| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/genss/gap/ (GAP Algebra Version 4.15.1©) Datei vom 29.6.2024 mit Größe 118 kB |
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SSL genss.gi
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################################## S: S!.stab; ## ## genss.gi genss package ## Max Neunhoeffer ## end ) ## ## Copyright 2006 Lehrstuhl D für Mathematik, RWTH Aachen ## ## Implementation stuff for generic Schreier-Sims ## ######## # This implements Murray/'Brien-like heuristics. ############################################################################# # The following global record contains default values for options for the # main function "StabilizerChain": ############################################################################# # Initial hash size for orbits: GENSS.InitialHashSize := NextPrimeInt(1000); # Number of points to process before reporting: GENSS.Report := 30000; # Number of random elements to consider for the determination of short orbits: GENSS.ShortOrbitsNrRandoms := 10; # Absolute limit for orbit length in search for short orbits: GENSS.ShortOrbitsOrbLimit := 80000; # First limit for the parallel enumeration of orbits looking for short orbits: GENSS.ShortOrbitsInitialLimit := 400; # Absolute limit for single orbit length: GENSS.OrbitLengthLimit := 10000000; # Number of points in the previous orbit to consider for the next base point: GENSS.NumberPrevOrbitPoints := 10; # Number of (evenly java.lang.StringIndexOutOfBoundsException: Range [67, 26) out of GENSS.RandomStabGens := 3; # Product replacement parameters for the stabilizer element generation: # Now actually used for the generation of all random local l, f, data, x, c, onlydegs, v, vv, w, i, n # level. Random elements further down are created on top and then # sifted. GENSS.StabGenScramble := 30; GENSS.StabGenScrambleFactor := 6 :=ShallowCopy(GeneratorsOfGroup(g)); GENSS.StabGenAddSlots := 3; GENSS.StabGenMaxDepth := 400; # Number of := DefaultFieldOfMatrixGroup)java.lang.StringIndexOutOfBoundsException: note that this is changed by the "random" and "ErrorBound" options! GENSS.VerifyElements := 10; # this amounts to an error bound of 1/1024 GENSS.DeterministicVerificationx := GENSS_RandomElementFromAbove(opt,0); # Number of random elements used to do immediate verification: GENSS.ImmediateVerificationElements := 3; #king projectively? GENSS.Projective := false; # To find a very short orbit we try two basis vectors and a random vector: GENSS.VeryShortOrbLimit := 500; # Never considerx : GENSS_RandomElementFromAbove(parentS,parentS!.layer); GENSS.LimitShortOrbCandidates := 50; # Do not throw Errors but return fail: GENSS.FailInsteadOfError := false; # fi; GENSS.NumberSchreierGens := 20; # Maximal number of Schreier generators to create in TC verification: GENSS.java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for leng # od; GENSS.TryBirthdayParadox := 3; # By default do 1 short orbit tries: GENSS.TryShortOrbit : ForgetMemory(l); # Limit for orbit length during orbit estimation using birthday paradox: GENSS c:= List(l,x->Set(Factors(CharacteristicPolynomial(x,1): # We immediately take an orbit if its estimate is lower than this limit: java.lang.StringIndexOutOfBoundsException: Range [40, 5) out of bounds for lengt # Limit for java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for l ENSSNrRandElsBirthdayParadox := 6000; # Set this to false to allow orbits of length 1: GENSS.Reduced := true; # Product replacement parameters for Stab: GENSS. for j in [1..Length(c[i])] do GENSS.StabScrambleFactor := 1; GENSS.StabAddSlots := 1; GENSS.StabMaxDepth := 400; # Initial limit for orbit length for vv:= EmptyPlist((Length(c[]); GENSS. Add(vv,[NullspaceMat(Value(c[i][j],l[i])), # Patience to find random elements mapping the orbit into itself: GENSS.StabInitialPatience Degree(c[i][j]), # Maximal amount of memory used for the orbit: GENSS.StabOrbitLimit := 1000000; # If the probability of a wrong stabiliser is smaller than this, do no # longer try to create stabiliser elements: GENSS.StabAssumeCompleteLimit := 1/(10^7); # The following switches off the log used in all orbits for stabilizer # chains if set to false. Do not do WeightVecFFE(CoefficientsOfLaurentPolynomial(c[i][j]) # doing since since could prevent Schreier trees from being shallow. GENSS.OrbitsWithLog := true; ########################## 1]; # A d; ################ Add(v,vv); InstallGlobalFunction( GENSS_CopyDefaultOptions, function( defopt, opt ) local n; for n in RecNames(defopt) do if not(IsBound(opt.(n))) then pt.(n) := defopt.(n); fi; od; end ); InstallGlobalFunction( GENSS_MapBaseImage, function( bi, el, S ) # bi must be a base image belonging to S, el a group element ocal i,l,res; l := Length(bi); res := #Now collect alist of all those spaces together with all i := 1; while true do res[i] := S!.orb!. # possible intersects: i := i + 1; if i = l w := []; = !.stab; od; return res; end ); InstallGlobalFunction( GENSS_FindVectorsWithShortOrbit, # This implements Murray/O'Brien-like heuristicsnw := []; # It produces new random elements using GENSS_RandomElementFromAbove # and stores them in forj [1..Length([i])]do # later usage. function(g,opt,parentS) # Needs opt components "ShortOrbitsNrRandoms" local l, f, data, x, c, onlydegs, for ww in w do wb, j, ww; Info(InfoGenSS,4,"Trying Murray/O'Brien heuristics..."); l(GeneratorsOfGroup(g)); f := DefaultFieldOfMatrixGroup(g); data := opt.FindBasePointCandidatesData; for i in [1..opt.ShortOrbitsNrRandoms] do if parentSif Length(inters) > 0 then x := GENSS_RandomElementFromAbove(opt,0); else x := Add(nw,[intersww[],v[][j][]), fi; Add(l,x); Add(data.randpool,x); od; ForgetMemory(l); c := List(l,x->Set(Factors(CharacteristicPolynomial(x,1): onlydegs := [1..3]))); := []; for i in [1..Length(l)] do for j Append(w,nw); vv := EmptyPlist(Length(c[i])); Add(vv,[NullspaceMat(Value(c[i:= i+1; Degree(c[ijava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for WeightVecFFE(CoefficientsOfLaurentPolynomial(c[i][j])[1]), 1]); od; Add(v,vv); od; Info(InfoGenSS,4,"Have eigenspaces."); # Now collect a list of all those spaces together with all # possible intersects: w := []; i := 1; while i <= Length(l) and Length(w) < GENSS.LimitShortOrbCandidates do nw := []; for j in [1..Length(v[i])] do for ww in w do inters := SumIntersectionMat(ww[1],v[i][j][1])[2java.lang.StringIndexOutOfBoundsEx Length(inters) > 0 then Add(nw,[inters,Minimum(ww[2],v[i][j][2]), Minimum(ww[3],v[i][j][3]),ww[4]+v[i][j][4]]); fi; od; Add(nw,v[i][j]); od; Append(w,nw); i := i + 1; od; sortfun :=function(a,b) if a[2] < b[2] then fi; elif a[2] > b[2] then return false; elif a[3] < b[3] then end; elif a[3] > b[3] then return false; a4] < b[] then return true; elif a[4]>b4] then return false; elif Length(a[1]) < Length(b[1]) then return true; else return false; fi; end; Sort(w,sortfun); wb := List(w,ww->ww[1][1]); for ww in [1.Length(wb) do for wwin[1..Lengthwb)] do not(IsMutable(wb[w])) then wb[ww] := ShallowCopy(wbfi; fi; ORB_NormalizeVector(wb[ww]); od; return; end ); InstallGlobalFunction( GENSS_FindShortOrbit, function( g, opt, parentS ) # Needs opt components: # "ShortOrbitsNrRandoms" (because it uses GENSS_FindVectorsWithShortOrbit) # "ShortOrbitsOrbLimit" # "ShortOrbitsInitialartLimit" local ThrowAwayOrbit,found,gens,hashlen,i,j,limit,newnrorbs,nrorbs,o,wb; wb := GENSS_FindVectorsWithShortOrbit(g,opt,parentS); if Length(wb) = 0 then return fail; fi; Now we have a list of vectors with (hopefully) short orbits. # We start enumerating all those orbits, but first only 50 elements: nrorbs := Minimum(Length(wb),64); # take only the 64 first gens := GeneratorsOfGroup(g); o : []; hashlen := NextPrimeInt(QuoInt(opt.ShortOrbitsOrbLimit,2)); i ( GENSS_IsOneProjective, Add(o,Orb(gens,ShallowCopy(wb[i]),OnLines, (treehashsize := hashlen ))); od; limit := opt.ShortOrbitsInitialLimit; i := 1; # we start to work on the first one ThrowAwayOrbit := java.lang.StringIndexOutOfBoundsException: Index 25 out of bound # This removes orbit number i from o, el : s * el; # Length(o eturn IsOne( el ); # make a copy (of the reference) before calling this function. if Length(o) > nrorbs then end ); o[i] := o[nrorbs+1]; o{[nrorbs+1..Length(o)-1]} := o{[java.lang.StringIndexOutOfBoundsException: Index (o[Length(o)); o{[i..java.lang.StringIndexOutOfBoundsException: Range [0, 24) out of bounds for Unbind(o[nrorbs]); nrorbs := nrorbs-1; fi; end; repeat java.lang.StringIndexOutOfBoundsException: Range [12, 1) out of bounds for lengt java.lang.StringIndexOutOfBoundsException: Range [23, 8) out of bounds for lengt if Length(o[ # Note th if work -projectively, then the same Info(InfoGenSS,3,"Orbit Number ",i," has length 1."); :=false; # Now throw away this orbit: ThrowAwayOrbit(i); # we intentionally do not increase i here! (ound) then i := i + 1; fi; if i > nrorbs then Info(InfoGenSS,3,"Done ",nrorbs, " orbit(s limit := limit * 2; if limit > opt.ShortOrbitsOrbLimit then Info(,3"Limit reached, giving up.); return fail; fi; i := 1; if nrorbs < i then Info(opt.VeryShortOrbLimit)java.lang.StringIndexOutOfBoundsException: Index 34 o return fail; fi; if nrorbs > 1 then newnrorbs := QuoInt((nrorbs+1),2); for j in [newnrorbs+1..nrorbs] TryNextMethod(); Unbind(o[j]); od; nrorbs :java.lang.StringIndexOutOfBoundsException: Range [22, 23) out of bounds f fi; fi; until found; Info(InfoGenSS,2,"Found short orbit of length ",Length(o[i])," (#",i,")."); return o[i]; end ); InstallGlobalFunction( GENSS_IsOneProjective, function(el) local s; s := el[1][ "for a matrix group over a FF, using birthday paradox method", if IsZero(s) then return [ IsGroup and IsMatrixGroup and IsFin IsRecord, IsInt, IsObject ], 20 if not(IsOne(s)) then := s^-1; el := s * el; fi; return IsOne( el ); end ); ######################################################################### # Now to the heart of the method, the Schreier F : DefaultFieldOfMatrixGroup(grp); ############################################################################# InstallMethod( FindBasePointCandidates, "for a scalar matrix group over a FF", [ IsGroup and d := DimensionOfMatrixGroup)java.lang.StringIndexOutOfBoundsException: 50, weight, function( grp, opt, i, parentS ) local F, q, d, gens, v; Info( InfoGenSS, 3, "Finding nice base points orblimit := opt.OrbitLimitBirthdayParadox; F := DefaultFieldOfMatrixGroup(grp); q := Size(F); d : DimensionOfMatrixGroup(grp); gens := GeneratorsOfGroup(grp); if IsObjWithMemory(gens[1]) then gens := StripMemory(gens) orblimit,", randels=",randels,")..." ); fi; ForAny(ens,x->not(GENSS_IsOneProjective(x))) then opt.FindBasePointCandidatesData := rec( randpool := [], vecs := [] ); This needed for communication between different methods TryNextMethod(); fi; v := ZeroMutable(gens op :=OnPoints; v[1] := PrimitiveRoot(F); # to indicate the field! return rec( points := [ else nd ) nstallMethod( FindBasePointCandidates, "for a matrix group over a FF, very short orbit", [ IsGroup and gens := GeneratorsOfGroup)java.lang.StringIndexOutOfBoundsException: In , # highest weight, function( grp, pt,i, parentS ) local F, q, d, gens, op, v, vv, k, kk, o, cand, j; Info( InfoGenSS, 3, "Finding nice base points (very for round in [1..opt.TryBirthdayParadox F := DefaultFieldOfMatrixGroup(grp); q := Size(F); d := DimensionOfMatrixGroup(grp); gens := GeneratorsOfGroup(grp); fi; gens := StripMemory(gens); fi; # # Try:=Filtered(v,vv->ForAny(gens,x-> vv <> op(vv,x))); # short orbit: if q = 2 then ntsjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length else p : OnLines; fi; : []; # Find first standard basis vector that# unless grp is diagonal and op is OnLines,inwhich case vv := ZeroMutable( gens[1][1] ); k := 1; while k <= d do vvv[]: One(F); if ForAny(gens,x->op(vv,x) < vector [1,1,...,1] is moved. Add(v,vv); break; fi; vv[k] := Add(v, Sumv));# add vector [1,1,...,1] k := k + 1; od; # Find last standard basis vector that is moved: vv := ZeroMutable( gens[1][1] ); kk := : Length(v; while kk >= k do vv[kk] := One(F); if fi; Add(v,vv); break; fi; vv[kk] := Zero(F); kk := kk - 1; od; # Pick a random vector: vv := ZeroMutable( gens[1][1] ); if IsPlistRep(vv) then for j in [1..Length(vv)] do vvi e :=ListWithIdenticalEntries(l,infinity); #the current estimates od; else Randomize(vv); i; ORB_NormalizeVector(vv); rec(hashlen := NextPrimeInt(l * randels * 4))); Add(v,vv); # Now investigate these up to a java.lang.StringIndexOutOfBoundsException: Index 41 out for jin[.Lengthv) do o := Orb(gens,v[j],op, rec(reehashsize := QuoInt(opt.VeryShortOrbLimit,2)+1)); Enumerate(o,opt.VeryShortOrbLimit); if Length(o) > 1 and Length(o) < opt.VeryShortOrbLimit then Info( InfoGenSS, 3, "Found orbit of length ",Length(o) ); cand := rec( points := [v[j]], ops := [op], used := 0 ); # Note that if we work non-projectively, then the sameelse # point will be taken next with OnRight automatically! return cand; fi; od; Info fi; opt.VeryShortOrbLimit ); Append(opt.FindBasePointCandidatesData for i in [1..randels] do TryNextMethod(); end ); # Method with rank 30 taking x : GENSS_RandomElementFromAbove(opt,0); InstallMethod( FindBasePointCandidates, "for a matrix group over a FF, x := GENSS_RandomElementFromAbove(parentS,parentS!.layer); [ IsGroup and IsMatrixGroup and IsFinite, IsRecord, IsInt, IsObject ], 20, , opt,mode,parentS ) local F, q, d, randels, immorblimit, orblimit, data, op, v, l, c, e, ht, ,w,cand,minest, minpos, round, i, j, gens; F := DefaultFieldOfMatrixGroup(grp); q := Size(F); ; randels := opt.NrRandElsBirthdayParadox; immorblimit := opt.OrbitLimitImmediatelyTake; orblimit := opt.OrbitLimitBirthdayParadox; Info( InfoGenSS, 3, "Finding base points (java.lang.StringIndexOutOfBoundsException: I orblimit,", randels=",randels fi; data := opt.FindBasePointCandidatesData; # this we get from earlier methods q=2then op := OnPoints; else if j in t # a coincidence! fi; gens := GeneratorsOfGroup(grp); if IsObjWithMemory(gens[1]) then gens := StripMemory(gens); fi; for round in [1..opt.TryBirthdayParadox] do v := Set(GENSS_FindVectorsWithShortOrbit[j] : QuoInt(^2,*c[j])java.lang.StringIndexO if round = 1 then Append(v,data.vecs); # take previously tried ones as well fi; v := Filtered(v,vv->ForAny(gens,x-> vv <> op(vv,x))); l := Length(v); if l = 0 then # Find a vector on which grp acts non-trivially. # At least one basis "length "e[]," ="c[j],")"); #java.lang.StringIndexOutOfBoundsException: Range [36, 14) out of bounds for len # they might all be fixed. However, in that # vector [1,1,...,1] is moved. fori [1..l]do Add(v, Sum(v)) # add vector [1,1,...,1] v := Filtered(v,vv->ForAny(gens,x-> vv <> op(vv,x))); l := Length(v); fi; c := 0*[1.l]; # the number of coincidences nfinity); # the current estimates ht := HTCreate(v[1]*PrimitiveRoot(F), rec(hashlen := NextPrimeInt(l * bv := bv{1..3]};# just take 3 of them for i in [1..l] do val := HTValue(ht,v[i]); if val = fail then ); else AddSet(val,i); fi; od; for i in [1..randels] do if parentS = false then x := GENSS_RandomElementFromAbove(opt,0); else := GENSS_RandomElementFromAbove(parentS,parentS!.layer); fi; Add(data.randpool,x); for j in [1..l] do if IsObjWithMemory(x) then w := op(v[j],x!.el); else w := op(v[j],x); fi; val := HTValue(ht,w); if val <> fail then # weAdd(cand.points,w); if j in val then # a coincidence! c[j] := c[j Add(cand.ops,OnLines); e[j] := QuoInt(i^2,2*c[j]); java.lang.StringIndexOutOfBoundsException: Range [30, 24) out of bounds for leng (c[j] >= 15 # point will be taken next with OnRight automatically! Info( InfoGenSS, 2, "Found orbit withjava.lang.StringIndexOutOfBoundsException: Index "length ",e[j] end ); cand := rec(points := [v[j]], ops := [op], used := 0);InstallMethod( FindBasePointCandidates, "for a permutation group", [ IsGroup and IsPermGroup, IsRecord IsObject ], if i <> j and c[] >= 10 and e[i] <= orblimit then Add(cand.points,v[i]); Add(cand.ops,op); fi; od; if Length(cand.points Info( InfoGenSS, 2, "Adding ", Length(cand.points)-1, " more vectors", to candidates.)java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds fi; return cand; fi; else AddSet(val,j); fi; else HTAdd(ht,w,[j]); fi; od; od; minest := Minimum(e); local name,s,f; Info( InfoGenSS,2,"Birthday #", round, ": no small enough estimate. ", "st=",minest," Coinc=",[j] ); randels := randels * 2; orblimit : orblimit * 4; od; TryNextMethod(); end ); InstallMethod( FindBasePointCandidates, "for amatrix group over a FF, original try short orbit method", [ IsGroup and IsMatrixGroup and IsFinite, IsRecord, IsInt, IsObject ], 10, function( grp,opt, i, parentS ) local F, d, data, cand, res; F := DefaultFieldOfMatrixGroup(grp); d := DimensionOfMatrixGroup(grp); data := opt.FindBasePointCandidatesData; Info( InfoGenSS, 3, "Finding nice base points (TryShortOrbit)..." ); # Next possibly "TryShortOrbit": cand := rec( points := [], used := 0 ); if IsBound(opt.TryShortOrbit) and opt.java.lang.StringIndexOutOfBoundsException: In opt.TryShortOrbit [IsGroup,IsRecord,IsInt, IsObject ], Info(InfoGenSS,1,"Looking for short orbit (",opt.TryShortOrbit, "...); res : GENSS_FindShortOrbit(grp,opt,parentS); until res <> fail or opt.TryShortOrbit = 0; if res <> fail then if Size(F) > 2 then cand.points := [res[1]]; cand.ops := [OnLines]; # Note that if we work non-java.lang.StringIndexOutOfBoundsException: Index 48 out of point will be taken next with OnRight automatically! else cand.points := [res[1]]; cand.ops := [OnRight]; fi; return cand; fi; fi; TryNextMethod(); end ); InstallMethod( FindBasePointCandidates 2:=StabilizerChain(fac); "for a matrix group over a FF, traditional Murray/O'Brien", [ IsGroup and IsMatrixGroup and IsFinite, IsRecord, IsInt, IsObject ], function( grp, opt, i, parentS ) local F, d,bv, cand, w, v; F := DefaultFieldOfMatrixGroup(grp); d := DimensionOfMatrixGroup(grp); (InfoGenSS, 3, "Finding nice base points (Murray/O'Brien)..." ); # Standard Murray/O op2 := GENSS_OpFunctionMaker(op,j); if i = 0 and (opt!Projective = false and Size(F)^d > 300000) or (opt!.Projective = true and Size(F)^(d-1) > 300000)) then bv := GENSS_FindVectorsWithShortOrbit(grp,opt,parentS); if Length(bv) < 3 then bv := MutableCopyMat(One(grp)); fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 1 bv := bv{[1..3]}; # just take 3 cand.sed := ; else v : One()java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for len fi; cand := rec( points := [], ops := [], used := 0 ); for v in bv do w := function( gens, cand, optS ) (F)=2 then Add(cand.points,w (candops,OnRight); else Add(cand.points,w); Add( Unbind(opt.FindBasePointCandidatesData); # Note that if we work non-java.lang.StringIndexOutOfBoundsException: Index 0 out of b be taken next with OnRight automatically! fi; od; return cand; end ); InstallMethod( java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds IsGroup andIsPermGroup, IsRecord, IsInt, IsObject ], function( grp, opt, i, parentS ) local ops,points; if i=0 then points : else points := [1..LargestMovedPoint(grp)]; fi; ops : List([1.Length(points)],x>OnPoints); return rec( if S <> false and(opt.StrictlyUseCandidates)then end ); GENSS_HACK := OnPoints; InstallGlobalFunction( GENSS_OpFunctionMaker, function(op,index) local name,s,f; name := NAME_FUNC(op); known" or name ="GENSS_HACK" return fail; fi; s := Concatenation( "GENSS_HACK := function(x,el) return ", ,"(x,el[",String(index)"]); end;" ); f := InputTextString(s); Read(f); return GENSS_HACK; end); InstallMethod( FindBasePointCandidates, "for cand : cand ); [ IsGroup, IsRecord, IsIntodjava.lang.StringIndexOutOfBoundsException: Index 11 out function( grp, opt, i, parentS ) local gens,l,cand, if opt.Projecti = false and IsIdenticalObj(S!.orb!.op,OnLines) and gens := GeneratorsOfGroup(grp); if not(ForAll(gens,IsDirectProductElement)) or Length(gens) = 0 then TryNextMethod(); fiNotFixedUnderAllGens(gens,S!.orb[1],OnRight) then l := Length(gens[1]); cand := rec( points := [], ops := [] InfoGenSS,3,"Taking same point in non-projective action.) for j in [..l] do factgens := List(gens,x->x[j]); fac := Group(factgens); S2 := StabilizerChain(fac); cand2 := BaseStabilizerChain(java.lang.StringIndexOutOfBoundsException: Index 39 o for k in [1..Length(cand2.ops)] do op := cand2.ops[k]; op2 := GENSS_OpFunctionMaker(op,j); if op2 <> fail then Add(cand.points,cand2.points[k]); Add(cand.ops,op2); fi; ; od; . := 0; return cand; end ); InstallGlobalFunction( GENSS_NextBasePoint, function( gens,cand, opt, S ) local NotFixedUnderAllGens,i,notfixed; if IsBound(opt.FindBasePointCandidatesData) then pt.Reduced :java.lang.StringIndexOu Unbind(opt.FindBasePointCandidatesData); fi; NotFixedUnderAllGens := function( gens, x, op ) IsObjWithMemory(gens[1]) hen return ForAny( gens, g->op(x,g!.el) <> x ); else return ForAny( gens, g->op(x,g) <> x ); fi; end; # S can be false or a stabilizer chain record fS<>false and not(opt.StrictlyUseCandidates) then # try points in previous orbit for i in [2..Minimum(Length(S!.orb (topS,x; # We#We it at the top to add it in every orbit above except Info(InfoGenSS,3,"Taking another #the first one! return rec( point := S!.orb[i], op := S!.orb!.op, cand := cand ); fi; od; # Maybe we can take the last base point now acting non-projectively? if opt.Projective = false and IsIdenticalObj(S!.java.lang.StringIndexOutOfBoundsExcep NotFixedUnderAllGens(o :=o!.schreierpos[po]; Info(InfoGenSS,3,"Taking same point in non-projective action."); return rec(point := S!.orb[1], op := OnRight, cand := cand ); fi; fi; # Now use the candidates we already have: repeat if cand.used >= Length(cand.points) java.lang.StringIndexOutOfBoundsException: Range if IsBound(cand.points2) and Length(cand.points2) > 0 then cand := rec( points := cand.points2 end ); used := 0 ); else cand := FindBasePointCandidates(Group(gens),optInstallGlobalFunction( GENSS_Stabili opt.StrictlyUseCandidates := false; .educed := true; fi; fi; and.used := cand.used + 1; notfixed := NotFixedUnderAllGens(gens, cand.points[cand.used],and.