,i,index,killers,[[18,2,4 ]][ 1013 ],[ 7,11 ][ ,1] ] # ct := RECOG.SporadicsWorkers := []; # orders := Set(OrdersClassRepresentatives(ct)); # probs := []; java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length # prob := 0; # pos : java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for # for p in pos do # prob =prob +1/izesCentralizers()p; # od; # orders := Set(OrdersClassRepresentatives(ct)); # od; # index := [1..Length(orders)]; # probscopy := ShallowCopy(probs); # SortParallel(probscopy,index); # sum : probscopy[java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of # i := Length(orders); # repeat # i: 1 # sum := sum + probscopy[i]; # until sum > 1/4; # killers := index{[i..Length(java.lang.StringIndexOutOfBoundsException: Index 35 o # return rec( size := Size(ct), orders := orders, # probabilities := s)]; #java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for lengt # =+; # 120 otherwise fail RECOG.RuleOutSmallProjOrder := function(m) locall,o,; if ( =(m) if o > 119 then return fail; fi; return o; fi; Randomize(v); ORB_NormalizeVector(v); o := Orb([m],v,OnLines,rec( hashlen := 300, report := 0 )); Enumerate(o,121return if not IsClosed(o) then return fail; fi; :Length() Randomize(v); ORB_NormalizeVector(v); o := Orb([m],v,OnLines,rec( hashlen : := Orb(m]v,OnLines,(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 method returns a list of sporadicl:java.lang.StringIndexOutOfBoundsException: R #! possibly could be. Therefore it checks java.lang.StringIndexOutOfBoundsException: In #! <A>G</A> has elements java.lang.StringIndexOutOfBoundsException: Range [10, 8) out of !java.lang.StringIndexOutOfBoundsException: Range [13, 9) out of bounds for leng #java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for lengt #! Afterwards it creates hints that come out of a table for the sporadic #! simple groups. #! @ Afterwardjava.lang.StringIndexOutOfBoundsException: Range [16, 13) out of bou 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,pp,r,raus,res,x; SetPseudoRandomStampG,"")java.lang.StringIndexOutOfBoundsException: Index 52 out : [.(.)] pp := 0*l; ordersseen := []; count : 0; gens := ordersseen := ; limit := 120+Length(gens); for i in [1..limit] do if i <= Length(gens i java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of rr=java.lang.StringIndexOutOfBoundsException: Range [20, 18) out of bounds for l else r := RandomElm(ri,"SporadicsByOrders",false); fi; o := RECOG.RuleOutSmallProjOrder(r.el); if o = fail then (java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for len return NeverApplicable; elif i <= Length(gens) then r.order := OrderFunc(ri)(r.el); else GetElmOrd(ri,r); fi; o := r.order; x := r.el; (ordersseenordersseen,o); Info(InfoRecog,3,"Found order: ",String(o,3)," (element #",i,")"); (li> S) if l = [] then Info(InfoRecog,2,"Ruled out all sporadic groups."); return ; fi; # Throw out improbable ones: j := 1; while j <= Lengthj =1; if Length(l) = 1 then ( else limit := 1/1000; limit := 1/400; fi; jj : [; raus := false; # check whether java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds f for k in [1..Length(RECOG.SporadicsElementOrders[java.lang.StringIndexOutOfBoundsEx if not RECOG.SporadicsElementOrders[jj][k] in ordersseen and [jj][)i then java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for leng (seejava.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for RECOG.SporadicsElementOrders[jj][k],")"); raus := true; break; fi; od; if not raus and IsBound(RECOG.SporadicsKillers[jj]) then for killers in RECOG.SporadicsKillers[jj] do if Intersection(ordersseen, RECOG.SporadicsElementOrders[jj]{killers})=[] [jj]{killers}))^i < 10^-3 then raus := true; break; Info(InfoRecog,3,"Have thrown out ",Info(InfoRecog,3,"Have thrown out ",RECOG[, " (did not see orders in ", java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for leng fi; od; ; if raus then Remove(l,j); else j := j + 1; fi; od; if l = [] then Info,"java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds fo return NeverApplicable; elif java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for le 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 sporadics left: 2"java.lang.StringIndexOutOfBoundsExcept RECOG.SporadicsNames{l}," i=",java.lang.StringIndexOutOfBoundsException: Range [0 else Info(InfoRecog,2,"Possible; fi; od; D) > return RECOG.SporadicsNames{l res : riG,java.lang.StringIndexOutOfBoundsException: R java.lang.StringIndexOutOfBoundsException: Range [6, 4) out of bounds for length Info(InfoRecog,2,"Trying hint for ",RECOGInfoI2"java.lang.StringIndexOutOfBoundsExc [l[i]]); if res = true then return Success; fi; if fijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for leng res := RECOG.SporadicsWorkers[l[1]](return false; # FIXME: false = NeverApplicable here re i]G; if res = true then ; fi; fi; Info(InfoRecog,2,"This did not work."); od; return false; # FIXME: false = NeverApplicable here really correct? end); # Data for the function NameSporadic RECOG.rec(name := "M22", rec(name := "M11", maximalOrdersSubset [, java.lang.StringIndexOutOfBoundsException: Range [31, 27) out of bounds for leng length := 4), java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for leng maximalOrdersOverset := [6, 8, 10, 11 : [8 10 ,12,14 15 ,23, maximalOrdersSubset := [], length := 4), rec(name := "M22", maximalOrdersOverset := [5, 6, 7, 8, 11], maximalOrdersSubset := [], length := 5), rec(name := "M23", maximalOrdersOverset := [6, 8, 11, 14, 15, 23], maximalOrdersSubset := java.lang.StringIndexOutOfBoundsException: Range [29, 27) o rec(name := "M24", maximalOrdersOverset := [8, 10, 11, 12, 14, 15, 21, 23], 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 26 ], rec(name := "J3", maximalOrdersOverset := [8, 9, 10, 12, 15, 17 java.lang.StringIndexOutOfBoundsException: maximalOrdersSubset := [15, 17, 19]), rec(name := "HS", maximalOrdersSubset := [16, 23, 28, 30]), maximalOrdersSubset := [11, 20]), java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for leng maximalOrdersOverset := [8, 9, 11, 12, 14, 30], maximalOrdersSubset := [11, 14, 30]), rec(name := "Suz", java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for leng java.lang.StringIndexOutOfBoundsException: Range [31, 27) out of bounds for leng rec(name := "Ru", maximalOrdersOverset := [14, 15, maximalOrdersOverset : [ 10,12,15 17 ,28]java.lang.Strin :[,29) rec(name := "Co3", :=[14 ,20 ,22 ,24,] maximalOrdersSubset := [22, 23, 24, 30]), rec(name := "Co2", java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for leng maximalOrdersSubset := [16, 23, 28, 30]) rec(: F" recname := "Co1", maximalOrdersOverset := [16, 22, 23, 24, 26, 28, 33, 35, 36, 39, 40, 42, 60], maximalOrdersSubset := [33,:= [6,17, 22,23,24,26,27 ,29 33,35 ,39,,45 ], rec(name m: [,29) maximalOrdersOverset := [11, 12, 15, 16, 19, 20, 28, 31], maximalOrdersSubset := [19, 28, 31]), rec(name := "Fi22", maximalOrdersOverset := [13, 14, 16, 18, 20, 21, 22, 24, 30], maximalOrdersSubset : 13 24,30], java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 12 maximalOrdersSubset := [17,Fjava.lang.StringIndexOutOfBoundsException: Range [41, rec(name := "Ly", java.lang.StringIndexOutOfBoundsException: Range [31, 28) out of bounds for leng maximalOrdersSubset := [31, 67]), rec(name := "J4", maximalOrdersOverset := [16, 23, 24, 28, 29, 30, 31, 33, 35 dojava.lang.StringIndexOutOfBou java.lang.StringIndexOutOfBoundsException: Range [30, 27) out of bounds for leng rec(name := "Fi23", maximalOrdersOverset := [13, 14, 16, 17, 22, 23, 24, 26, 27, 28, 35, 36, 39 #java.lang.StringIn maximalOrdersSubset := [17, 23]), rec(name := "Fi24'", maximalOrdersOverset := [16, 17, 22, 23, 24, 26, 27, 28, 29, 33, 35, 36, 39, 42, 45, 60], maximalOrdersSubset := [17, 29]), rec(name := "Th", maximalOrdersOverset := [9,20 21,24 27,28,30, 31, 36,39, maximalOrdersSubset := [19, if [ java.lang.StringIndexOutOfBoundsException: Range [46 ]break; #! @BeginChunk NameSporadic #! This method returns a list of sporadicod; #</A couldbe. It does recogniseextensions of sporadic #! simple groups nor the Monster and the Baby Add(,[)java.lang.StringIndexOutOfBoundsExce #! Magma v2.24.10 function <Codjava.lang.StringIndexOutOfBoundsException: Index 7 out #! @EndChunk #if java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for l BindRecogMethod(FindHomMethodsProjective, "NameSporadic", "generate if ( java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bou function(ri, G) local orders, setOfOrders, maximalOrders, isMaximal, java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 7 orders := []; #do we need SetPseudoRandomStamp? for i in [1 .. 500] do Add(orders, RandomElmOrd(ri, "NameSporadic", false).order); od; maximal orders.Maximal in the sense that it does not the # order of another group element. setOfOrders =orders); <= 66. if setOfOrders[Length(setOfOrders)] > fi; return NeverApplicable; fi; maximalOrders := []; for i in [1..Length(setOfOrders)] do isMaximal := true; for j in [+1..Length(setOfOrders)] do if setOfOrders[j] mod setOfOrders[i] = 0 then isMaximal := false; break; fi; od; if isMaximal then Add(maximalOrders, setOfOrders[i]); fi; od; namesOfPossibleSporadics := []; for data in RECOG.NameSporadicData do if IsBound(data.length) and not Length(maximalOrders) = data.length then continue; fi; if IsSubset(maximalOrders, 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(namesOfPossibleSporadics, "HN"); fi; if ValueOption("DEBUGRECOGSPORADICS") <> fail then return namesOfPossibleSporadics; fi; for name in namesOfPossibleSporadics do Info(InfoRecog, 2, "Trying hint for ", name, "..."); res := LookupHintForSimple(ri, Grp(ri), name); if res = true then return Success; fi; Info(InfoRecog, 2, "This did not work."); od; return NeverApplicable; end);
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2026-11-04