From 151efa9674a71bc2b2fb91eede4b358d89a8f037 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Mon, 28 Jun 2021 16:33:07 +0200 Subject: [PATCH 01/14] Add framework and some code for wreath product recognition --- PackageInfo.g | 4 +- gap/WPR.gd | 14 ++- gap/WPR.gi | 271 +++++++++++++++++++++++++++++++++++++++++++++++++- tst/testall.g | 2 +- 4 files changed, 283 insertions(+), 8 deletions(-) diff --git a/PackageInfo.g b/PackageInfo.g index e46d9af..9fa34dc 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -64,8 +64,8 @@ PackageDoc := rec( ), Dependencies := rec( - GAP := ">= 4.11", - NeededOtherPackages := [ ], + GAP := ">= 4.12", + NeededOtherPackages := [ ["recog", ">= 1.3.2"] ], SuggestedOtherPackages := [ ], ExternalConditions := [ ], ), diff --git a/gap/WPR.gd b/gap/WPR.gd index 8350c02..b7ef4be 100644 --- a/gap/WPR.gd +++ b/gap/WPR.gd @@ -16,4 +16,16 @@ #! @Description #! Insert documentation for your function here -DeclareGlobalFunction( "WPR_Example" ); +DeclareGlobalFunction( "WreathProductRecognition" ); +DeclareGlobalFunction( "WPR_SimpleSingleComponent" ); +DeclareGlobalFunction( "WPR_SimpleSingleComponentBaseStep" ); +DeclareGlobalFunction( "WPR_SimpleSingleComponentSuccessProb" ); +DeclareGlobalFunction( "WPR_TopGroupDomain" ); +DeclareGlobalFunction( "WPR_TopComponentImage" ); +DeclareGlobalFunction( "WPR_Image" ); +DeclareGlobalFunction( "WPR_ImageAltGeneric" ); +DeclareGlobalFunction( "WPR_ImageAltFilter" ); +DeclareGlobalFunction( "WPR_SLPforElement" ); +DeclareGlobalFunction( "WPR_StandardGensSingleComponent" ); +DeclareGlobalFunction( "WPR_StandardGensSingleComponentAlt" ); +DeclareGlobalFunction( "WPR_Verification" ); \ No newline at end of file diff --git a/gap/WPR.gi b/gap/WPR.gi index d0c5de2..5fefe68 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -3,8 +3,271 @@ # # Implementations # -InstallGlobalFunction( WPR_Example, -function() - Print( "This is a placeholder function, replace it with your own code.\n" ); -end ); +InstallGlobalFunction( WreathProductRecognition, +function(ri, G, SimpleGroupFamily...) + local N, L, m, eps, gensSingleComponent, S, riS, gensS, domainData, t, domain, proj, lambda, phi, imagesG, H, riH, SLPforElementFunc, gensC; + if Length(SimpleGroupFamily) = 0 then + # TODO: try to deduce simple group family or set this to unknown. + SimpleGroupFamily := "Alt"; + elif Length(SimpleGroupFamily) = 1 then + SimpleGroupFamily := SimpleGroupFamily[1]; + elif Length(SimpleGroupFamily) > 1 then + ErrorNoReturn("too many arguments"); + fi; + if IsPermGroup(G) then + # TODO: make good bounds + # TODO: if G is primitive use O'Nan Scott Type for bounds. + N := NrMovedPoints(G); + L := N; + m := N; + else + ErrorNoReturn("TODO: Implement matrix and projective representation"); + fi; + eps := 1/100; + # TODO: maybe call subprocedures with smaller error bound? + # + # # # # # # # # # # # # # # + # Single-Component Group # + # # # # # # # # # # # # # # + # + # # # # # # + # Step 1 # + # # # # # # + # TODO: if G is primitive, we could compute a single component group as a socle factor directely. + # elms with memory in G + gensSingleComponent := WPR_SimpleSingleComponent(ri, SimpleGroupFamily, L, m, eps); + if not IsList(gensSingleComponent) then + return gensSingleComponent; + fi; + # # # # # # + # Step 2 # + # # # # # # + # TODO: give hints to recog node (G is almost simple, etc.) and abort if assumptions do not hold. + # TODO: we need an isomorphism from S to T or maybe an embedding from S to the standard copy of Aut(T) > T. + S := Group(StripMemory(gensSingleComponent)); + riS := RecogniseGroup(S); + # TODO: we need very special nice generators. + # elms with memory in G + gensS := CalcNiceGens(riS, gensSingleComponent); + # + # # # # # # # # # # # # # # # # + # Top Group Action and Domain # + # # # # # # # # # # # # # # # # + # + # # # # # # + # Step 3 # + # # # # # # + domainData := WPR_TopGroupDomain(ri, gensS); + t := domainData.t; + domain := domainData.domain; + # # # # # # + # Step 4 # + # # # # # # + proj := function(g) + return WPR_TopComponentImage(g, ri, domain); + end; + # # # # # # # # # # # # # # # # # + # Step 5 and 6 are theoretical # + # # # # # # # # # # # # # # # # # + # + # # # # # # # # # # # + # Image Computation # + # # # # # # # # # # # + # + # # # # # # + # Step 7 # + # # # # # # + lambda := fail; + phi := function(g) + return WPR_Image(g, ri, SimpleGroupFamily, riS, t, proj, lambda); + end; + imagesG := List(ri!.gensHmem, g -> phi(g)); + # + # # # # # # # # # # # + # Image Computation # + # # # # # # # # # # # + # + # # # # # # + # Step 8 # + # # # # # # + H := Group(List(StripMemory(ri!.gensHmem), g -> proj(g))); + # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. + riH := RecogniseGroup(H); + # # # # # # + # Step 9 # + # # # # # # + WPR_StandardGensSingleComponent(ri, SimpleGroupFamily, riS, riH, imagesG); + # + # # # # # # # # # # # + # Correctness Check # + # # # # # # # # # # # + # + # # # # # # + # Step 10 # + # # # # # # + SLPforElementFunc := function(w) + return WPR_SLPforElement(w, riS, riH); + end; + gensC := WPR_Verification(ri, SimpleGroupFamily, riS, riH, imagesG, SLPforElementFunc); + if not IsList(gensC) then + return gensC; + fi; +end); + +InstallGlobalFunction( WPR_SimpleSingleComponent, +function(ri, SimpleGroupFamily, L, m, eps) + local S, A, P, logEps, l1, l2, delta, i; + A := ri!.gensHmem; + P := WPR_SimpleSingleComponentSuccessProb(SimpleGroupFamily); + if P = fail then + return NeverApplicable; + fi; + logEps := Log(Float(1 / eps)); + l1 := Int(Ceil(logEps/Log(Float(1 / (1 - P[1]))))); + # TODO: make bound m tighter after l1 steps. + l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); + delta := eps / (l1 + l2); + # TODO: split into two for loops? + for i in [1 .. l1 + l2] do + A := WPR_SimpleSingleComponentBaseStep(A, L, delta); + od; + return A; +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentBaseStep, +function(A, L, delta) + local y, ord, z, n; + # TODO: how to generate random elements? + y := PseudoRandom(Group(A)); + # TODO: use upper bounds for order for iterative computation + ord := Order(StripMemory(y)); + if IsEvenInt(ord) then + z := y ^ (ord / 2); + # TODO: how to choose n with respect to L and delta? + n := 10; + return FastNormalClosure(A, [z], n); + else + # TODO: return fail and count fails in main function + return A; + fi; +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentSuccessProb, +function(SimpleGroupFamily) + if SimpleGroupFamily = "Alt" then + return [1/2, 1/3]; + fi; + return fail; +end); + +InstallGlobalFunction( WPR_TopGroupDomain, +function(ri, gensS) + local t, domain, i, Si, Sj, Sig, g, breakLoop, sig, sj; + # TODO: what is the correct way to construct the identity with memory? + t := [ri!.gensHmem[1] ^ 0]; + domain := [gensS]; + i := 1; + while i <= Length(domain) do + Si := domain[i]; + for g in ri!.gensHmem do + Sig := OnTuples(Si, g); + breakLoop := false; + # check if [Si ^ g, Sj] = 1 for all j + for Sj in domain do + for sig in Sig do + for sj in Sj do + if not docommute(ri)(sig, sj) then + breakLoop := true; + break; + fi; + od; + if breakLoop then + break; + fi; + od; + if breakLoop then + break; + fi; + od; + if breakLoop = false then + Add(t, t[i] * g); + Add(domain, Sig); + fi; + od; + i := i + 1; + od; + return rec(t := t, domain := domain); +end); + +InstallGlobalFunction( WPR_TopComponentImage, +function(g, ri, domain) + local m, images, i, j, Sig, Sj, breakLoop, sig, sj; + m := Length(domain); + images := EmptyPlist(m); + for i in [1 .. m] do + Sig := OnTuples(StripMemory(domain[i]), StripMemory(g)); + for j in [1 .. m] do + Sj := domain[j]; + breakLoop := false; + for sig in Sig do + for sj in Sj do + if not docommute(ri)(sig, sj) then + images[i] := j; + breakLoop := true; + break; + fi; + od; + if breakLoop then + break; + fi; + od; + if breakLoop then + break; + fi; + od; + od; + return PermList(images); +end); + +InstallGlobalFunction(WPR_Image, +function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) + if SimpleGroupFamily = "Alt" then + # TODO: check if filter works faster + return