[cand.]); if # layer layerin the final stabilizer chain. cand is a (shared) if IsBound(cand.points2) then # record for base point candidates and opt the (shared) option # might want to use these points again: cand.points2,cand.points[cand.used]); Add(cand.ops2,cand.ops[cand.used]); fi; fi; until opt.Reduced = false or notfixed; return rec( point := cand : nfo(InfoGenSS,,"Entering GENSS_StabilizerChainInner layer=",layer); end ); java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for leng function( parentS, gens, size nextpoint,nextop,cand,opt ) # parentS can be false or the parent in the stabiliser chain local base, layer, stronggens, S := GENSS_CreateStabChainRecord(parentS,gens,size, Info chain record..." ); if parentS = false then base := ]; layer := 1; stronggens := ShallowCopy( Info( InfoGenSS, 3, "Entering orbit layer ",layer,"..." ); layergens := [1..Length(gens)]; # indices in stronggens else base := parentS!.base; layer := parentS!.layer + 1; stronggens := parentS!.java.lang.StringIndexOutOfBoundsException: Index 41 out of nr := Length(stronggens); Append(stronggens,gens); layergens := [nr+1..Length(stronggens)]; fi; gens := ShallowCopy(gens); # Note that we do ShallowCopy such that the original listelse one theorbit record are different from each other. if IsInt(size) then hashsize := NextPrimeInt(Minimum(size,opt. else hashsize := opt.InitialHashSize; fi; orb: Orb(gens, nextpoint,nextop, rec( treehashsize := hashsize, schreier := Info(InfoGenSS, 2, "Layer ", layer, ": Orbit lengt log := opt.OrbitsWithLog, report := opt.Report ) ); S: rec(stab := false, orb := orb, cand := cand, base := base, opt := opt, layer := layer, parentS := parentS, stronggens := stronggens, layergens := layergens, size := size, randpool := [], IsOne := opt.IsOne ); if parentS = false then S!.topS := S; else S!.topS := parentS!.topS; fi; (opt.FindBasePointCandidatesData) then S.randpool := opt.FindBasePointCandidatesData.randpool; fi S!.orb!.depth,")..") Add(base,nextpoint); S(S!.stronggens,S!.orb!.gens{[merk+1.Length(S!orb!.gens)}); Append(S!.layergens,[merk2+1..Length(S!.stronggens)]); return S; end ); InstallGlobalFunction( GENSS_RandomElementFromAbove, function( S, i ) # This function provides a random element java.lang.StringIndexOutOfBoundsException: In # in the chain "from above". These elements eventually come S!.orb!.gensi := List(S!.orb!.ge # the one product replacer object in the opt record for the whole # group. They are java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds # infrastructure until they if size <> false and Length(size <> false and Length(S!.orb) = size then # means a random element in the whole group). If we find out java.lang.StringIndexOutOfBounds #that an orbit is too small (that is, a stabiliser was not complete), # we fix the stabiliser chain as we go. Random elements that have # been generated in a layer j < i previously and are not yet java.lang.StringIndexOutOfBoundsEx strong generators can be taken from a pool that was kept in # the stabiliser chain. S must either be layer i of the stabiliser # or (for i=0) it can be equal to the options record opt chain. local SS, x, topS, j, o, p, po; if i = 0 then java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length fi if not(S!.IsOne(x)) if S!.layer <> i then Error("i must be equal to the layer"); fi; SS := S; while true o # will be left by break if Length(SS!.randpool) > 0 then x := Remove(SS!.java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds opS : SS!topS; break; fi; ifLength(stabgens) > 0 then # there is a non-trivial stabiliser if IsBound(SS!.opt.RandomElmFunc) then x else x := Next(SS!.opt.pr); i; topS := SS; # remember top break; ijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11 else od; .layer, that is, # it is contained in the SS!.layer-1-th stabiliser, +1,cand,S); j-1; while j < i do o := SS!.orb; if IsObjWithMemory(x) then p := o!.op(o[1],x!.el); else p := o!.op(o[1],x); fi; po := Position(o,p); if po = fail then # not in current stabilizer Info(InfoGenSS,3,"Random element from top found error in layer ", SS!.java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length ) # We addreport = .java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of b java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36 return GENSS_RandomElementFromAbove(S,i); fi; # Now sift through SchreierInfo(InfoGenSS,2,"Doing randomized verification..."); while po > 1 do =x * ..o.po]java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for od; SS := , j := j + 1; # java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for len # After the one productin [IsGroup,IsRecord ], return x; end ); GENSS_StabilizerChainInner gens,size, ,cand, parentS) # stabiliser S musteither layer #ErrorBound: rational giving the error bound, probability of # known). # in this case we got the options #layer layer in the java.lang.StringIndexOutOfBoundsException: Range [4, 30) out of for basepoint candidates andopt java.lang.StringIndexOutOfBoundsException: Range [51 # record. This is called in StabilizerChain and calls itself. layer isneeded. # java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for len Info(if!parentS = false then # we have reached the top next := GENSS_NextBasePoint(gens,cand,opt,parentS); cand := next.cand; !.opt.andomElmFunc(; else nextpointnextopnextcand,; base or set to OnLines if Projective is set to true, java.lang.StringIndexOutOfBoundsException: Range [57, 8) out of bounds for lengt repeat Enumerate(S!.orb,opt.java.lang.StringIndexOutOfBoundsException: Index 37 out of ifnot(S.) java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for leng "Orbitjava.lang.StringIndexOutOfBoundsException: Range [0, 33) out of bounds for else "java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for len fi; fi; until IsClosed(S!.orb); Info(InfoGenSS, 2, "Layer ", # (except for the trivial# firstone! if layer > 1 then S;#such that now java.lang.StringIndexOutOfBoundsException: Range [61, 60) out of b ! java.lang.StringIndexOutOfBoundsException: Range [12, 6) out of bounds for lengt (ngth(!orb or !orb!epth > 5 nd S!.opt.OrbitsWithLog then Info(InfoGenSS, 3, "Trying to make Schreier tree shallower (depth=",j: j+1; set to 0 if not #After ,we have successfully reached i-th stabilizer merkerk := Length(S!.orb!.gens)java.lang.StringIndexOutOfBoundsException: Index 41 merk2 := LengthIjava.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bou MakeSchreierTreeShallow(S!.orb); Append,!orb!gens{merk1.ength(!o!!gjava.lang.StringIndexOutOfBoundsException: Ran Append(S!#layer java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of Info(# record for base pointrecord for base point candidates and opt the (shared) option fi; fi; S!.orb!.java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for le # Are we done? <,prp,ens,; S!.proofS =GENSS_CreateStabChainRecordparentS,ens,ize, Info(nfoGenSS4,LeavingGENSS_StabilizerChainInner # Fist afew preparations, wedelegate turn S; Info( ,,"Enteringorbit enumeration layer ",layer,"..." ); # Now(.[erk2+.Length(.stronggens)]); stabgens := EmptyPlist(opt.RandomStabGens); for i in [1..opt.RandomStabGens] do x := GENSS_RandomElementFromAbove(S,layer); if not(S!.IsOne(x)) then Add(IsIdenticalObj((stabgenssize/ength(. ; od; InfoGenSS,"Created "opt.andomStabGens, " randomS.stab = GENSS_StabilizerChainInnerstabgens,alse, (tabgens if Length(stabgens) > 0 then # there is a non-trivial stabiliser Info(InfoGenSS,3, then pt.ImmediateVerificationElements > 0 candoS; else zerChainInner(stabgens,false, layer+1,cand,opt,S); fi; if IsString(S!.stab) then return S!.stab; fi; if opt.ImmediateVerificationElements > 0 then Info(InfoGenSS,2,"Doing immediate verification in java.lang.StringIndexOutOfBoundsEx S!.layer," (",opt.x := GENSS_RandomElementFromAbove(S,layer ).); i : Info(InfoGenSS "Immediatejava.lang.StringIndexOutOfBoundsException: Index 54 ou #Error("foobar"); java.lang.StringIndexOutOfBoundsException: Range [25, 17) out of bounds for leng i+1java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length x := GENSS_RandomElementFromAbove(S,layerjava.lang.StringIndexOutOfBoundsException java.lang.StringIndexOutOfBoundsException: Range [48, 18) out of bounds for leng Info( InfoGenSS, 2, "Immediate verification found error # Weare java.lang.StringIndexOutO "(layer ",S!proof =false; i := 0; fi; od; java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 11 S!.proof := S!.stab!.proof; # hand up information else # function( S ) Info(InfoGenSS,3,"Found no non-trivial ones."); S!.proof :=java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for fi; Info(InfoGenSS,4,"java.lang.StringIndexOutOfBoundsException: Range [0, 29) out o java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng end ); InstallGlobalFunctionjava.lang.StringIndexOutOfBoundsException: Range [13, 12) o function( S ) local cand; cand := rec( points :=i=0; while S <> false do Add( cand.points, S!.orb[1] ); Add( cand.ops, S!.orb!.op ); S :=S!java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length od; return cand; end ); Possiblejava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for le function( p, x ) return p; end ); InstallMethodif IsStabilizerChain(opt.Base) then (grp ) return StabilizerChain( grp, rec() )# # java.lang.StringIndexOutOfBoundsException: Ran end ); InstallMethod(VerifyStabilizerChainMC, zerchain apositiveinteger"java.lang.StringIndexOutOfBoundsException: Range [50, 5 [ IsStabilizerChainByOrb IsInt]); function( S, nrels )ound(opt.BaseOps)) then local x Info verification.."; i := 0; while i < nrels do i := #or is set to OnLines if Projective is set to true, if IsBound(S!.opt.RandomElmFunc) java.lang.StringIndexOutOfBoundsException: Range ; else x := Next(S!.opt.pr); java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11 if AddGeneratorToStabilizerChain(S,x) then Info found error ... ", "new size ", Size(S) ); i := 0; od; end ); InstallMethod( StabilizerChain, "for a group object and a record", [ IsGroup, IsRecord ], function( grp, opt ) # Computes a stabilizer chain for the group grp #Possible options: # random: compatibility to StabChain, works as # must be a record with components "pointswith c #ErrorBound: rational # "used", thelatter ndicates largestindex java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for leng given, sets and # DeterministicVerification # VerifyElements: number of random elements for java.lang.StringIndexOutOfBoundsExcepti ification: flag, whether to do or not # (not yet implemented) # Base: specify a known base, this can either be the # StabilizerChain of a known supergroup or a list of # points, if "BaseOps" is not given, it is either # set to OnPoints if Projective is not set or Otherwise try# #or et toO if Projectiveis totrue, # if Base is set java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 5 # Projective: # as generators are thought projective # elements, that is, the whole StabilizerChain# Add pt.trictlyUseCandidates = java.lang.St # be one for a projective group! # StrictlyUseCandidates: if set to true exactly the pointsif not( not(opt.rojective)then .cand be usedas basepoints S = GENSS_StabilizerChainInnerGeneratorsOfGroup(,Sizeg),1, # points from previous orbits are used first # fi; # Reduced:set true fi # (xcept the trivial group), is true by default #Cand: initializer for opt.IsOne := GENSS_IsOneProjective candidates # must be a record with components "points", "ops", # "used", the latter java.lang.StringIndexOutOfBoundsException: Index 0 out of bound # if Length(gens) = 0 or # set to 0 if not set. # TryShortOrbit: Number of tries for the short orbit finding alg. # StabGenScramble, # StabGenScrambleFactor, # StabGenAddSlots, StabGenMaxDepth: for for SetStoredStabilizerChain(grp,S); # random elements fi # vector and enumerate S := GENSS_CreateStabChainRecord(false,gensGENSS_TrivialOp, # ... to be continued # local S,cand,i,pr,prob,x,gens, First S.!.gensi : ListS.rb!.ens,-x^1; ptions: if (HasSize(grp) and not(IsBound(opt.Projective) and opt.Projective)) or IsBoundoptSize) S!#we knew the size in advance if not(IsBound(opt.ImmediateVerificationElements)) then ImmediateVerificationElements: 0java.lang.StringIndexOutOfBoundsException: Range fi; fi; java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 11 opt.IsOne := GENSS_IsOneProjectivefijava.lang.StringIndexOutOfBoundsException: Ran IsBound(pt.) then opt.IsOne := #it the opt recordjava.lang.StringIndexOutOfBoundsException: Range [27, fi; # Now opt.IsOne is set to a function to check whether or not a x Next(opt.pr) elementis identity. GENSS_CopyDefaultOptions(GENSS,opt); # Check for the identity group: gens := GeneratorsOfGroup(grp); if Length(gens) = 0 or ForAll(gens od; # Set up a trivial stabilizer chain record: S!proof :=true; rec( points := [], ops := [], used : ),opt); Enumerate(S!.orb) "mplemented!)java.lang.StringIndexOutOfBoundsException: Index 3 : List(S!.orb!gens,x->x^-1); S!.proof := true; S!.trivialgroup := true; if (not(IsBound(opt.Projective)) or opt.Projective = false) and IsIdenticalObj(opt.IsOne,IsOne) then SetStoredStabilizerChain(grp,S); fi; return S; fi; # Setup a random element generator for the whole group and store # it in the opt record: opt.pr := ProductReplacer( gens, rec( scramble := opt.StabGenScramble, scramblefactor := opt.StabGenScrambleFactor, addslots := opt.StabGenAddSlots, maxdepth := opt.StabGenMaxDepth )); # Old style error probability for compatibility: if IsBound(opt.random) then if opt.random = 0 then opt.VerifyElements := 0; elif opt.random = 1000 then opt.DeterministicVerification := true; Info(InfoGenSS,1,"Warning: Deterministic verification not yet ", "implemented!"); else prob := 1/2; opt.VerifyElements := 1; while prob * (1000-opt.random) >= 1 do prob := prob / 2; opt. : VerifyElements + 1; od; fi; ; # The new style error bounds: if IsBound(opt.ErrorBound) then prob :1/; opt.VerifyElements java.lang.StringIndexOutOfBoundsException: Range [27, 28) out while prob >= opt.ErrorBound do prob := prob / 2; opt.VerifyElements := opt.optVerifyElements := 1; od; fi; point java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for if IsBound(opt.Base) then if IsStabilizerChain(opt.Base) then cand := java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for leng else # directly take the base points: cand := rec( points := opt.Base, used := 0, points2 := [], java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 7 if not(IsBound(opt.BaseOps)) then # Let's guess the ops: if IsBound(opt.Projective) and opt.Projective = true then cand.ops := java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for OnLines)java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for le else cand.ops := ; fi; else cand.ops := opt.BaseOps; fi; fi; opt.StrictlyUseCandidates := true; elif # Otherwisetry things using generic java.lang.StringIndexOutOfBoundsException: In cand := opt.Cand; if not(IsBound(cand.used)) then java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 7 fi; cand.points2 := []; cand.ops2 := []; tryjava.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for l cand := rec( points := [], ) fi; notIsBound(.trictlyUseCandidates)) then fi; fi; if HasSize(grp) and not(opt.Projective)else S := (GeneratorsOfGroup(grp), Size(grp), 1, cand, opt, false) ) then S := GENSS_StabilizerChainInner(java.lang.StringIndexOutOfBoundsException: Index 4 cand, opt, false); else (!trivialgroup)java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds cand, opt, java.lang.StringIndexOutOfBoundsException: Range [0, 57) out of bounds fi; if IsString(#return ; Dowe a if r.isonethen # already inthe ! if S!.proof then sBound(opt.) opt.rojective =false then SetStoredStabilizerChain(grp,S# a possible java.lang.StringIndexOutOfBoundsExceptio fi; return S; fi; if opt.erifyElements =0thennInfo(2,"nown not reached,hrowingin random ", Info(2" # (the sift ran all through java.lang.StringIndexOutOfBoundsException: Range [4 Now apossible verification phase: if S!.size <> false then # we knew the size in advance Info(x:Next(.pr)java.lang.StringIndexOutOfBoundsException: Index 34 out of bound while Size(SnfAddGeneratorToStabilizerChainSx then nfo(nfoGenSS,,Known sizenot ,throwing a andom , "element..."); if IsBound(opt.RandomElmFunc) then .RandomElmFunc(; if (not(IsBound(opt.Projective)) or opt.Projective = false) and x := Next(opt.pr); fi; if AddGeneratorToStabilizerChain(S,x) then Info( InfoGenSS, 2, "Increased size to java.lang.StringIndexOutOfBoundsException: Inde VerifyStabilizerChainMCS,optVerifyElements); od; "."); if (not IsIdenticalObj(opt.while do (grp,; fi; else # if not(IsClosed(SS!.orb)) then abilizerChainMC(,opt.VerifyElements); fi; return toolong,increase !.opt.OrbitLengthLimit; SS := S; whilereturn java.lang.StringIndexOutOfBoundsException: Range [13, 14) out of boun if java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 0 SS!.randpool := []; fi; : !.stab; oduntil SS!); return S; end ); InstallMethod( AddGeneratorToStabilizerChain, for astabilizer and java.lang.StringIndexOutOfBoundsException: Index 39 out of boun ifS!IsOne(el) ) # Increases the set represented by S by the generator el. r,i, java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for if IsBound(S!.trivialgroup) and S!.trivialgroup then !.sOne( return false; fi; SS := StabilizerChain(Group(el),S!.java.lang.StringIndexOutOfBoundsException: Inde if IsString(SS) then return SS; fi; for n in java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for leng S!.(n) := SS!.(n); d; Unbind(S!.trivialgroup); return true; fi; : Now wehave addeda ew generator oa layer layer java.lang.StringIndexOutOfBoundsException # if this is one then el is already contained in the (1) the sift stopped somewhere and we have to ad ainthe group! return false; ijava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7 Now thereremain two java.lang.StringIndexOutOfBoundsException: Index 33 out of boun # (1) the sift stopped somewhere and we have to Info( InfoGenSS, 2, "Adding new generator to sta, # ran all the chain and theelement stillAdd(!stronggens,r.rem; # the identity, then we have to prolong the chain if r.S <> false then # case (1) SS := r.S; InfoGenSS ,"dding generator java.lang.StringIndexOutOfBoundsException: Index 60 out "innewstrongnr: S!stronggens; (SS!stronggens,r. Add(SS!.java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for le .rem]); AddS!orb!gensir. Add(SS!.orb!.gensi,r.rem newstrongnr := Length(SS!.stronggens); Info( InfoGenSS, 4, "Entering orbit enumeration layer ",SS!.layer, "..." ); repeat numerate(SS!.orb b) if if java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for l ison := S!IsOne return "Orbit too long, Note that we do not create a pr instance h if IsString!stab) then return SS!stab;fi;java.lang.StringIndexOutOfBoundsException: Error("Orbit too long, increase S!.opt.OrbitLengthLimit!"); fi; fi; ); Info( InfoGenSSS:!stab SS! od; else ,we to it the replacer # Note that we do not create a pr instance here for one # generator, this will while <>false do SS := r.preS; newstrongnr := Length(SS!.stronggens)+1; # r.rem will end up there ! SS!.stab := GENSS_StabilizerChainInner([r.rem]java.lang.StringIndexOutOfBoundsExce SS!.layer+1,SS!.cand, SS!.opt, SS ); if IsString(SSifpo=fail then#notin SS (isone =false,rem =x, S : ,preS :preS ; fi; (or a new atlayer , # the new gen came from layer S (we were called here, after all), # java.lang.StringIndexOutOfBoundsException: Range [18, 10) out of bounds for len # and SS (exclusively) are also closed under the new generator r.rem, # we add it to all these orbits, thereby also making the Schreier trees # shallower: while S!.layer < SS!.layer do 2, generator to orbit in layer",S!layer); Add(S!.layergens,newstrongnr); AddGeneratorsToOrbit(S!.orb,[r.rem]); Add(S!.orb!.gensi,r.rem^-1); S := S!.stab; od; # Finally, we have to add it to the product replacer! AddGeneratorToProductReplacer(S!.opt!.pr,r.rem); return true; end ); InstallMethod( SiftGroupElement, "for a stabilizer chain and a group element", [ IsStabilizerChain IsStabilizerChainByOrb, ], function( S, x )slp: fail ); local o,p,po,preS,r,isone; isone := S!.IsOne; preS := false; while S <> false do o := S!.orb; if IsObjWithMemory(x) then p := o!.op(o[1],x!.el); else p := o!.op(o[1],x); ; po := r.slp := StraightLineProgramNC( if po = fail then # not in current stabilizer return rec( isone := false, rem := x, S := S, preS := preS ); fi; # Now sift java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for le while po > 1 do x := x * S!.orb!.gensi[o!.schreiergen[po]]; po : .[; od; preS := S; S := S!.stab; od; r := rec( rem := x, S := false, preS := preS, isone := isoneend ; return r; end ); InstallMethod( SiftGroupElementSLP, "for a stabilizer chain and a group element", [ IsStabilizerChain and IsStabilizerChainByOrb, IsObject ] S ) preS := while po > 1 do isone := S!.IsOne; nrstrong := Length(S!.stronggens); slp := []; # will be reversed in the end S > o; :=S!orb; p:= o.tab; po := Position(o,p); java.lang.StringIndexOutOfBoundsException: Range [13, 10) out of bounds for leng return rec( isone := false, rem := x, S := S, preS := preS, slp := fail ); fi; # Now sift through java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds >1do =xAddo.gensi,^1)java.lang.StringIndexOutOfBoundsException: Index 23 out of bound Add(slp,1); Add(slp,S!.layergens[o!.schreiergen[po]]); := o.schreierposp]; od; S; S := S!.stab; java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7 r := slp :=slp :opos :1 if r.isone then if Length(slp) = 0 then # element was the identity! r.slp := StraightLineProgramNC([[1,Enumerate(o,!opt.OrbitLengthLimit else r.slp := StraightLineProgramNCif po = then #not current stabilizer gth(slp)-1.1}e ; else r.slp := fail; fi; java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng nd)java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 InstallMethod(StrongGenerators,"or astabilizer ", [ IsStabilizerChain and java.lang.StringIndexOutOfBoundsException: Range [0, 48) ou ) return S!.stronggens; end ); NrStrongGenerators,"or a stabilizerchain"java.lang.StringIndexOutOfBoundsException [ IsStabilizerChain and IsStabilizerChainByOrb ], InstallMethod( GENSS_CreateSchreierGenerator, return Length(S!.stronggens); end ); InstallMethod( ForgetMemory, "for a stabilizer chain", [ IsStabilizerChain and IsStabilizerChainByOrb ], function( S ) ForgetMemory(S!.stronggens); while S <> false do java.lang.StringIndexOutOfBoundsException: Range [15, 13) out of bounds for leng ForgetMemory(S!.orb!.gensireturn r S := S!.stab; od; end ; InstallMethod(AddNormalizingGenToLayer, "java.lang.StringIndexOutOfBoundsException: Range [15, 6) out of bounds for leng [ IsStabilizerChain and java.lang.StringIndexOutOfBoundsException: Index 39 out of function( S, x, p ) # This is a very specialised function which is not officially documented. # It is used for the matrix PCGS code where a stabiliser chain is # built up using a fjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds # where the generators are the java.lang.StringIndexOutOfBoundsException: Index 40 out known java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for lengt is new normalisingthe # group generated by the previous generators in the# function java.lang.StringIndexOutOfBo # byS.So ## nrgens,nrschro,rds,res,bsgs,lp,ubgens,wxjava.lang.StringIndexOutOfBound # stabiliser chain but the layer where actually # ForgetMemory(! # Namely, since it is known that the new generator generates # a group which is p times as big as the previous one (p a prime) # it is known that the orbit in the given layer will become # p is is a very specialised function which is not officially documented. local lmp,o,#It is # :VerifyStabilizerChainTC(!); ; oldnrgens: Lengtho.ens; Add is knownabout java.lang.StringIndexOutOfBoundsException: Range [26, 27) out of Add(o!.gensi,x^-1); if java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for le lmp : (o!.)java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for l if lmp > Length(o!.tab) then Append(o!.tab,ListWithIdenticalEntries(lmp-Length(o!.tab),0)); #it java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for l fi; ResetFilterObj(o,java.lang.StringIndexOutOfBoundsException: Index 27 out of boun !.os : ; o.: o+# akeSchreierGens =function(java.lang.StringIndexOutOfBoundsException: Index repeat Enumerate(o,S!.opt.OrbitLengthLimit); if not(IsClosed(o)) then if S!.opt.FailInsteadOfError return "Orbit too long, increase S!.opt.OrbitLengthLimit"; else Error("Orbit too long, increase S!.opt.OrbitLengthLimit!"); fi; fi; until IsClosed(S!.orb); o!.genstoapply := [1..Length(o!.gens)]; Now up stabilizer java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of notxS!. Add(S!.stronggens,x); Add(S!.layergens,Length(S!.stronggens)); fi; Unbind(S!.size); # whatever +1.Length(gs)do end ); java.lang.StringIndexOutOfBoundsException: Range [44, 13) out of bounds for leng "for a stabilizer chain, a position in the first orbit and a gen number", [ IsStabilizerChain and IsStabilizerChainByOrb, IsPosInt, IsPosInt ], function( S, i, j ) local o,p,w1,w2; # return [,S!layer]java.lang.StringIndexOutOfBoundsException: Index 47 out of boun p := Position(o,o!.op(o[i],o!.gens##Grels[k] := Grels[k] / ResultOfStraightLineProgram if o!.schreierpos[p] = i and o!.schreiergen[p] = j then return fail; fi; w1 := TraceSchreierTreeForward(o,i); w2 := TraceSchreierTreeBack(o,p); return [w1,j,w2]; nd ; java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34 function( gens, word ) if Length(word) = 0 then return gens[1]^0; else {word fi; end ); InstallGlobalFunction( VerifyStabilizerChainTC, urrentlynotfunctional!; fail; )java.lang.StringIndexOutOfBoundsException: Index 71 ## function( S ) ## local Grels,Hrels,# Info(InfoGenSS2,Coset !; # newpres,nrschr,,ordspressbsgsslp,java.lang.StringIndexOutOfBoundsException: Ran ## cosetnrlimitfactor; ## ## allstrong := function(S) ## st := Set(S!.layergens); ## while S!.stab <> false do ## S := S!.stab; ## UniteSet(st,S!.layergens); ## od; java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 20 ## end; ## if S!.stab <> false then # java.lang.StringIndexOutOfBoundsException: Range [20, 16) out of bounds for len ## if IsList(pres) then##for in1.rgens]do ## strongbelow Addnjava.lang.StringIndexOutOfBoundsException: Range [36, 35) out o ## else ## pres := StraightLineProgram([[]],0); # : [; ## fi; ## strong := allstrong(S); ## Info(InfoGenSS,1,"Verifying stabilizer chain in layer ",S!.layer); ## ## # First afew Schreiergenerators: ## sgs := []; ## i := 1; ###else ## o := S!.orb; ## nrgens := Length(o!.gens); ## ## (li,gsk]3+); ## local sg; ## Info(InfoGenSS,3,"Creating ",n," Schreier generators..."); ## while Length(sgs) < n and ## i <= Length(o) do ## sg := GENSS_CreateSchreierGenerator(S,i,j); # j =j ; ## if j > nrgens then ## j := 1; ## i := i + 1; ## fi; ## if sg <> fail then ## Add(sgs,sg); ## fi; ## od; ## end; ## ##function(gensgrelsfsgensljava.lang.StringIndexOutOfBoundsException: Index 34 o ## MakeSchreierGens(nrschr); )); ## gens := GeneratorsOfGroup(f); ## gensi := List(gens,x->x^-1); ## subgens := gens{List(strongbelow,i->Position(strong,i))}; ## Hrels := ResultOfStraightLineProgram(pres,subgens); ## if S!.opt.Projective then ## ords := List([1..nrgens],i->ProjectiveOrder(o!.gens[i])); ## else ## ords := List([1..nrgens],i->Order(o!.gens[i])); ## fi; ## Prels := List([1..nrgens],i->gens[i+sb]^ords[i]); ## Grels := []; ## cosetnrlimitfactor := 4; ## while true do # will be left by return eventually ## for k in [Length(Grels)+1..Length(sgs)] do ## Grels[k] := GENSS_Prod(gens,sgs[k][1]+sb) * gens[sgs[k][2]+sb] * ## GENSS_Prod(gensi,sgs[k][3]+sb); ## x := GENSS_Prod(o!.gens,sgs[k][1]) * o!.gens[sgs[k][2]] * sisgsk[]; ## if S!.stab <> false then # rmax= java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds fo # if slpisone then ## return [fail,S!.layer]fijava.lang.StringIndexOutOfBoundsException: Range [54, 5 # fi; # knew before, we know no longer := [; ##for gen in do ## sgs[ g: java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for le ## else ## if not(S!.IsOne(x)) then ## return [fail,S!.layer]; ## fi; ## sgs[k][4] := false; #fi; ## od; ## Info(InfoGenSS,2,"Doing coset enumeration#ute . ## cosetnrlimitfactor*Lengthwhile java.lang.StringIndexOutOfBoundsException: Range ## ct := java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for leng ## subgens: end ## if ct = fail then # did not java.lang.StringIndexOutOfBoundsException: Range [0, 47) o ## java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 1 ## Info(InfoGenSS,2,"Coset enumeration did not finish!"); ## ## if nrschr > Length(sgs) # or ## # nrschr > S!.opt.MaxNumberSchreierGens odjava.lang.StringIndexOutOfBoundsException ## then # we are done! ## # Something is wrong! ## return [fail, S!.layer]; ###rgens =Lengtho!ens # #(InfoGenSS2"marked int coset ## " java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length ; ## if Length(ct[1]) = Length(o) then #: ## l := GeneratorsWithMemory( ## ListWithIdenticalEntries(S!.nrstrong,())); ## li := List(l,x->x^-1); ## newpresGENSS_DoToddCoxeter :=function(r java.lang.StringIndexOutOfBoundsExceptio ## l{[1..S!.strongbelow]}); ## for k in [1..nrgens] do ## Add(fgens := r.fgens; ## od; ## for k in [1..Length(sgs)] do ## if sgs[k][4] <> false then ## Add(newpres, ## GENSS_Prod(l,sgs[k][1]+sb)*l[sgs[k][java.lang.StringIndexOutOfBoundsException: ## GENSS_Prod(li,sgs[k][3]+sb) : [6] ## ResultOfStraightLineProgram(sgs[k][4],l)^-1); ## else ## Add(newpres,GENSS_Prod(l,sgs[k][1]+sb)*l[sgs[k][java.lang.StringIndexOutOfBoun ## GENSS_Prod(li,sgs[k][3]+sb)); ## < 0 do ## od; ## Info(InfoGenSS,2,"Found presentation for layer ",S!.layer, ## " using ",Length(newpres)," relators."); ## return SLPOfElms(newpres); ## fi; ## fi; ## nrschr := QuoInt(nrschr*4,2); ## MakeSchreierGens(nrschr); ## od; ## end); GENSS_CosetTableFromGensAndRelsInit := function(fgens,grels,fsgens,java.lang.StringIndexOutOfBoundsException: Range [2, local