WPR_ImageAltGeneric(g, ri, SimpleGroupFamily, riS, t, proj, lambda); + fi; + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_ImageAltGeneric, +function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_ImageAltFilter, +function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_SLPforElement, +function(w, ri, riS) + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_StandardGensSingleComponent, +function(ri, SimpleGroupFamily, riS, riH, images) + if SimpleGroupFamily = "Alt" then + return WPR_StandardGensSingleComponentAlt(ri, SimpleGroupFamily, riS, riH, images); + fi; + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, +function(ri, SimpleGroupFamily, riS, riH, images) + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_Verification, +function(ri, SimpleGroupFamily, riS, riH, imagesG, SLPforElementFunc) + return ErrorNoReturn("TODO"); +end); \ No newline at end of file diff --git a/tst/testall.g b/tst/testall.g index 835acb2..9066c3b 100644 --- a/tst/testall.g +++ b/tst/testall.g @@ -6,7 +6,7 @@ # LoadPackage( "WPR" ); -TestDirectory(DirectoriesPackageLibrary( "WPR", "tst" ), +TestDirectory(DirectoriesPackageLibrary( "WPR", "tst/files" ), rec(exitGAP := true)); FORCE_QUIT_GAP(1); # if we ever get here, there was an error From f29cf84a3e0d6177167d589a406227bf40c7d669 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Tue, 29 Jun 2021 13:25:14 +0200 Subject: [PATCH 02/14] Further work on framework and Alt example --- gap/WPR.gd | 1 + gap/WPR.gi | 197 +++++++++++++++++++++++++++++++++++++++++++++++------ 2 files changed, 177 insertions(+), 21 deletions(-) diff --git a/gap/WPR.gd b/gap/WPR.gd index b7ef4be..d7e3475 100644 --- a/gap/WPR.gd +++ b/gap/WPR.gd @@ -20,6 +20,7 @@ DeclareGlobalFunction( "WreathProductRecognition" ); DeclareGlobalFunction( "WPR_SimpleSingleComponent" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentBaseStep" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentSuccessProb" ); +DeclareGlobalFunction( "WPR_StandardGensAlmostSimple" ); DeclareGlobalFunction( "WPR_TopGroupDomain" ); DeclareGlobalFunction( "WPR_TopComponentImage" ); DeclareGlobalFunction( "WPR_Image" ); diff --git a/gap/WPR.gi b/gap/WPR.gi index 5fefe68..5985cf4 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -6,7 +6,8 @@ InstallGlobalFunction( WreathProductRecognition, function(ri, G, SimpleGroupFamily...) - local N, L, m, eps, gensSingleComponent, S, riS, gensS, domainData, t, domain, proj, lambda, phi, imagesG, H, riH, SLPforElementFunc, gensC; + local N, L, m, eps, gensSingleComponent, S, riS, stdGensS, domainData, t, domain, proj, lambda, phi, imagesG, H, riH, SLPforElementFunc, gensC, + recogData, isoData, degree, lambdaImageFunc, lambdaSlpFunc, lambdaPreImageFunc, swapSLP, slpToLambdaGens, lambdaGens, T, AutT, W; if Length(SimpleGroupFamily) = 0 then # TODO: try to deduce simple group family or set this to unknown. SimpleGroupFamily := "Alt"; @@ -46,10 +47,45 @@ function(ri, G, SimpleGroupFamily...) # TODO: give hints to recog node (G is almost simple, etc.) and abort if assumptions do not hold. # TODO: we need an isomorphism from S to T or maybe an embedding from S to the standard copy of Aut(T) > T. S := Group(StripMemory(gensSingleComponent)); - riS := RecogniseGroup(S); + # riS := RecogniseGroup(S); # TODO: we need very special nice generators. # elms with memory in G - gensS := CalcNiceGens(riS, gensSingleComponent); + # stdGensS := CalcNiceGens(riS, gensSingleComponent); + if SimpleGroupFamily = "Alt" then + riS := EmptyRecognitionInfoRecord(rec(), S, false); + recogData := RECOG.RecogniseSnAn(riS, eps, N); + if not IsRecord(recogData) then + return TemporaryFailure; + fi; + if recogData.type <> "An" then + return ErrorNoReturn("TODO"); + fi; + isoData := recogData.isoData; + degree := isoData[3]; + lambdaImageFunc := function(g) + return RECOG.FindImageAn(riS, degree, g, isoData[1][1], isoData[1][2], + isoData[2][1], isoData[2][2]); + end; + # slp from (1,2,3), (1,2)(3,..n) + lambdaSlpFunc := function(x) + return RECOG.SLPforAn(degree, x); + end; + lambdaPreImageFunc := function(x) + local slp; + slp := RECOG.SLPforAn(degree, x); + return ResultOfStraightLineProgram(slp, Reversed(isoData[1])); + end; + swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); + slpToLambdaGens := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); + lambdaGens := ResultOfStraightLineProgram(slpToLambdaGens, gensSingleComponent); + T := AlternatingGroup(degree); + AutT := SymmetricGroup(degree); + lambda := GroupHomomorphismByFunction(S, T, lambdaImageFunc, lambdaPreImageFunc); + else + ErrorNoReturn("TODO"); + fi; + # elms with memory in G + stdGensS := WPR_StandardGensAlmostSimple(SimpleGroupFamily, lambda, lambdaSlpFunc, lambdaGens); # # # # # # # # # # # # # # # # # # Top Group Action and Domain # @@ -58,14 +94,15 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 3 # # # # # # # - domainData := WPR_TopGroupDomain(ri, gensS); + domainData := WPR_TopGroupDomain(ri, stdGensS); t := domainData.t; domain := domainData.domain; + m := Length(domain); # # # # # # # Step 4 # # # # # # # proj := function(g) - return WPR_TopComponentImage(g, ri, domain); + return WPR_TopComponentImage(StripMemory(g), ri, StripMemory(domain)); end; # # # # # # # # # # # # # # # # # # Step 5 and 6 are theoretical # @@ -78,9 +115,9 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 7 # # # # # # # - lambda := fail; + W := WreathProduct(AutT, SymmetricGroup(m)); phi := function(g) - return WPR_Image(g, ri, SimpleGroupFamily, riS, t, proj, lambda); + return WPR_Image(StripMemory(g), ri, SimpleGroupFamily, StripMemory(stdGensS), StripMemory(t), proj, lambda); end; imagesG := List(ri!.gensHmem, g -> phi(g)); # @@ -91,13 +128,13 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 8 # # # # # # # - H := Group(List(StripMemory(ri!.gensHmem), g -> proj(g))); + H := Group(List(ri!.gensHmem, g -> proj(g))); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. riH := RecogniseGroup(H); # # # # # # # Step 9 # # # # # # # - WPR_StandardGensSingleComponent(ri, SimpleGroupFamily, riS, riH, imagesG); + WPR_StandardGensSingleComponent(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W); # # # # # # # # # # # # # Correctness Check # @@ -161,12 +198,28 @@ function(SimpleGroupFamily) return fail; end); +InstallGlobalFunction( WPR_StandardGensAlmostSimple, +function(SimpleGroupFamily, lambda, lambdaSlpFunc, lambdaGens) + local n, t, s; + if SimpleGroupFamily = "Alt" then + n := NrMovedPoints(Image(lambda)); + t := ResultOfStraightLineProgram(lambdaSlpFunc((1,2,3)), lambdaGens); + if IsEvenInt(n) then + s := ResultOfStraightLineProgram(lambdaSlpFunc((1,2)*CycleFromList([3 .. n])), lambdaGens); + else + s := ResultOfStraightLineProgram(lambdaSlpFunc(CycleFromList([3 .. n])), lambdaGens); + fi; + return [t, s]; + fi; + return fail; +end); + InstallGlobalFunction( WPR_TopGroupDomain, -function(ri, gensS) +function(ri, stdGensS) local t, domain, i, Si, Sj, Sig, g, breakLoop, sig, sj; # TODO: what is the correct way to construct the identity with memory? t := [ri!.gensHmem[1] ^ 0]; - domain := [gensS]; + domain := [stdGensS]; i := 1; while i <= Length(domain) do Si := domain[i]; @@ -206,7 +259,7 @@ function(g, ri, domain) m := Length(domain); images := EmptyPlist(m); for i in [1 .. m] do - Sig := OnTuples(StripMemory(domain[i]), StripMemory(g)); + Sig := OnTuples(domain[i], g); for j in [1 .. m] do Sj := domain[j]; breakLoop := false; @@ -231,21 +284,70 @@ function(g, ri, domain) end); InstallGlobalFunction(WPR_Image, -function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) +function(g, ri, SimpleGroupFamily, stdGensS, t, proj, lambda) if SimpleGroupFamily = "Alt" then # TODO: check if filter works faster - return WPR_ImageAltGeneric(g, ri, SimpleGroupFamily, riS, t, proj, lambda); + return WPR_ImageAltGeneric(g, ri, stdGensS, t, proj, lambda); fi; return ErrorNoReturn("TODO"); end); InstallGlobalFunction(WPR_ImageAltGeneric, -function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) - return ErrorNoReturn("TODO"); +function(g, ri, stdGensS, t, proj, lambda) + local n, m, top, base, i, j, k, a, b, aCycles, bCycles, aPoints, bPoints, abPoints, 3Point, 3PosInA, 3PosInB, images; + n := NrMovedPoints(Image(lambda)); + m := Length(t); + top := proj(g); + if top = fail then + return TemporaryFailure; + fi; + base := EmptyPlist(m); + for i in [1 .. m] do + j := i ^ top; + images := EmptyPlist(n); + a := (stdGensS[1] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; + if a = fail then + return TemporaryFailure; + fi; + b := (stdGensS[2] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; + if b = fail then + return TemporaryFailure; + fi; + # aPoints contains images of [1 .. 