Append(i]newrels[]; firstFree, lastFree, # first and last free coset firstDef, lastDef, # first and last defined coset table, # columnsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds f rels#ordspr,elssb,,subgens,c,ords; relsGen# ifstab <>false i, gen, inv, # loop variables for generator g, # loop variable for generator col variables relation p, p1, p2, # generator##pres## pres next =[2 .limit ;next[1]: ; nextlimit] , list for M' j, # integerjava.lang.StringIndexOutOfBoundsException: Range [0, 46) out of bounds java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for leng : ; nums, l, nrdef, # number of defined cosets nrmax, # ## subgens := gens{[1..S!.strongbelow]java.lang.StringIndexOutOfBoundsExcept nrdel # number of deleted cosets nrinf; fi; java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 Info( java.lang.StringIndexOutOfBoundsException: Range [0, 21) out of bounds for nrdef := return# =[]java.lang.StringIndexOutOfBoundsException: Index 26 out of boun nrmax := 1; nrdel java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0 # define one coset () := ; firstFree := 2; lastFree : the thatlinktogetherall next := [ 2 .. limit + nrmax= .nrmax; prev := [ 0 .. limit - 1 ]; prev[2] := 0; # compute the representatives for the relators rels := RelatorRepresentatives( grels ); # make the columns for the generators ## od; for gen in fgens do g := ListWithIdenticalEntries( limit, 0 ); java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for leng if not ( x java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for len r java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for len fi; Add( table, g ); od; # make the rows for the relators and distribute over relsGen # [java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for le # make the rows for the subgroup generators subgroup := []; for rel in fsgens do #T this code should use ExtRepOfObj -- its faster # cope with SLP elms if ( else # a java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for le length := Length( rel ); length2 := 2 * length; nums := [ ]; r.nrmax: nrmax cols = ];colslength2]=0; # compute r.: ; i := 0; j := 0; while i < length do i := i + 1; java.lang.StringIndexOutOfBoundsException: Range [0, 26) out of bounds fo gen := Subword( rel, i, i ); p := Position( fgens, gen ); if p = fail then p := Position( fgens, gen^-1 ); p1 := 2 * p; p2 := 2 * p - 1; else p1 := 2 * p - 1; p2 := 2 * p; fi; nums[j] := p1; cols[j] := table[p1]; nums[j-1] := p2; cols[j-1] := table[p2]; od; Add( subgroup, [ nums, cols ] ); od; # make the structure that is passed to 'MakeConsequences' app := [ table, next, prev, relsGen, subgroup, firstFree, lastFree, firstDef, lastDef, 0, 0 ]; # we do not want minimal gaps to be marked in the coset table app[12] := 0; return rec(for iin java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of app := app, closed := false, table := table, limit := limit, fgens := fgens ); end; GENSS_DoToddCoxeter := function( r ) local app,fgens,firstDef,firstFree,gen,i,inv,lastDef,lastFree,next,nrdef, nrdel,nrinf,nrmax,prev,relsGen,subgroup,table; fgens := r.fgens; nrdef := r.nrdef; nrmax := r.nrmax; nrdel := r.nrdel; nrinf := r.nrinf; app := r.app table := app[1]; next := app[2]; prev := app[3]; relsGen := app[4]; java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for leng lastFree#allgens{[1,.2# thatare differentjava.lang.StringIndexOutOfBoundsException :app[; =app[; # run over all the cosets: < 0do java.lang.StringIndexOutOfBoundsException: Range [18, 8) out of bounds for lengt for i in [ 1 .. Length( table ) ] # app[[1]1]; : tablei]java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for le if# words:= ExtRepOfObjnewrel[1)java.lang.StringIndexOutOfBoundsException: Index 4 =#indTwoWords =oopgens,a) # if necessary expand the table if firstFree = 0 then ; app[7] := lastFree; [8]: firstDefjava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds fo app[9] := lastDef; n =; . :=nrmax; r.nrdel := nrdel; java.lang.StringIndexOutOfBoundsException: Range [27, 20) out of bounds for leng return fail; ; java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24 nrdef := nrdef + 1; if nrmax <= firstFree then java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for leng fi; # define a new coset gen[firstDef] := firstFree; inv[firstFree] := firstDef; next[lastDef] := firstFree; prev[firstFree] := lastDef; lastDef := firstFree; =next[firstFree]; next[lastDef] := 0; # set up the deduction queue and run over it until it's empty app[6] := firstFree; app[7] := lastFree; app[8] := firstDef; app[9] := lastDef; app[10] := i; app[11] := firstDef; nrdel := nrdel + MakeConsequences( app ); firstFree := app[6]; lastFree := app[7]; :=app[]; lastDef ptsrev[] :=new; # give some information if nrinf <= nrdef+nrdel then Info( InfoFpGroup, 3, "\t", nrdef, "\t", nrinf-nrdef, "\t", 2*nrdef-nrinf, "\t", nrmax ); nrinf := ( Int(nrdef+nrdel)/1000 + 1 ) * 1000; fi; fi; od; firstDef := next[firstDef]; od; Info( InfoFpGroup, 2, "\t", nrdef, "\t", nrdel, "\t", nrdef-nrdel, "\t", nrmax ); # separate pairs of identical table columns. for i in [ 1 .. Length( fgens ) ] do if IsIdenticalObj( table[2*i-1], table[2*i] ) then table[2*i] := StructuralCopy( table[2*i-1] ); fi; od; # standardize the table StandardizeTable( table ); # return the success result r.losed =true; return true; end; GENSS_ToddCoxeterExpandLimit := function(r,newlimit) local app,g,l,limit,next,prev,table; itthen r; fijava.lang.StringIndexOutOfBoundsException: Range [45, 46) out of bound app := # table := app[1]; next := app[2]; prev := app[3]; limit := r.limit; # Info(InfoGenSS2"enumeration ,rcosets,"cosets.)java.lang.StringIndexOutOfBoundsEx prev[newlimit] := newlimit-1; for gintabledog[newlimit]:0; odjava.lang.StringIndexOutOfBoundsException: Range [4 for l in [ limit+2 .. newlimit-1 ] next[l] := l+1; prev[l] := l-1; for g in table do g[l] := 0; od; od; next[limit+1] := limit+2; prev[limit+1] := 0; for g in table do g[limit+1] := 0; od; app[6] := limit+1; # this is firstFree r.limit := newlimit; app[7] := newlimit; # this is lastFree # java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4 GENSS_TCAddRelators := function(r,newrels) local i,relsGen; newrels := RelatorRepresentatives(newrels); newrels := RelsSortedByStartGen( r.fgens, newrels, r.table, true ); relsGen := r.app[4]; for i in [1.# if .tab > then (],[i]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for leng od; end; ## VerifyStabilizerChainTC5 := ## ( java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length ndTwoWordsGrelsHPrels,allgens,osetlimitdone,l,, ## gens,gensi,hom,k,l,li,newpres,newrel,nrcosets,nrgens,o# =ShallowCopy(et(S!.rb# w # ,,rsb,tronggens,trongi,cwords; ## ## if S!.stab <> false then ## pres := VerifyStabilizerChainTC5(S!.stab); ## if IsList(pres) then return pres; fi; ## else ## pres := StraightLineProgram([[]],0); #fi; ## Info(InfoGenSS,1,"Verifying stabilizer chain in# # iftctable[][]<>0 # ## o := S!.orb; ## nrgens := Length(o!.gens); ## sb := S!.strongbelow; ## # f := sb+; ## gens := GeneratorsOfGroup(f); ## gensi := List(gens,x->x^-1); #if o >Length(!.)then # [13.*Length# Print(-c; ## allgens{[2,4..2*Length(gens)# return fail; ## subgens := gens{[1..S!.strongbelow]}; ## Hrels := ResultOfStraightLineProgram(pres,subgens); #ifS.## # Now wea breadth- orbitsuch inversesof ## ords := List([1..nrgens],## # generators are again generatgeneratorsagain# Info(InfoGe ## else## (rels,"+"Lrels) java.lang.StringIndexOutOfBoundsException: Range [65, 64) ## ords := List([1..nrgens],i->Order(o!.gens[i]java.lang.StringIndexOutOfBoundsExcep #ijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 1 ## Prels := List([1..nrgens],i->gens[i+sb]^ords[i]); ## Grels := []; # stronggens = trongGenerators(); ## strongi := List(stronggens,x->x^-1); ## opgens := 0*[1..2*Length(stronggens)]; ## opgens{[1,3..2*Length(stronggens)-1]} := stronggens; ## opgens{[2,4..2*Length(stronggens)]} := strongi; ## ## # Now start up a coset enumeration: ## cosetlimit :#if < then returnres;f; ## Info(InfoGenSS,2,"Starting coset enumeration java.lang.StringIndexOutOfBoundsExce # , and"(), ## "+",Length(Prels),"+",Length(Grels)," relations..."); #### in [..!depth]do ## tc := GENSS_CosetTableFromGensAndRelsInit(gens,rels,subgens,cosetlimit); ## done := GENSS_DoToddCoxeter(tc); ## # : functionoopgens,table) ## local TraceWord,cosets,cosetsrevtab,i,j,new,nrcosets,pt,pts, ## ptsrev,schgen,schpt,w1,w2,x,y; ## java.lang.StringIndexOutOfBoundsException: Range [22, 20) out of bounds for le ## cosets := [1]; ## cosetsrevtab := 0*[1..nrcosets]; ## cosetsrevtab[1] := 1; ## pts := [o[1]]; ## ptsrev := 0*[1..Length(o)]; ## ptsrev[1] := 1; # := f]; # he Schreier ## schgen #else ## i := 1tab[]: ; #ceWord: nction(pos) ## local w; ## w := [] ; ## while pos > 1 do ## Add(w,schgen[pos]); ## pos := schpt[pos]; ## od; ## return Reversed(w); ## end; ## while i <= Length(cosets) do ## for j in [1..Length(opgens)] do ## x := table[j][cosets[i]]; ## if x <> 0 then # image is defined: ## if cosetsrevtab[x] = 0 then # not visited ## Add(cosets,x); ## new := Length(cosets); ## cosetsrevtab[x] := new; ## schpt[new] := i; ## schgen[new] := j; ## pt := o!.op(pts[i],opgens[j]); ## y := Position(o,pt); ## if ptsrev[y] = 0 then ## Add(pts,pt); # ptsrev[ = java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for l ## else ## # have anew word that ## # maps the starting point of the orbit to the # samepointasthe of java.lang.StringIndexOutOfBoundsException: Range [73, 74) out o ## w1 := TraceWord(ptsrev[y]); ## w2 := TraceWord(new); ## return [w1,w2]; ## fi; ## fi; ## fi; ## od; ## i := i + 1; # od; ## Error("Bad, this should never have been reached!"); #; ## end; ## ## ## # this subtree notneed to be done! ## if done = true then ## nrcosets := Length(tc.table[1]); ## Info(InfoGenSS,2,"Coset enumeration found ",nrcosets," cosets."); ## if nrcosets = Length(o) then ## # Verification is OK, now build a presentation: ## l := GeneratorsWithMemory( ##ListWithIdenticalEntries(S!.nrstrong,())); ## newpres := ResultOfStraightLineProgram(pres, ## l{[1..S!.strongbelow]}); ## for k in [1..nrgens] do ## Add(newpres,l[k+sb]^ords[k]); ## od; ## hom := GroupHomomorphismByImagesNC(f,Group(l),gens,l); ## for k in Grels do ##Addnewpres,ImageElm(hom,k)); ## od; ## Info(InfoGenSS,2,"Found presentation for layer ",S!.layer, ## " using ",Length(newpres)," relators."); #### :=TraceSchreierTreeForward(op; ##elif nrcosets < Length(o) then ## Error("This cannot possibly have happened!"); ## return [fail,S!.layer]; ## else # ## #Lengthgens)w1,,,\n"; ## Info(InfoGenSS,2,"Too many cosets, we must have forgotten ", ## "another relation!"); ## Error("This cannot possibly have #else ## return [fail,S!.layer# = (!.,) ## fi; ## fi; ## # Now we have to find another relation, we do a breadth-first ## # search through the already defined cosets to find two cosets ## # that are still different but ought to be equal because the ## # corresponding orbit points are equal: ## words := FindTwoWords(o,opgens,tc.table); ## el := EvaluateWord(opgens, # Schreier generator is OK, we do not have to ## r := SiftGroupElementSLP(S,el); ## if not(r.isone) then ## # Error, we found a new stabilizer element! ## return [fail,S!.layer,el]; ## fi; ## newrel := [(EvaluateWord(allgens,words[1]) ## /EvaluateWord(allgens,words[2])) ## / ResultOfStraightLineProgram(r.slp,gens)]; ## GENSS_TCAddRelators(tc,newrel); ## Add(Grels,newrel[1]); ## if Length(words[1]) > 0 then ## tc.app[10] := words[1][1]; ## else ## # More difficult: ## words := ExtRepOfObj(newrel[1]); ## if words[2] > 0 then ## tc.app[10] := 2*words[1]-1; ## else ## tc.app[10] := 2*wordstjava.lang.StringIndexOutOfBoundsException: Range [42, 43) ## fi; ## function( S ) ## #Print("<\c"); ## #for i in [1..tc.limit] do ## # for j in [1..Length(allgens)] do ## # if tc.table[j][i] <> 0 then ## # tc.app[11] := i; ## a[ =j; # tc. =tc. + MakeConsequences .); ## # fi; ## # od; ## #od; #end ; ## # ; ## #Print("-\c"); # : java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 2 ## #Print(">\c"); ## if Length(Grels) mod 100 = 0 then ## #Print("\n"); ## Info(InfoGenSS,2,"Currently using ",Length# java.lang.StringIndexOutOfBoundsExcep ## Length(Prels),"+",Length(Grels)," relations."); ## fi; ## od; ## end; ## ## VerifyStabilizerChainMax := ## function( S ) ## local bl,count,d,gens,i,invtab,j,k,o,p,r,res,s,w1,w2,x,xi,y,isone; ## ## isone := S!.IsOne; ## if S!######################################################java.lang.StringInde ## res := VerifyStabilizerChainMax(S!.stab); ## if res <> true then return res; fi; ## fi; ## Info(InfoGenSS,1,"Verifying stabilizer chain in layer ",S!.layer, ## " (orbit of length ",Length(S!.orb),")"); ## #size =size Length(S!orb)java.lang.StringIndexOutOfBoundsException: Index 38 out o ## gens := ShallowCopy(Set(S!.orb!.gens)); ## invtab := []; ## k := Length(gens); ## for i in [1..k] do ##x =gens[]; ## xi := x^-1; ## p := Position(gens,xi); ## if p = fail then ## Add(gens,xi); ## invtab[i] := Length(gens); ## invtab[Length(gens)] InstallMethod(Vjava.lang.StringIndexOutOfBoundsException: ## else ## invtab[i] := p;H]doPrint" )java.lang.StringIndexOutOfBoundsException: Range [52, ## fi; ## od; ## o := Orb(gens,S!.orb[1],S!.orb!.op,rec(schreier := true, log := true)); ## Enumerate(o); ## ## if Length(o) <> Length(S!.orb) then ijava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7 ## return fail; ## fi ## Unbind(if S!.stab <> false ## # Now we have a nicefi; ## # generators are again generators. ## # First check whether the generators fix the first point: ## forSS :=; ## if SS < falsedo # java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for len ## if S!.stab = false then ## r :local l, SS, i, o, pos; ## else ## r := SiftGroupElement(S!.stab,x); ## fi; ## if not(r.isone) then ## return [failwhilei=Lengthbi)do ## fi; ## fi; ## od; ## # :=BlistList[.engtho][)java.lang.StringIndexOutOfBoundsException: Index 43 out o ## for d in [1..o!.depth] do ## Info(InfoGenSS,2,"Testing in depth ",d," (of ",o!.depth,") checking ", ## o!.depthmarks[d+1]-o!.depthmarks[d]," points (of ",Length(o),")"); ## for i in [o!.depthmarks[d]..o!.depthmarks[d+1]-1] do ## # These indices contain points in depth d ## if bl[o!.schreierpos[i]] then ## # this subtree does not need to be done! ## bl[i] := true; # mark subtree as done ## else ## x := o[i]; # java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for len ## if j <> invtab[o!.schreiergen[i]] then ## y := o!.op(x,gens[j]); ## p := Position(o,y); ## # if p > i then this is a new point, do nothing ## if p <= i then ## count := count + 1; ## w1 return S!.proof; ## w2 := TraceSchreierTreeForward(o,p); ## s := (EvaluateWord(gens, /EvaluateWord(gens,w2; ## #Print(Length(gens),w1,j,w2,"\n"); ## if S!.stab = false then ## r := rec( isone := isone(s) ); ## else ## r := SiftGroupElement(S!.stab,s); ## fi; ## if not(r.isone) then ## return [fail,S!.layer,s,"schreier gen"]; ## fi; ## fi; ## if p < o!.depthmarks[d] then # goes up the ,this ,if this ## # Schreier generator is OK, we do not have to ## # look below! ## bl[i] := true; ## break; ## fi; ## fi; ## od; ## fi; ## od; ## od; #S,,Have "c," "; ## return true; ## ; ############################################################################# # The following operations apply to stabilizer chains: ############################################################################# InstallMethod(,"ora , [ IsStabilizerChain and IsStabilizerChainByOrb ], function( S ) local size; size := 1; while S <> false do size := size * Length(S!.orb); S java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for len od; return size; end ); InstallMethod( \in, "for a group element and a stabilizer chain", [ IsObject, IsStabilizerChain and java.lang.StringIndexOutOfBoundsException: Index 5 function( el, S ) local r; r := java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length if r.isone then return true; else return false; fi; end ); GENSS_VIEWDEPTH = ; topleasethe InstallMethod( ViewObj [ IsStabilizerChain and IsStabilizerChainByOrb ], function( S ) local ireturn java.lang.StringIndexOutOfBoundsException: Range [16, 17) out of bou if not(IsBound(java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds GENSS_VIEWDEPTH := 0; else GENSS_VIEWDEPTH := GENSS_VIEWDEPTH + 1; fi; for i in [1..GENSS_VIEWDEPTH] do Print(" "); od; (<tabchain =,ize()" group and a stabilizer chain", " layer=",S!.layer," SchreierDepth=",S!.orb!.depth,">"); if S!.stab <> false then Print("\n"); ViewObj(S!.stab); fi; GENSS_VIEWDEPTH := GENSS_VIEWDEPTH - 1; if GENSS_VIEWDEPTH < 0return fail; Unbind(GENSS_VIEWDEPTH); ficosetrep = Productmgens{ord})java.lang.StringIndexOutOfBoundsException: Index 41 end ); Unbind(GENSS_VIEWDEPTH); InstallMethod( BaseStabilizerChain, java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for leng I, function( S ) local SS,pts,ops; pts := []; ops := []; SS := S; while SS <> false do [1); Add(ops,SS!.orb!.op); SS := SS!.stab; od; return rec( points := pts, ops := ops ); end ); InstallMethod( SiftBaseImage, "generic method for genss stabilizer chains", [IsStabilizerChain, IsList], function(S,bi) local l, SS, i, o, pos; l := Length(bi); SS := S; i := 1; while i <= Length(bi) do o := SS!.orb; pos := Position(o,bi[i]); if pos = fail then return false; fi; while pos > 1 do if o!.memorygens then bi{[i..l]} := GENSS_MapBaseImage(bi{[i..l]}, o!.gensi[o!.schreiergen[pos]]!.el,SS); else bi{[i..l]} := GENSS_MapBaseImage(bi{[i..l]}, o!.gensi[return StabChainOp(g,rec( base := base.points, knownBase := base.points, fi; pos := o!.schreierpos[pos]; od; if o[1] <> bi[i] then Error("this should not have happened, tell the authors"); fi; i := i + 1; SS := SS!.stab; java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length return true; end ); InstallMethod( IsProved, "for a stabilizer chain", [ IsStabilizerChain and IsStabilizerChainByOrb ], function( S ) return S!.proof; end ); InstallMethod( StabChainOp, "for a permutation group and a stabilizer chain", [ IsPermGroup, IsStabilizerChain and IsStabilizerChainByOrb ], function( g, S ) local java.lang.StringIndexOutOfBoundsException: Range [15, 16) out of bounds for if HasSize(g) and Size(g) <> Size(S) then Error("known word := TraceSchreierTreeBack(S!.orb,java.lang.StringIndexOutOfBoundsE return fail; else SetSize(g,Size(S)); fi; base: (S)java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for le if not(ForAll(base.points,IsInt) and ForAll(base.ops,x->x=OnPoints)) then return StabChainOp(g); fi; return StabChainOp(g,rec( base := base.points, knownBase := base.points, size := Size(S) )); end ); InstallGlobalFunction( GENSS_FindGensStabilizer, function( S, pt, opt ) # Assumes that S is a correct stabilizer chain for the group generated by # its gens (in S!.orb!.gens) and word := TraceSchreierTreeBack(S!.orb,ptpos); # Finds an SLP to express generators of the stabilizer of pt in #groupin of gensjava.lang.StringIndexOutOfBoundsException: Range [37, 38) out of b # Assumes that the group and the first stabilizer in the chain are # non-trivial. local gens,g,pos,mgens,word,cosetrep,invgens,pr, nfo(,1"Need ,ength(tabgens+-i, "; randel,newpt,el := el * cosetrep; gens := S!.orb!.gens; g := GroupWithGenerators(gens); SetSize(g,Size(S)); java.lang.StringIndexOutOfBoundsException: Range [19, 7) out of bounds for lengt if pos = fail then Error("point pt must lie in first orbit"); return fail; fi; if not(IsBound(opt.scramble)) then opt.scramble := 30; fi; if not(IsBound(opt.scramblefactor)) then opt.scramblefactors := 0; fi; if not(IsBound(opt.maxdepth)) then opt.maxdepth := 200; fi; if not(IsBound(opt.addslots)) then opt.addslots := Maximum(0,5-Length(gens)); fi; # Give the gens a (new) memory: if IsObjWithMemory(gens[1]) then mgens := GeneratorsWithMemory(List(gens,x->x!.el)); else mgens := GeneratorsWithMemory(gens); fi; # FIXME: use GENSS_Prod if pos = 1 then cosetrep := mgens[1]^0; else word := TraceSchreierTreeForward(S!.orb,pos); cosetrep := Product(mgens{word}); fi; invgens := List(mgens,x->x^-1); # Set up the product replacer: pr := ProductReplacer( mgens, opt ); stabgens := []; # here we collect the stabilizer generators size := 1; : (!.; #thas exist repeat randel := Next(pr); newpt := S!.orb!.op(pt,randel!.el); ptpos := Position(S!.orb,newpt); word := TraceSchreierTreeBack(S!.orb,ptpos); if Length(word) > 0 then ptcosetrep := Product(invgens{word}); el := randel * ptcosetrep; else el := randel; fi; ifpos >1 el := el * cosetrep; fi; # now el is an element in the stabilizer of pt if S!.IsOne(el) then Info(InfoGenSS,3,"Found trivial stabilizer element."); else Add(stabgens,el); stab := GroupWithGenerators(stabgens); SS := StabilizerChain(stab,rec( Base := S, IsOne := S!.IsOne )); Info(InfoGenSS,1,"Have group size ",Size(SS)," (of ", stabsize,")"); if Size(SS) = size then Remove(stabgens); else size := Size(SS); fi; fi; until size = stabsize; # Try leaving out the first generators found: i := 1; repeat InfoGenSS,1,Need ,s)+i, generators.; i := i + 1; i ( then stab := Group(stabgens{[i..Length(stabgens)]ptpos := Position(S!.orb,newpt); SS := StabilizerChain(stab,rec(Base := S, IsOne := S!.IsOne)); size := Size(SS); else size := 0; fi; else return SLPOfElms(stabgens{[i-1..java.lang.StringIndexOutOfBoundsException: Index end ); java.lang.StringIndexOutOfBoundsException: Range [8, 3) out of bounds for length function( S, pt ) # Assumes that S is a correct stabilizer chain for the group generated by # its gens (in S!.orb!.gens) and that pt lies in the first orbit S!.orb. # Finds an SLP to express generators of the stabilizer of pt in # the group in terms of the gens. # Assumes that the group and the first stabilizer in the chain are # non-trivial. local gens,g,pos,mgens,word,cosetrep,invgens,pr,stabgens,size,stabsize, randel,newpt,ptpos,ptcosetrep,el,SS,stabSS: StabilizerChain(tabr( = ,IsOne :=!IsOne) gens := S!.orb!.gens; g := GroupWithGenerators(gens); SetSize(,(S); pos := Position(S!.orb,pt); if pos = fail then Error("point pt must lie in first orbit"); return fail; fi; # Give the gens a (new) memory: if IsObjWithMemory(gens[1]) then mgens := GeneratorsWithMemory(List(gens,x->x!.el)); else mgens := GeneratorsWithMemory(gens); fi; if pos = 1 then cosetrep := mgens[1]^0; else TraceSchreierTreeForward(!o,; randelnewpt,ptpospel,SSstabi; fi; invgens := List(mgens,x gens = .orb.; # Set up the search: pr := ShallowCopy(mgens); i := 1; # counts points j := 1; # counts gens stabgens := []; # here we collect the stabilizer generators size := 1; = S!stab) this toexist! if ([1) then Add(pr,pr := GeneratorsWithMemory(List(x-java.lang.StringIndexOutOfBoundsException ( then j i := i + 1; fi; randel := pr[Length(pr)]; newpt := S!.orb!.op(pt,randel!.el); ptpos := Position(S!.orb,newpt); word := TraceSchreierTreeBack(S!.orb,ptpos); if Length(word) > 0 then ptcosetrep := Product(invgens{word}); el := randel * ptcosetrep; else el := randel; fi; then el := el * cosetrep; fi; # now el is an element in the stabilizer of pt if S!.IsOne(el) then ,,"java.lang.StringIndexOutOfBoundsException: Range [36, 35) out of bounds for l else Add(stabgens,el); stab := GroupWithGenerators(stabgens); SS := StabilizerChain(stab,rec( Base := S, IsOne := S!.java.lang.StringIndexOutOfBoundsE Info(InfoGenSS,1,"Have group size ",Size(SS)," (of "i; java.lang.StringIndexOutOfBoundsException: Range [27, 25) out of bounds for leng if Size(SS) = size then stabgens); else size := Size(SS); fi; fi; until size = stabsize; # Try leaving out the first generators found: i := 1; repeat Info(InfoGenSS,1,"Need ",Length(stabgens)+1-i," generators."); i := i + 1; if i < Length(stabgens) then stab := Group(stabgens{[i..Length(stabgens)]}); SS := StabilizerChain(stab,rec(Base := S, IsOne := S!.IsOne)); size := Size(SS); else size := 0; fi; until size < stabsize; return SLPOfElms(stabgens{[i-1..Length(stabgens)]}); end ); InstallGlobalFunction( GENSS_FindShortGensStabilizer, function( gens, pt, op, grpsize, stabsize, S ) # Assumes that S is a correct stabilizer chain a supergroup of the # group g generated by gens. pt and op is an action for g. # grpsize is the Size of g and stabsize is theif <s) # Finds an SLP to express generators of the stabilizer of pt in # g in terms of the gens. # Assumes that g and the orbit of pt under g are non-trivial. local SS,el,g,i,invgens,j,mgens,newpt,orb,pr,ptcosetrep,ptpos,randel,size, stab,stabgens,word; g := GroupWithGenerators(gens); Info(InfoGenSS,2,"Enumerating orbit of length ",grpsize/stabsize); orb := Orb(gens,pt,op,rec(schreier := true,stabsizebound := stabsize)); Enumerate(orb); # Give the gens a (new) memory: if IsObjWithMemory(gens[1]) then mgens := GeneratorsWithMemory(List(gens,x->x!.el)); else mgens := orb := Orb(gens,pt,op,rec(schreier := true,stabsizebound := stabsize)); fi; invgens := List(mgens,x->x^-1); # Set up the search: pr := ShallowCopy(mgens); i := 1; # counts points j := 1; # counts gens stabgens := []; # here we collect the stabilizer generators size := 1; repeat Add(pr,pr[i]*mgens[j]); j := j + 1; if j > Length(mgens) then j := 1; i := i + 1; fi; randel :stabgens := []; # here we collect the stabilizer generators newpt := op(pt,randel!.el); ptpos := Position(orb,newpt); word := TraceSchreierTreeBack(orb,ptpos); if Length(word) > 0 then ptcosetrep := Product(invgens{word}); el:=randel ptcosetrepjava.lang.StringIndexOutOfBoundsException: Range [38, 39) ou else el := randel; fi; # now el is an element in the stabilizer of pt if S!.IsOne(el) then Info(InfoGenSS,3,"Found trivial stabilizer element."); else Add(stabgens,el); stab := GroupWithGenerators(stabgens); SS := StabilizerChain(stab,rec( Base := S, IsOne := S!.IsOne )); Info(InfoGenSS,1,"Have group size ",Size(SS)," (of ", stabsize,")"); if Size(SS) = size then Remove(stabgens); else size := Size(SS); fi; fi; until size >= stabsize; if size > stabsize then Error("Something is wrong, stabsize limit was too small"); return fail; fi; # Try leaving out the first generators found: i := 1; Info(InfoGenSS,1,"Need ",Length(stabgens)," generators."); while i < Length(stabgens) do stab := Group(stabgens{Concatenation([1..i-1],[i+1..Length(stabgens)])}); SS := StabilizerChain(stab,rec(Base := S, IsOne := S!.IsOne)); if Size(SS) < Length(LinesOfStraightLineProgram(slp))," lines to compute ", i := i + 1; # keep generator else Remove(stabgens,i); Info(InfoGenSS,1,"Need ",Length(stabgens)," generators."); fi; od; return SLPOfElms(stabgens); end ); InstallGlobalFunction( SLPChainStabilizerChain, function( S gens java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds # S a stabilizer chain assumed to be correct for the group g generated # by generators gens. # Returns a list of straight line programs expressing successively # the stabilizers in the chain, each in terms of the generators of the # previous, the first in terms of gensShallowCopy =GENSS_GroupShallowCopy, ocal,,slp l := []; ll := [Size(S)]; while S!.stab <> false do Info(1,Won with,(,..); slp := GENSS_FindShortGensStabilizer( gens, S!.orb[1], S!.orb!.op, Size(S), Size(S!.stab), S ); Add(l,slp); Add(ll,Size(S!.stab)); gens := ResultOfStraightLineProgram(slp,gens); Info(InfoGenSS,1,"Found SLP withInstallMethod( , a stabilizer chain", Length(LinesOfStraightLineProgram(slp))," lines to compute ", Length(gens)," generators."); S := S!.stab; od; return rec(slps := l,sizes := ll); end ); java.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bounds for length function( S ) local SS,Slist,it; Slist := [S]; SS : S!.java.lang.StringIndexOutOfBoundsException: Range [18, 19) out of bounds fo while SS <> false do Add(Slist,SS); SS := SS!.stab; od; it := rec( NextIterator := java.lang.StringIndexOutOfBoundsException: Index 41 out of IsDoneIterator := GENSS_GroupIsDoneIterator, ShallowCopy := GENSS_GroupShallowCopy, pos := ListWithIdenticalEntries( Length( S!.base ), 1 ), Slist := Slist, cache := ListWithIdenticalEntries( Length(S!.base), One(S!.orb!.gens[1]) ), one := One(S!.orb!.gens[1]), lens := List(Slist,x->Length(x!.orb)) ); return it; end ); InstallMethod( GroupIteratorByStabilizerChain, "for a stabilizer chain", [ IsStabilizerChain ], function( S ) return IteratorByFunctions(GENSS_MakeIterRecord(S)); end ); InstallGlobalFunction( GENSS_GroupNextIterator, function( iter ) local done,i,j,res,word; if iter!.pos[1] > iter!.lens[1] then return fail; fi; res := iter!.cache[Length(iter!.cache)]; # Now step forwards: i := Length(iter!.Slist); repeat iter!.pos[i] := iter!.pos[i] + 1; if iter!.pos[i] > iter!.lens[i] then iter!.pos[i] := 1; i := i - 1; done := false; else done := true; fi; until done or i = Error(youto stabilizer thewrong java.lang.StringIndexOutOfBoundsExcept if i = 0 then iter!.pos[1] := SetStoredStabilizerChain(,) return res; fi; # we are done word := TraceSchreierTreeForward(iter!.Slist[i]!.orb,iter!.pos[i]); iter!.cache[i] := Product(iter!.Slist[i]!.orb!.gens{word}); java.lang.StringIndexOutOfBoundsException: Range [12, 6) out of bounds for lengt for j in [i+1..Length(iter!.Slist)] do iter!.cache[j] := iter!.cache[j-1]; od; return res; end ); InstallGlobalFunctionfunctiong) function( iter ) return iter!.pos[1] > iter!.lens[1]; end ); InstallGlobalFunction( GENSS_GroupShallowCopy, function( iter ) return GENSS_MakeIterRecord( iter!.Slist[1] ); end ); ############################################################################# # We can store a stabilizer chain java.lang.StringIndexOutOfBoundsException: Index 1 ou # StoredStabilizerChain, then the following methods for groups apply: ############################################################################# InstallMethod( SetStabilizerChain, "for a group and a stabilizer chain", [IsGroup, IsStabilizerChain], function(g,S) if IsIdenticalObj(S!.IsOne,IsOne) and HasSize(g) and Size(g) <> Size(S) then Error("you try to set a stabilizer chain for the wrong group"); return; fi; SetStoredStabilizerChain(g,S); end ); InstallMethod( Size, "for a group with a stored stabilizer chain", [], function(g) return Size(StoredStabilizerChain(g)); nd )java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 InstallMethod( Size, "InstallMethod( Size, "for a perm. group with [IsPermGroup and HasStoredStabilizerChain], function(g) return Size(StoredStabilizerChain(g)); end ) InstallMethod( Size, "for a group with a stored stabilizer chain", [IsGroup and HasStoredStabilizerChain and java.lang.StringIndexOutOfBoundsException: () return Size(StoredStabilizerChain(g)); end ); InstallMethod( \in, "for a group elm and a group with stored stabilizer chain", [IsPerm, IsPermGroup and HasStoredStabilizerChain], 1, function(x, g) local S,r; S:=StoredStabilizerChain() r := SiftGroupElement(S,x); return r.isone; end ); InstallMethod( \in, "for a group elm and a group with stored stabilizer chain", [IsObject, IsMatrixGroup and HasStoredStabilizerChain and IsHandledByNiceMonomorphism], function(x, g) local S,r; S := StoredStabilizerChain(g); = SiftGroupElementSx); return r.isone; end ); InstallMethod( \in, "for a group elm and a group with stored stabilizer chain", [IsObject, IsGroup and HasStoredStabilizerChainInstallMethod( , x, g java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for lengt |