3] up to cyclic shifting + aCycles := Cycles(a, [1 .. n]); + if Set(aCycles, Length) <> [1, 3] then + return TemporaryFailure; + fi; + aPoints := First(aCycles, c -> Length(c) = 3); + # bPoints contains images of [3 .. n] up to cyclic shifting + bCycles := Cycles(b, [1 .. n]); + if IsEvenInt(n) and Set(bCycles, Length) <> [2, n - 2] then + return TemporaryFailure; + elif not IsEvenInt(n) and Set(bCycles, Length) <> [1, n -2] then + return TemporaryFailure; + fi; + bPoints := First(bCycles, c -> Length(c) = n - 2); + # the image of 3 is the unique intersection point of aPoints and bPoints + abPoints := Intersection(aPoints, bPoints); + if Length(abPoints) <> 1 then + return TemporaryFailure; + fi; + 3Point := abPoints[1]; + images[3] := 3Point; + 3PosInA := Position(aPoints, 3Point); + images[1] := aPoints[(3PosInA + 1 - 1) mod 3 + 1]; + images[2] := aPoints[(3PosInA + 2 - 1) mod 3 + 1]; + 3PosInB := Position(bPoints, 3Point); + for k in [1 .. n - 3] do + images[3 + k] := bPoints[(3PosInB + k - 1) mod (n - 2) + 1]; + od; + base[i] := PermList(images); + od; + return Concatenation(base, [top]); end); InstallGlobalFunction(WPR_ImageAltFilter, -function(g, ri, SimpleGroupFamily, riS, t, proj, lambda) +function(g, ri, stdGensS, t, proj, lambda) return ErrorNoReturn("TODO"); end); @@ -255,16 +357,69 @@ function(w, ri, riS) end); InstallGlobalFunction(WPR_StandardGensSingleComponent, -function(ri, SimpleGroupFamily, riS, riH, images) +function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W) if SimpleGroupFamily = "Alt" then - return WPR_StandardGensSingleComponentAlt(ri, SimpleGroupFamily, riS, riH, images); + return WPR_StandardGensSingleComponentAlt(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W); fi; return ErrorNoReturn("TODO"); end); InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, -function(ri, SimpleGroupFamily, riS, riH, images) - return ErrorNoReturn("TODO"); +function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W) + local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats; + Wmem := GroupWithMemory(List(imagesG, g -> WreathProductElementList(W, g))); + # elms with mem in W + stdGensW := GeneratorsOfGroup(Wmem); + H := Grp(riH); + m := NrMovedPoints(H); + # elms with mem in W > H + stdGensH := CalcNiceGens(riH, GeneratorsOfGroup(Wmem)); + # elms with mem in W + stdGensSW1 := List(stdGensS, s -> ResultOfStraightLineProgram(SLPOfElm(s), stdGensW)); + stdGensSW := List([1 .. m], i -> OnTuples(stdGensSW1, ResultOfStraightLineProgram(SLPOfElm(t[i]), stdGensW))); + b := EmptyPlist(m); + repeats := 0; + while repeats < m + Int(Ceil(Log2(Float(1/eps)))) do + repeats := repeats + 1; + wMem := PseudoRandom(Wmem); + wList := ListWreathProductElement(W, StripMemory(wMem)); + pi := wList[m + 1]; + if pi <> One(H) then + slpToPi := SLPforElement(riH, pi); + vMem := ResultOfStraightLineProgram(slpToPi, stdGensH); + wMem := vMem ^ -1 * wMem; + wList := ListWreathProductElement(W, StripMemory(wMem)); + fi; + for i in Reversed([1 .. m]) do + g := wList[i]; + if SignPerm(g) = 1 then + slpToG := lambdaSlpFunc(g); + else + slpToG := lambdaSlpFunc(g * (1,2)); + fi; + vMem := ResultOfStraightLineProgram(slpToG, stdGensSW[i]); + wMem := vMem ^ -1 * wMem; + if IsBound(b[i]) then + wMem := b[i] ^ -1 * wMem; + else + b[i] := wMem; + break; + fi; + wList := ListWreathProductElement(W, StripMemory(wMem)); + od; + if IsBound(b[1]) then + break; + fi; + od; + if IsBound(b[1]) then + c := stdGensSW1[2] * stdGensSW1[1]; + n := NrMovedPoints(Image(lambda)); + if IsEvenInt(n) then + c := b[1] * c; + fi; + return List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), ri!.gensHmem)); + fi; + return TemporaryFailure; end); InstallGlobalFunction(WPR_Verification, From 82db1a3feb9e6ae7b81528813fa2e4186d4d4c99 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Tue, 29 Jun 2021 17:20:04 +0200 Subject: [PATCH 03/14] Only use `master` GAP branch in `CI.yml` --- .github/workflows/CI.yml | 1 - 1 file changed, 1 deletion(-) diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml index fa42fb7..1de186f 100644 --- a/.github/workflows/CI.yml +++ b/.github/workflows/CI.yml @@ -16,7 +16,6 @@ jobs: matrix: gap-branch: - master - - stable-4.11 HPCGAP: ['no'] steps: From ab003ea34eac0e5f7842f18d94744e37048c1713 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Wed, 30 Jun 2021 09:33:21 +0200 Subject: [PATCH 04/14] Add a solid framework --- gap/WPR.gd | 2 + gap/WPR.gi | 158 +++++++++++++++++++++++++++++++++-------------------- 2 files changed, 102 insertions(+), 58 deletions(-) diff --git a/gap/WPR.gd b/gap/WPR.gd index d7e3475..e904c22 100644 --- a/gap/WPR.gd +++ b/gap/WPR.gd @@ -29,4 +29,6 @@ DeclareGlobalFunction( "WPR_ImageAltFilter" ); DeclareGlobalFunction( "WPR_SLPforElement" ); DeclareGlobalFunction( "WPR_StandardGensSingleComponent" ); DeclareGlobalFunction( "WPR_StandardGensSingleComponentAlt" ); +DeclareGlobalFunction( "WPR_SLPforAlmostSimple" ); +DeclareGlobalFunction( "WPR_StandardGensTopGroup" ); DeclareGlobalFunction( "WPR_Verification" ); \ No newline at end of file diff --git a/gap/WPR.gi b/gap/WPR.gi index 5985cf4..313eadc 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -5,15 +5,16 @@ # InstallGlobalFunction( WreathProductRecognition, -function(ri, G, SimpleGroupFamily...) +function(ri, G, simpleGroupFamily...) local N, L, m, eps, gensSingleComponent, S, riS, stdGensS, domainData, t, domain, proj, lambda, phi, imagesG, H, riH, SLPforElementFunc, gensC, - recogData, isoData, degree, lambdaImageFunc, lambdaSlpFunc, lambdaPreImageFunc, swapSLP, slpToLambdaGens, lambdaGens, T, AutT, W; - if Length(SimpleGroupFamily) = 0 then + recogData, isoData, degree, lambdaImageFunc, slpFuncForT, lambdaPreImageFunc, swapSLP, slpToLambdaGens, lambdaGens, T, AutT, W, + stdGensData, stdGensBaseComponent, groupDataBaseComponent, stdGensBase, slpFuncForK, stdGensTop; + if Length(simpleGroupFamily) = 0 then # TODO: try to deduce simple group family or set this to unknown. - SimpleGroupFamily := "Alt"; - elif Length(SimpleGroupFamily) = 1 then - SimpleGroupFamily := SimpleGroupFamily[1]; - elif Length(SimpleGroupFamily) > 1 then + simpleGroupFamily := "Alt"; + elif Length(simpleGroupFamily) = 1 then + simpleGroupFamily := simpleGroupFamily[1]; + elif Length(simpleGroupFamily) > 1 then ErrorNoReturn("too many arguments"); fi; if IsPermGroup(G) then @@ -35,11 +36,11 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 1 # # # # # # # - # TODO: if G is primitive, we could compute a single component group as a socle factor directely. + # TODO: if G is primitive, we could compute a single component group as a socle factor directly. # elms with memory in G - gensSingleComponent := WPR_SimpleSingleComponent(ri, SimpleGroupFamily, L, m, eps); + gensSingleComponent := WPR_SimpleSingleComponent(ri, simpleGroupFamily, L, m, eps); if not IsList(gensSingleComponent) then - return gensSingleComponent; + return TemporaryFailure; fi; # # # # # # # Step 2 # @@ -51,7 +52,7 @@ function(ri, G, SimpleGroupFamily...) # TODO: we need very special nice generators. # elms with memory in G # stdGensS := CalcNiceGens(riS, gensSingleComponent); - if SimpleGroupFamily = "Alt" then + if simpleGroupFamily = "Alt" then riS := EmptyRecognitionInfoRecord(rec(), S, false); recogData := RECOG.RecogniseSnAn(riS, eps, N); if not IsRecord(recogData) then @@ -67,13 +68,9 @@ function(ri, G, SimpleGroupFamily...) isoData[2][1], isoData[2][2]); end; # slp from (1,2,3), (1,2)(3,..n) - lambdaSlpFunc := function(x) - return RECOG.SLPforAn(degree, x); - end; + slpFuncForT := WPR_SLPforAlmostSimple(rec(family := "Alt", degree := degree)); lambdaPreImageFunc := function(x) - local slp; - slp := RECOG.SLPforAn(degree, x); - return ResultOfStraightLineProgram(slp, Reversed(isoData[1])); + return ResultOfStraightLineProgram(slpFuncForT(x), Reversed(isoData[1])); end; swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); slpToLambdaGens := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); @@ -85,7 +82,7 @@ function(ri, G, SimpleGroupFamily...) ErrorNoReturn("TODO"); fi; # elms with memory in G - stdGensS := WPR_StandardGensAlmostSimple(SimpleGroupFamily, lambda, lambdaSlpFunc, lambdaGens); + stdGensS := WPR_StandardGensAlmostSimple(simpleGroupFamily, lambda, slpFuncForT, lambdaGens); # # # # # # # # # # # # # # # # # # Top Group Action and Domain # @@ -117,7 +114,7 @@ function(ri, G, SimpleGroupFamily...) # # # # # # W := WreathProduct(AutT, SymmetricGroup(m)); phi := function(g) - return WPR_Image(StripMemory(g), ri, SimpleGroupFamily, StripMemory(stdGensS), StripMemory(t), proj, lambda); + return WPR_Image(StripMemory(g), ri, simpleGroupFamily, StripMemory(stdGensS), StripMemory(t), proj, lambda); end; imagesG := List(ri!.gensHmem, g -> phi(g)); # @@ -128,13 +125,19 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 8 # # # # # # # - H := Group(List(ri!.gensHmem, g -> proj(g))); + # TODO: remove trivial generators in a better way? + H := Group(Filtered(List(ri!.gensHmem, g -> proj(g)), pi -> pi <> ())); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. riH := RecogniseGroup(H); # # # # # # # Step 9 # # # # # # # - WPR_StandardGensSingleComponent(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W); + # TODO: this is slow, too many slp's for Wmem to handle. + stdGensData := WPR_StandardGensSingleComponent(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W); + stdGensBaseComponent := stdGensData.stdGens; + groupDataBaseComponent := stdGensData.groupData; + stdGensBase := List([1 .. m], i -> OnTuples(stdGensBaseComponent, t[i])); + slpFuncForK := WPR_SLPforAlmostSimple(groupDataBaseComponent); # # # # # # # # # # # # # Correctness Check # @@ -143,20 +146,19 @@ function(ri, G, SimpleGroupFamily...) # # # # # # # Step 10 # # # # # # # - SLPforElementFunc := function(w) - return WPR_SLPforElement(w, riS, riH); - end; - gensC := WPR_Verification(ri, SimpleGroupFamily, riS, riH, imagesG, SLPforElementFunc); - if not IsList(gensC) then - return gensC; - fi; + stdGensTop := WPR_StandardGensTopGroup(ri, stdGensBase, imagesG, slpFuncForK, riH); + # TODO: exploit that top group is transitive and thus use only stdGensTop and stdGensBaseComponent, i.e. exploit slp stdGensTop -> gensH -> t + # isCorrect := WPR_Verification(ri, simpleGroupFamily, riS, riH, imagesG, SLPforElementFunc); + # if not isCorrect then + # return TemporaryFailure; + # fi; end); InstallGlobalFunction( WPR_SimpleSingleComponent, -function(ri, SimpleGroupFamily, L, m, eps) +function(ri, simpleGroupFamily, L, m, eps) local S, A, P, logEps, l1, l2, delta, i; A := ri!.gensHmem; - P := WPR_SimpleSingleComponentSuccessProb(SimpleGroupFamily); + P := WPR_SimpleSingleComponentSuccessProb(simpleGroupFamily); if P = fail then return NeverApplicable; fi; @@ -191,23 +193,23 @@ function(A, L, delta) end); InstallGlobalFunction( WPR_SimpleSingleComponentSuccessProb, -function(SimpleGroupFamily) - if SimpleGroupFamily = "Alt" then +function(simpleGroupFamily) + if simpleGroupFamily = "Alt" then return [1/2, 1/3]; fi; return fail; end); InstallGlobalFunction( WPR_StandardGensAlmostSimple, -function(SimpleGroupFamily, lambda, lambdaSlpFunc, lambdaGens) +function(simpleGroupFamily, lambda, slpFuncForT, lambdaGens) local n, t, s; - if SimpleGroupFamily = "Alt" then + if simpleGroupFamily = "Alt" then n := NrMovedPoints(Image(lambda)); - t := ResultOfStraightLineProgram(lambdaSlpFunc((1,2,3)), lambdaGens); + t := ResultOfStraightLineProgram(slpFuncForT((1,2,3)), lambdaGens); if IsEvenInt(n) then - s := ResultOfStraightLineProgram(lambdaSlpFunc((1,2)*CycleFromList([3 .. n])), lambdaGens); + s := ResultOfStraightLineProgram(slpFuncForT((1,2)*CycleFromList([3 .. n])), lambdaGens); else - s := ResultOfStraightLineProgram(lambdaSlpFunc(CycleFromList([3 .. n])), lambdaGens); + s := ResultOfStraightLineProgram(slpFuncForT(CycleFromList([3 .. n])), lambdaGens); fi; return [t, s]; fi; @@ -284,8 +286,8 @@ function(g, ri, domain) end); InstallGlobalFunction(WPR_Image, -function(g, ri, SimpleGroupFamily, stdGensS, t, proj, lambda) - if SimpleGroupFamily = "Alt" then +function(g, ri, simpleGroupFamily, stdGensS, t, proj, lambda) + if simpleGroupFamily = "Alt" then # TODO: check if filter works faster return WPR_ImageAltGeneric(g, ri, stdGensS, t, proj, lambda); fi; @@ -352,26 +354,32 @@ function(g, ri, stdGensS, t, proj, lambda) end); InstallGlobalFunction(WPR_SLPforElement, -function(w, ri, riS) - return ErrorNoReturn("TODO"); +function(wList, slpFuncForK, riH) + ErrorNoReturn("TODO"); end); InstallGlobalFunction(WPR_StandardGensSingleComponent, -function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W) - if SimpleGroupFamily = "Alt" then - return WPR_StandardGensSingleComponentAlt(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W); +function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) + if simpleGroupFamily = "Alt" then + return WPR_StandardGensSingleComponentAlt(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W); fi; return ErrorNoReturn("TODO"); end); InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, -function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, imagesG, W) - local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats; +function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) + local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData; + H := Grp(riH); + m := NrMovedPoints(H); + n := NrMovedPoints(Image(lambda)); + if ForAll(imagesG, g -> ForAll([1 .. m], i -> SignPerm(g[i]) = 1)) then + stdGens := stdGensS; + groupData := rec(family := "Alt", degree := n); + return rec(stdGens := stdGens, groupData := groupData); + fi; Wmem := GroupWithMemory(List(imagesG, g -> WreathProductElementList(W, g))); # elms with mem in W stdGensW := GeneratorsOfGroup(Wmem); - H := Grp(riH); - m := NrMovedPoints(H); # elms with mem in W > H stdGensH := CalcNiceGens(riH, GeneratorsOfGroup(Wmem)); # elms with mem in W @@ -393,17 +401,19 @@ function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, im for i in Reversed([1 .. m]) do g := wList[i]; if SignPerm(g) = 1 then - slpToG := lambdaSlpFunc(g); + slpToG := slpFuncForT(g); else - slpToG := lambdaSlpFunc(g * (1,2)); + slpToG := slpFuncForT(g * (1,2)); fi; vMem := ResultOfStraightLineProgram(slpToG, stdGensSW[i]); wMem := vMem ^ -1 * wMem; - if IsBound(b[i]) then - wMem := b[i] ^ -1 * wMem; - else - b[i] := wMem; - break; + if SignPerm(g) = -1 then + if IsBound(b[i]) then + wMem := b[i] ^ -1 * wMem; + else + b[i] := wMem; + break; + fi; fi; wList := ListWreathProductElement(W, StripMemory(wMem)); od; @@ -413,16 +423,48 @@ function(ri, eps, SimpleGroupFamily, lambda, stdGensS, lambdaSlpFunc, t, riH, im od; if IsBound(b[1]) then c := stdGensSW1[2] * stdGensSW1[1]; - n := NrMovedPoints(Image(lambda)); if IsEvenInt(n) then c := b[1] * c; fi; - return List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), ri!.gensHmem)); + stdGens := List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), ri!.gensHmem)); + groupData := rec(family := "Sym", degree := n); + return rec(stdGens := stdGens, groupData := groupData); fi; return TemporaryFailure; end); InstallGlobalFunction(WPR_Verification, -function(ri, SimpleGroupFamily, riS, riH, imagesG, SLPforElementFunc) +function(ri, simpleGroupFamily, riS, riH, imagesG, SLPforElementFunc) return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_StandardGensTopGroup, +function(ri, stdGensBase, imagesG, slpFuncForK, riH) + local H, m, l, k, baseElm, g, gList, gensH; + H := Grp(riH); + m := NrMovedPoints(H); + l := Length(imagesG); + gensH := EmptyPlist(l); + for k in [1 .. l] do + g := ri!.gensHmem[k]; + gList := imagesG[k]; + baseElm := Product([1 .. m], i -> ResultOfStraightLineProgram(slpFuncForK(gList[i]), stdGensBase[i])); + gensH[k] := baseElm ^ -1 * g; + od; + return CalcNiceGens(riH, gensH); +end); + +InstallGlobalFunction(WPR_SLPforAlmostSimple, +function(groupData) + if groupData.family = "Alt" then + return function(x) + return RECOG.SLPforAn(groupData.degree, x); + end; + elif groupData.family = "Sym" then + return function(x) + return RECOG.SLPforSn(groupData.degree, x); + end; + else + return ErrorNoReturn("TODO"); + fi; end); \ No newline at end of file From 5df77a691c3a0f88962a77722e17398b08995bed Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Wed, 30 Jun 2021 14:43:23 +0200 Subject: [PATCH 05/14] Optimize `WPR_StandardGensSingleComponentAlt` --- gap/WPR.gi | 32 +++++++++++++++++++------------- 1 file changed, 19 insertions(+), 13 deletions(-) diff --git a/gap/WPR.gi b/gap/WPR.gi index 313eadc..f142685 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -125,14 +125,13 @@ function(ri, G, simpleGroupFamily...) # # # # # # # Step 8 # # # # # # # - # TODO: remove trivial generators in a better way? - H := Group(Filtered(List(ri!.gensHmem, g -> proj(g)), pi -> pi <> ())); + # TODO: take care of trivial generators + H := Group(List(ri!.gensHmem, g -> proj(g))); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. riH := RecogniseGroup(H); # # # # # # # Step 9 # # # # # # # - # TODO: this is slow, too many slp's for Wmem to handle. stdGensData := WPR_StandardGensSingleComponent(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W); stdGensBaseComponent := stdGensData.stdGens; groupDataBaseComponent := stdGensData.groupData; @@ -368,7 +367,7 @@ end); InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) - local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData; + local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData, stdGensT, gens; H := Grp(riH); m := NrMovedPoints(H); n := NrMovedPoints(Image(lambda)); @@ -377,14 +376,20 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag groupData := rec(family := "Alt", degree := n); return rec(stdGens := stdGens, groupData := groupData); fi; - Wmem := GroupWithMemory(List(imagesG, g -> WreathProductElementList(W, g))); - # elms with mem in W - stdGensW := GeneratorsOfGroup(Wmem); - # elms with mem in W > H - stdGensH := CalcNiceGens(riH, GeneratorsOfGroup(Wmem)); + if IsEvenInt(n) then + stdGensT := [(1,2,3), (1,2)*CycleFromList([3 .. n])]; + else + stdGensT := [(1,2,3), CycleFromList([3 .. n])]; + fi; + stdGensW := List(imagesG, g -> WreathProductElementList(W, g)); + stdGensSW := List([1 .. m], i -> List(stdGensT, g -> g ^ Embedding(W, i))); + stdGensH := CalcNiceGens(riH, stdGensW); # elms with mem in W - stdGensSW1 := List(stdGensS, s -> ResultOfStraightLineProgram(SLPOfElm(s), stdGensW)); - stdGensSW := List([1 .. m], i -> OnTuples(stdGensSW1, ResultOfStraightLineProgram(SLPOfElm(t[i]), stdGensW))); + gens := GeneratorsWithMemory(Concatenation(stdGensW, Concatenation(stdGensSW), stdGensH)); + stdGensW := gens{[1 .. Length(stdGensW)]}; + stdGensSW := List([1 .. m], i -> gens{[1 + Length(stdGensW) + Length(stdGensT) * (i - 1) .. Length(stdGensW) + Length(stdGensT) * i]}); + stdGensH := gens{[1 + Length(stdGensW) + Length(stdGensT) * m .. Length(gens)]}; + Wmem := Group(stdGensW); b := EmptyPlist(m); repeats := 0; while repeats < m + Int(Ceil(Log2(Float(1/eps)))) do @@ -422,11 +427,12 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag fi; od; if IsBound(b[1]) then - c := stdGensSW1[2] * stdGensSW1[1]; + c := stdGensSW[1,2] * stdGensSW[1,1]; if IsEvenInt(n) then c := b[1] * c; fi; - stdGens := List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), ri!.gensHmem)); + gens := Concatenation(ri!.gensHmem, Concatenation(List([1 .. m], i -> OnTuples(stdGensS, t[i]))), CalcNiceGens(riH, ri!.gensHmem)); + stdGens := List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), gens)); groupData := rec(family := "Sym", degree := n); return rec(stdGens := stdGens, groupData := groupData); fi; From f4123542a12ddcfb0e62a6af9078ea899f92fb94 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Wed, 30 Jun 2021 15:43:36 +0200 Subject: [PATCH 06/14] Restructure code and add draft of hint system --- gap/WPR.gd | 6 ++- gap/WPR.gi | 153 +++++++++++++++++++++++++++++++++-------------------- 2 files changed, 101 insertions(+), 58 deletions(-) diff --git a/gap/WPR.gd b/gap/WPR.gd index e904c22..bca0697 100644 --- a/gap/WPR.gd +++ b/gap/WPR.gd @@ -18,6 +18,8 @@ #! Insert documentation for your function here DeclareGlobalFunction( "WreathProductRecognition" ); DeclareGlobalFunction( "WPR_SimpleSingleComponent" ); +DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsFirstPhase" ); +DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsSecondPhase" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentBaseStep" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentSuccessProb" ); DeclareGlobalFunction( "WPR_StandardGensAlmostSimple" ); @@ -31,4 +33,6 @@ DeclareGlobalFunction( "WPR_StandardGensSingleComponent" ); DeclareGlobalFunction( "WPR_StandardGensSingleComponentAlt" ); DeclareGlobalFunction( "WPR_SLPforAlmostSimple" ); DeclareGlobalFunction( "WPR_StandardGensTopGroup" ); -DeclareGlobalFunction( "WPR_Verification" ); \ No newline at end of file +DeclareGlobalFunction( "WPR_Verification" ); +DeclareGlobalFunction( "WPR_RecogniseAlmostSimple" ); +DeclareGlobalFunction( "WPR_RecogniseAlt" ); \ No newline at end of file diff --git a/gap/WPR.gi b/gap/WPR.gi index f142685..eee9922 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -6,8 +6,8 @@ InstallGlobalFunction( WreathProductRecognition, function(ri, G, simpleGroupFamily...) - local N, L, m, eps, gensSingleComponent, S, riS, stdGensS, domainData, t, domain, proj, lambda, phi, imagesG, H, riH, SLPforElementFunc, gensC, - recogData, isoData, degree, lambdaImageFunc, slpFuncForT, lambdaPreImageFunc, swapSLP, slpToLambdaGens, lambdaGens, T, AutT, W, + local N, L, m, eps, origGensS, S, riS, stdGensS, domainData, t, domain, projFunc, lambda, phiImageFunc, imagesG, H, riH, + recogData, slpFuncForT, T, AutT, W, hintsForT, simpleCompData, stdGensData, stdGensBaseComponent, groupDataBaseComponent, stdGensBase, slpFuncForK, stdGensTop; if Length(simpleGroupFamily) = 0 then # TODO: try to deduce simple group family or set this to unknown. @@ -37,9 +37,11 @@ function(ri, G, simpleGroupFamily...) # Step 1 # # # # # # # # TODO: if G is primitive, we could compute a single component group as a socle factor directly. + simpleCompData := WPR_SimpleSingleComponent(ri, simpleGroupFamily, L, m, eps); # elms with memory in G - gensSingleComponent := WPR_SimpleSingleComponent(ri, simpleGroupFamily, L, m, eps); - if not IsList(gensSingleComponent) then + origGensS := simpleCompData.origGensS; + hintsForT := simpleCompData.hintsForT; + if not IsList(origGensS) then return TemporaryFailure; fi; # # # # # # @@ -47,42 +49,15 @@ function(ri, G, simpleGroupFamily...) # # # # # # # TODO: give hints to recog node (G is almost simple, etc.) and abort if assumptions do not hold. # TODO: we need an isomorphism from S to T or maybe an embedding from S to the standard copy of Aut(T) > T. - S := Group(StripMemory(gensSingleComponent)); - # riS := RecogniseGroup(S); # TODO: we need very special nice generators. + S := Group(StripMemory(origGensS)); + recogData := WPR_RecogniseAlmostSimple(S, simpleGroupFamily, hintsForT, eps); + T := recogData.T; + AutT := recogData.AutT; + slpFuncForT := recogData.slpFuncForT; # elms with memory in G - # stdGensS := CalcNiceGens(riS, gensSingleComponent); - if simpleGroupFamily = "Alt" then - riS := EmptyRecognitionInfoRecord(rec(), S, false); - recogData := RECOG.RecogniseSnAn(riS, eps, N); - if not IsRecord(recogData) then - return TemporaryFailure; - fi; - if recogData.type <> "An" then - return ErrorNoReturn("TODO"); - fi; - isoData := recogData.isoData; - degree := isoData[3]; - lambdaImageFunc := function(g) - return RECOG.FindImageAn(riS, degree, g, isoData[1][1], isoData[1][2], - isoData[2][1], isoData[2][2]); - end; - # slp from (1,2,3), (1,2)(3,..n) - slpFuncForT := WPR_SLPforAlmostSimple(rec(family := "Alt", degree := degree)); - lambdaPreImageFunc := function(x) - return ResultOfStraightLineProgram(slpFuncForT(x), Reversed(isoData[1])); - end; - swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); - slpToLambdaGens := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); - lambdaGens := ResultOfStraightLineProgram(slpToLambdaGens, gensSingleComponent); - T := AlternatingGroup(degree); - AutT := SymmetricGroup(degree); - lambda := GroupHomomorphismByFunction(S, T, lambdaImageFunc, lambdaPreImageFunc); - else - ErrorNoReturn("TODO"); - fi; - # elms with memory in G - stdGensS := WPR_StandardGensAlmostSimple(simpleGroupFamily, lambda, slpFuncForT, lambdaGens); + stdGensS := recogData.stdGensS; + lambda := recogData.lambda; # # # # # # # # # # # # # # # # # # Top Group Action and Domain # @@ -98,7 +73,7 @@ function(ri, G, simpleGroupFamily...) # # # # # # # Step 4 # # # # # # # - proj := function(g) + projFunc := function(g) return WPR_TopComponentImage(StripMemory(g), ri, StripMemory(domain)); end; # # # # # # # # # # # # # # # # # @@ -113,10 +88,10 @@ function(ri, G, simpleGroupFamily...) # Step 7 # # # # # # # W := WreathProduct(AutT, SymmetricGroup(m)); - phi := function(g) - return WPR_Image(StripMemory(g), ri, simpleGroupFamily, StripMemory(stdGensS), StripMemory(t), proj, lambda); + phiImageFunc := function(g) + return WPR_Image(StripMemory(g), ri, simpleGroupFamily, StripMemory(stdGensS), StripMemory(t), projFunc, lambda); end; - imagesG := List(ri!.gensHmem, g -> phi(g)); + imagesG := List(ri!.gensHmem, g -> phiImageFunc(g)); # # # # # # # # # # # # # Image Computation # @@ -126,7 +101,7 @@ function(ri, G, simpleGroupFamily...) # Step 8 # # # # # # # # TODO: take care of trivial generators - H := Group(List(ri!.gensHmem, g -> proj(g))); + H := Group(List(ri!.gensHmem, g -> projFunc(g))); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. riH := RecogniseGroup(H); # # # # # # @@ -153,9 +128,50 @@ function(ri, G, simpleGroupFamily...) # fi; end); +InstallGlobalFunction( WPR_RecogniseAlmostSimple, +function(S, simpleGroupFamily, hintsForT, eps) + if simpleGroupFamily = "Alt" then + return WPR_RecogniseAlt(S, simpleGroupFamily, hintsForT, eps); + else + ErrorNoReturn("TODO"); + fi; +end); + +InstallGlobalFunction( WPR_RecogniseAlt, +function(S, simpleGroupFamily, hintsForT, eps) + local riS, N, recogData, isoData, degree, T, AutT, slpFuncForT, swapSLP, slpToStdGensS, stdGensS, lambdaImageFunc, lambdaPreImageFunc, lambda; + riS := EmptyRecognitionInfoRecord(rec(), S, false); + recogData := RECOG.RecogniseSnAn(riS, eps, hintsForT.upperDegreeBound); + if not IsRecord(recogData) then + return TemporaryFailure; + fi; + if recogData.type <> "An" then + return ErrorNoReturn("TODO"); + fi; + isoData := recogData.isoData; + degree := isoData[3]; + T := AlternatingGroup(degree); + AutT := SymmetricGroup(degree); + # slp from (1,2,3), (1,2)(3,..n) + slpFuncForT := WPR_SLPforAlmostSimple(rec(family := "Alt", degree := degree)); + swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); + slpToStdGensS := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); + # elms with memory in G + stdGensS := ResultOfStraightLineProgram(slpToStdGensS, origGensS); + lambdaImageFunc := function(g) + return RECOG.FindImageAn(riS, degree, g, isoData[1][1], isoData[1][2], + isoData[2][1], isoData[2][2]); + end; + lambdaPreImageFunc := function(x) + return ResultOfStraightLineProgram(slpFuncForT(x), Reversed(isoData[1])); + end; + lambda := GroupHomomorphismByFunction(S, T, lambdaImageFunc, lambdaPreImageFunc); + return rec(T := T, AutT := AutT, slpFuncForT := slpFuncForT, stdGensS := stdGensS, lambda := lambda); +end); + InstallGlobalFunction( WPR_SimpleSingleComponent, function(ri, simpleGroupFamily, L, m, eps) - local S, A, P, logEps, l1, l2, delta, i; + local S, A, P, logEps, l1, l2, delta, i, hints, hintsForT; A := ri!.gensHmem; P := WPR_SimpleSingleComponentSuccessProb(simpleGroupFamily); if P = fail then @@ -163,14 +179,37 @@ function(ri, simpleGroupFamily, L, m, eps) fi; logEps := Log(Float(1 / eps)); l1 := Int(Ceil(logEps/Log(Float(1 / (1 - P[1]))))); - # TODO: make bound m tighter after l1 steps. + # TODO: we make bound m tighter after l1 steps. Thus delta could be much smaller. l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); delta := eps / (l1 + l2); - # TODO: split into two for loops? - for i in [1 .. l1 + l2] do + # go down into base group + for i in [1 .. l1] do A := WPR_SimpleSingleComponentBaseStep(A, L, delta); od; - return A; + # TODO: better hints system + hints := WPR_SimpleSingleComponentHintsFirstPhase(simpleGroupFamily, A, L, m); + m := hints.m; + hintsForT := hints.hintsForT; + l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); + # go down into single component group + for i in [1 .. l2] do + A := WPR_SimpleSingleComponentBaseStep(A, L, delta); + od; + # TODO: adjust hints after getting to a single component group + # hintsForT := WPR_SimpleSingleComponentHintsSecondPhase(hintsForT, simpleGroupFamily, A, L, m); + return rec(origGensS := A, hintsForT := hintsForT); +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentHintsFirstPhase, +function(simpleGroupFamily, A, L, m) + local hintsForT; + if simpleGroupFamily = "Alt" then + # TODO: compute some orders of random elms + hintsForT := rec(upperDegreeBound := L); + return rec(m := m, hintsForT := hintsForT); + else + ErrorNoReturn("TODO"); + fi; end); InstallGlobalFunction( WPR_SimpleSingleComponentBaseStep, @@ -200,15 +239,15 @@ function(simpleGroupFamily) end); InstallGlobalFunction( WPR_StandardGensAlmostSimple, -function(simpleGroupFamily, lambda, slpFuncForT, lambdaGens) +function(simpleGroupFamily, lambda, slpFuncForT, stdGensS) local n, t, s; if simpleGroupFamily = "Alt" then n := NrMovedPoints(Image(lambda)); - t := ResultOfStraightLineProgram(slpFuncForT((1,2,3)), lambdaGens); + t := ResultOfStraightLineProgram(slpFuncForT((1,2,3)), stdGensS); if IsEvenInt(n) then - s := ResultOfStraightLineProgram(slpFuncForT((1,2)*CycleFromList([3 .. n])), lambdaGens); + s := ResultOfStraightLineProgram(slpFuncForT((1,2)*CycleFromList([3 .. n])), stdGensS); else - s := ResultOfStraightLineProgram(slpFuncForT(CycleFromList([3 .. n])), lambdaGens); + s := ResultOfStraightLineProgram(slpFuncForT(CycleFromList([3 .. n])), stdGensS); fi; return [t, s]; fi; @@ -285,20 +324,20 @@ function(g, ri, domain) end); InstallGlobalFunction(WPR_Image, -function(g, ri, simpleGroupFamily, stdGensS, t, proj, lambda) +function(g, ri, simpleGroupFamily, stdGensS, t, projFunc, lambda) if simpleGroupFamily = "Alt" then # TODO: check if filter works faster - return WPR_ImageAltGeneric(g, ri, stdGensS, t, proj, lambda); + return WPR_ImageAltGeneric(g, ri, stdGensS, t, projFunc, lambda); fi; return ErrorNoReturn("TODO"); end); InstallGlobalFunction(WPR_ImageAltGeneric, -function(g, ri, stdGensS, t, proj, lambda) +function(g, ri, stdGensS, t, projFunc, lambda) local n, m, top, base, i, j, k, a, b, aCycles, bCycles, aPoints, bPoints, abPoints, 3Point, 3PosInA, 3PosInB, images; n := NrMovedPoints(Image(lambda)); m := Length(t); - top := proj(g); + top := projFunc(g); if top = fail then return TemporaryFailure; fi; @@ -348,7 +387,7 @@ function(g, ri, stdGensS, t, proj, lambda) end); InstallGlobalFunction(WPR_ImageAltFilter, -function(g, ri, stdGensS, t, proj, lambda) +function(g, ri, stdGensS, t, projFunc, lambda) return ErrorNoReturn("TODO"); end); From bfc10f9c2def43826aabffb1cc7cbb5f92290221 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Wed, 30 Jun 2021 20:17:39 +0200 Subject: [PATCH 07/14] Restructure code and adjust comments --- gap/Alt.gi | 169 ++++++++++++++++++++++ gap/WPR.gd | 7 +- gap/WPR.gi | 401 +++++++++++++++++------------------------------------ read.g | 2 + 4 files changed, 302 insertions(+), 277 deletions(-) create mode 100644 gap/Alt.gi diff --git a/gap/Alt.gi b/gap/Alt.gi new file mode 100644 index 0000000..c8d4941 --- /dev/null +++ b/gap/Alt.gi @@ -0,0 +1,169 @@ +InstallGlobalFunction( WPR_RecogniseAlt, +function(origGensS, simpleGroupFamily, hintsForT, eps) + local S, riS, recogData, isoData, degree, T, AutT, slpFuncForT, + swapSLP, slpToStdGensS, stdGensS, lambdaImageFunc, lambdaPreImageFunc, lambda; + S := Group(StripMemory(origGensS)); + riS := EmptyRecognitionInfoRecord(rec(), S, false); + recogData := RECOG.RecogniseSnAn(riS, eps, hintsForT.upperDegreeBound); + if not IsRecord(recogData) then + return TemporaryFailure; + fi; + if recogData.type <> "An" then + return ErrorNoReturn("TODO"); + fi; + isoData := recogData.isoData; + degree := isoData[3]; + T := AlternatingGroup(degree); + AutT := SymmetricGroup(degree); + slpFuncForT := WPR_SLPforAlmostSimple(rec(family := "Alt", degree := degree)); + swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); + slpToStdGensS := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); + # elms with memory in G + stdGensS := ResultOfStraightLineProgram(slpToStdGensS, origGensS); + lambdaImageFunc := function(g) + return RECOG.FindImageAn(riS, degree, g, isoData[1][1], isoData[1][2], + isoData[2][1], isoData[2][2]); + end; + lambdaPreImageFunc := function(x) + return ResultOfStraightLineProgram(slpFuncForT(x), Reversed(isoData[1])); + end; + lambda := GroupHomomorphismByFunction(S, T, lambdaImageFunc, lambdaPreImageFunc); + return rec( T := T, + AutT := AutT, + slpFuncForT := slpFuncForT, + stdGensS := stdGensS, + lambda := lambda); +end); + +InstallGlobalFunction(WPR_ImageAltGeneric, +function(g, ri, stdGensS, t, projFunc, lambda) + local n, m, top, base, i, j, k, a, b, aCycles, bCycles, aPoints, bPoints, abPoints, 3Point, 3PosInA, 3PosInB, images; + n := NrMovedPoints(Image(lambda)); + m := Length(t); + top := projFunc(g); + if top = fail then + return TemporaryFailure; + fi; + base := EmptyPlist(m); + for i in [1 .. m] do + j := i ^ top; + images := EmptyPlist(n); + a := (stdGensS[1] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; + if a = fail then + return TemporaryFailure; + fi; + b := (stdGensS[2] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; + if b = fail then + return TemporaryFailure; + fi; + # aPoints contains images of [1 .. 3] up to cyclic shifting + aCycles := Cycles(a, [1 .. n]); + if Set(aCycles, Length) <> [1, 3] then + return TemporaryFailure; + fi; + aPoints := First(aCycles, c -> Length(c) = 3); + # bPoints contains images of [3 .. n] up to cyclic shifting + bCycles := Cycles(b, [1 .. n]); + if IsEvenInt(n) and Set(bCycles, Length) <> [2, n - 2] then + return TemporaryFailure; + elif not IsEvenInt(n) and Set(bCycles, Length) <> [1, n -2] then + return TemporaryFailure; + fi; + bPoints := First(bCycles, c -> Length(c) = n - 2); + # the image of 3 is the unique intersection point of aPoints and bPoints + abPoints := Intersection(aPoints, bPoints); + if Length(abPoints) <> 1 then + return TemporaryFailure; + fi; + 3Point := abPoints[1]; + images[3] := 3Point; + 3PosInA := Position(aPoints, 3Point); + images[1] := aPoints[(3PosInA + 1 - 1) mod 3 + 1]; + images[2] := aPoints[(3PosInA + 2 - 1) mod 3 + 1]; + 3PosInB := Position(bPoints, 3Point); + for k in [1 .. n - 3] do + images[3 + k] := bPoints[(3PosInB + k - 1) mod (n - 2) + 1]; + od; + base[i] := PermList(images); + od; + return Concatenation(base, [top]); +end); + +InstallGlobalFunction(WPR_ImageAltFilter, +function(g, ri, stdGensS, t, projFunc, lambda) + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, +function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) + local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData, stdGensT, gens; + H := Grp(riH); + m := NrMovedPoints(H); + n := NrMovedPoints(Image(lambda)); + if ForAll(imagesG, g -> ForAll([1 .. m], i -> SignPerm(g[i]) = 1)) then + stdGens := stdGensS; + groupData := rec(family := "Alt", degree := n); + return rec(stdGens := stdGens, groupData := groupData); + fi; + if IsEvenInt(n) then + stdGensT := [(1,2,3), (1,2)*CycleFromList([3 .. n])]; + else + stdGensT := [(1,2,3), CycleFromList([3 .. n])]; + fi; + stdGensW := List(imagesG, g -> WreathProductElementList(W, g)); + stdGensSW := List([1 .. m], i -> List(stdGensT, g -> g ^ Embedding(W, i))); + stdGensH := CalcNiceGens(riH, stdGensW); + # elms with mem in W + gens := GeneratorsWithMemory(Concatenation(stdGensW, Concatenation(stdGensSW), stdGensH)); + stdGensW := gens{[1 .. Length(stdGensW)]}; + stdGensSW := List([1 .. m], i -> gens{[1 + Length(stdGensW) + Length(stdGensT) * (i - 1) .. Length(stdGensW) + Length(stdGensT) * i]}); + stdGensH := gens{[1 + Length(stdGensW) + Length(stdGensT) * m .. Length(gens)]}; + Wmem := Group(stdGensW); + b := EmptyPlist(m); + repeats := 0; + while repeats < m + Int(Ceil(Log2(Float(1/eps)))) do + repeats := repeats + 1; + wMem := PseudoRandom(Wmem); + wList := ListWreathProductElement(W, StripMemory(wMem)); + pi := wList[m + 1]; + if pi <> One(H) then + slpToPi := SLPforElement(riH, pi); + vMem := ResultOfStraightLineProgram(slpToPi, stdGensH); + wMem := vMem ^ -1 * wMem; + wList := ListWreathProductElement(W, StripMemory(wMem)); + fi; + for i in Reversed([1 .. m]) do + g := wList[i]; + if SignPerm(g) = 1 then + slpToG := slpFuncForT(g); + else + slpToG := slpFuncForT(g * (1,2)); + fi; + vMem := ResultOfStraightLineProgram(slpToG, stdGensSW[i]); + wMem := vMem ^ -1 * wMem; + if SignPerm(g) = -1 then + if IsBound(b[i]) then + wMem := b[i] ^ -1 * wMem; + else + b[i] := wMem; + break; + fi; + fi; + wList := ListWreathProductElement(W, StripMemory(wMem)); + od; + if IsBound(b[1]) then + break; + fi; + od; + if IsBound(b[1]) then + c := stdGensSW[1,2] * stdGensSW[1,1]; + if IsEvenInt(n) then + c := b[1] * c; + fi; + gens := Concatenation(ri!.gensHmem, Concatenation(List([1 .. m], i -> OnTuples(stdGensS, t[i]))), CalcNiceGens(riH, ri!.gensHmem)); + stdGens := List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), gens)); + groupData := rec(family := "Sym", degree := n); + return rec(stdGens := stdGens, groupData := groupData); + fi; + return TemporaryFailure; +end); \ No newline at end of file diff --git a/gap/WPR.gd b/gap/WPR.gd index bca0697..af8180e 100644 --- a/gap/WPR.gd +++ b/gap/WPR.gd @@ -14,25 +14,22 @@ #! This section will describe the example #! methods of WPR -#! @Description -#! Insert documentation for your function here DeclareGlobalFunction( "WreathProductRecognition" ); DeclareGlobalFunction( "WPR_SimpleSingleComponent" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsFirstPhase" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsSecondPhase" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentBaseStep" ); DeclareGlobalFunction( "WPR_SimpleSingleComponentSuccessProb" ); -DeclareGlobalFunction( "WPR_StandardGensAlmostSimple" ); DeclareGlobalFunction( "WPR_TopGroupDomain" ); DeclareGlobalFunction( "WPR_TopComponentImage" ); DeclareGlobalFunction( "WPR_Image" ); DeclareGlobalFunction( "WPR_ImageAltGeneric" ); DeclareGlobalFunction( "WPR_ImageAltFilter" ); -DeclareGlobalFunction( "WPR_SLPforElement" ); DeclareGlobalFunction( "WPR_StandardGensSingleComponent" ); DeclareGlobalFunction( "WPR_StandardGensSingleComponentAlt" ); DeclareGlobalFunction( "WPR_SLPforAlmostSimple" ); DeclareGlobalFunction( "WPR_StandardGensTopGroup" ); DeclareGlobalFunction( "WPR_Verification" ); DeclareGlobalFunction( "WPR_RecogniseAlmostSimple" ); -DeclareGlobalFunction( "WPR_RecogniseAlt" ); \ No newline at end of file +DeclareGlobalFunction( "WPR_RecogniseAlt" ); + diff --git a/gap/WPR.gi b/gap/WPR.gi index eee9922..8604734 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -6,9 +6,18 @@ InstallGlobalFunction( WreathProductRecognition, function(ri, G, simpleGroupFamily...) - local N, L, m, eps, origGensS, S, riS, stdGensS, domainData, t, domain, projFunc, lambda, phiImageFunc, imagesG, H, riH, - recogData, slpFuncForT, T, AutT, W, hintsForT, simpleCompData, - stdGensData, stdGensBaseComponent, groupDataBaseComponent, stdGensBase, slpFuncForK, stdGensTop; + local N, L, m, eps, simpleCompData, origGensS, hintsForT, + recogData, T, AutT, slpFuncForT, stdGensS, lambda, + domainData, t, domain, projFunc, + phiImageFunc, imagesG, H, riH, + W, stdGensData, stdGensBaseComponent, groupDataBaseComponent, stdGensBase, slpFuncForK, stdGensTop; + + #################################### + #### ------------------------ #### + #### Initialization of Bounds #### + #### ------------------------ #### + #################################### + if Length(simpleGroupFamily) = 0 then # TODO: try to deduce simple group family or set this to unknown. simpleGroupFamily := "Alt"; @@ -28,14 +37,17 @@ function(ri, G, simpleGroupFamily...) fi; eps := 1/100; # TODO: maybe call subprocedures with smaller error bound? - # - # # # # # # # # # # # # # # - # Single-Component Group # - # # # # # # # # # # # # # # - # - # # # # # # - # Step 1 # - # # # # # # + + ################################## + #### ---------------------- #### + #### Single-Component Group #### + #### ---------------------- #### + ################################## + + # ------------------------------------------------------------- # + # Step 1 : Compute a single-component group S isomorphic to T # + # ------------------------------------------------------------- # + # TODO: if G is primitive, we could compute a single component group as a socle factor directly. simpleCompData := WPR_SimpleSingleComponent(ri, simpleGroupFamily, L, m, eps); # elms with memory in G @@ -44,135 +56,122 @@ function(ri, G, simpleGroupFamily...) if not IsList(origGensS) then return TemporaryFailure; fi; - # # # # # # - # Step 2 # - # # # # # # + + # ----------------------------------------------------------- # + # Step 2 : Compute standard generators in S isomorphic to T # + # ----------------------------------------------------------- # + # TODO: give hints to recog node (G is almost simple, etc.) and abort if assumptions do not hold. # TODO: we need an isomorphism from S to T or maybe an embedding from S to the standard copy of Aut(T) > T. # TODO: we need very special nice generators. - S := Group(StripMemory(origGensS)); - recogData := WPR_RecogniseAlmostSimple(S, simpleGroupFamily, hintsForT, eps); + recogData := WPR_RecogniseAlmostSimple(origGensS, simpleGroupFamily, hintsForT, eps); T := recogData.T; AutT := recogData.AutT; slpFuncForT := recogData.slpFuncForT; # elms with memory in G stdGensS := recogData.stdGensS; lambda := recogData.lambda; - # - # # # # # # # # # # # # # # # # - # Top Group Action and Domain # - # # # # # # # # # # # # # # # # - # - # # # # # # - # Step 3 # - # # # # # # + + ####################################### + #### --------------------------- #### + #### Top Group Action and Domain #### + #### --------------------------- #### + ####################################### + + # ----------------------------------------------------------------- # + # Step 3 : Compute a faithful H-set { S ^ {t_1}, ..., S ^ {t_m} } # + # ----------------------------------------------------------------- # + domainData := WPR_TopGroupDomain(ri, stdGensS); t := domainData.t; domain := domainData.domain; m := Length(domain); - # # # # # # - # Step 4 # - # # # # # # + + # ------------------------------------------------ # + # Step 4 : Compute projection onto top component # + # ------------------------------------------------ # + projFunc := function(g) return WPR_TopComponentImage(StripMemory(g), ri, StripMemory(domain)); end; - # # # # # # # # # # # # # # # # # - # Step 5 and 6 are theoretical # - # # # # # # # # # # # # # # # # # - # - # # # # # # # # # # # - # Image Computation # - # # # # # # # # # # # - # - # # # # # # - # Step 7 # - # # # # # # + + ################################## + #### ---------------------- #### + #### Isomorphism Definition #### + #### ---------------------- #### + ################################## + + # ------------------------------------------------------------------------------ # + # Step 5 : theoretically define single-component group Shat > S isomorphic to K # + # ------------------------------------------------------------------------------ # + + # --------------------------------------------------------------- # + # Step 6 : theoretically define isomorphism phi from G to K wr H # + # --------------------------------------------------------------- # + + ############################# + #### ----------------- #### + #### Image Computation #### + #### ----------------- #### + ############################# + + # ---------------------------------------------------------------------- # + # Step 7 : Compute images of all generators of G under isomorphism phi # + # ---------------------------------------------------------------------- # + W := WreathProduct(AutT, SymmetricGroup(m)); phiImageFunc := function(g) return WPR_Image(StripMemory(g), ri, simpleGroupFamily, StripMemory(stdGensS), StripMemory(t), projFunc, lambda); end; imagesG := List(ri!.gensHmem, g -> phiImageFunc(g)); - # - # # # # # # # # # # # - # Image Computation # - # # # # # # # # # # # - # - # # # # # # - # Step 8 # - # # # # # # + + ################################ + #### -------------------- #### + #### PreImage Computation #### + #### -------------------- #### + ################################ + + # -------------------------------- # + # Step 8 : Recognise top group H # + # -------------------------------- # + # TODO: take care of trivial generators H := Group(List(ri!.gensHmem, g -> projFunc(g))); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. riH := RecogniseGroup(H); - # # # # # # - # Step 9 # - # # # # # # + + # -------------------------------------------------------- # + # Step 9 : Compute standard generators of base component # + # -------------------------------------------------------- # + stdGensData := WPR_StandardGensSingleComponent(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W); stdGensBaseComponent := stdGensData.stdGens; groupDataBaseComponent := stdGensData.groupData; stdGensBase := List([1 .. m], i -> OnTuples(stdGensBaseComponent, t[i])); slpFuncForK := WPR_SLPforAlmostSimple(groupDataBaseComponent); - # - # # # # # # # # # # # - # Correctness Check # - # # # # # # # # # # # - # - # # # # # # - # Step 10 # - # # # # # # + + # ------------------------------------------------------- # + # Step 10 : Compute standard generators of top component # + # ------------------------------------------------------- # + stdGensTop := WPR_StandardGensTopGroup(ri, stdGensBase, imagesG, slpFuncForK, riH); - # TODO: exploit that top group is transitive and thus use only stdGensTop and stdGensBaseComponent, i.e. exploit slp stdGensTop -> gensH -> t - # isCorrect := WPR_Verification(ri, simpleGroupFamily, riS, riH, imagesG, SLPforElementFunc); - # if not isCorrect then - # return TemporaryFailure; - # fi; -end); -InstallGlobalFunction( WPR_RecogniseAlmostSimple, -function(S, simpleGroupFamily, hintsForT, eps) - if simpleGroupFamily = "Alt" then - return WPR_RecogniseAlt(S, simpleGroupFamily, hintsForT, eps); - else - ErrorNoReturn("TODO"); - fi; -end); + ############################# + #### ----------------- #### + #### Correctness Check #### + #### ----------------- #### + ############################# -InstallGlobalFunction( WPR_RecogniseAlt, -function(S, simpleGroupFamily, hintsForT, eps) - local riS, N, recogData, isoData, degree, T, AutT, slpFuncForT, swapSLP, slpToStdGensS, stdGensS, lambdaImageFunc, lambdaPreImageFunc, lambda; - riS := EmptyRecognitionInfoRecord(rec(), S, false); - recogData := RECOG.RecogniseSnAn(riS, eps, hintsForT.upperDegreeBound); - if not IsRecord(recogData) then - return TemporaryFailure; - fi; - if recogData.type <> "An" then - return ErrorNoReturn("TODO"); - fi; - isoData := recogData.isoData; - degree := isoData[3]; - T := AlternatingGroup(degree); - AutT := SymmetricGroup(degree); - # slp from (1,2,3), (1,2)(3,..n) - slpFuncForT := WPR_SLPforAlmostSimple(rec(family := "Alt", degree := degree)); - swapSLP := StraightLineProgram([[[2, 1], [1, 1]]], 2); - slpToStdGensS := CompositionOfStraightLinePrograms(swapSLP, recogData.slpToStdGens); - # elms with memory in G - stdGensS := ResultOfStraightLineProgram(slpToStdGensS, origGensS); - lambdaImageFunc := function(g) - return RECOG.FindImageAn(riS, degree, g, isoData[1][1], isoData[1][2], - isoData[2][1], isoData[2][2]); - end; - lambdaPreImageFunc := function(x) - return ResultOfStraightLineProgram(slpFuncForT(x), Reversed(isoData[1])); - end; - lambda := GroupHomomorphismByFunction(S, T, lambdaImageFunc, lambdaPreImageFunc); - return rec(T := T, AutT := AutT, slpFuncForT := slpFuncForT, stdGensS := stdGensS, lambda := lambda); + # TODO: exploit that top group is transitive and thus use only stdGensTop and stdGensBaseComponent, i.e. exploit slp stdGensTop -> origGensH -> t + # if not WPR_Verification(TODO) then + # return TemporaryFailure; + # fi; end); InstallGlobalFunction( WPR_SimpleSingleComponent, function(ri, simpleGroupFamily, L, m, eps) - local S, A, P, logEps, l1, l2, delta, i, hints, hintsForT; - A := ri!.gensHmem; + local gens, P, logEps, l1, l2, delta, i, hints, hintsForT; + gens := ri!.gensHmem; P := WPR_SimpleSingleComponentSuccessProb(simpleGroupFamily); if P = fail then return NeverApplicable; @@ -184,24 +183,24 @@ function(ri, simpleGroupFamily, L, m, eps) delta := eps / (l1 + l2); # go down into base group for i in [1 .. l1] do - A := WPR_SimpleSingleComponentBaseStep(A, L, delta); + gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); od; # TODO: better hints system - hints := WPR_SimpleSingleComponentHintsFirstPhase(simpleGroupFamily, A, L, m); + hints := WPR_SimpleSingleComponentHintsFirstPhase(simpleGroupFamily, gens, L, m); m := hints.m; hintsForT := hints.hintsForT; l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); # go down into single component group for i in [1 .. l2] do - A := WPR_SimpleSingleComponentBaseStep(A, L, delta); + gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); od; # TODO: adjust hints after getting to a single component group - # hintsForT := WPR_SimpleSingleComponentHintsSecondPhase(hintsForT, simpleGroupFamily, A, L, m); - return rec(origGensS := A, hintsForT := hintsForT); + # hintsForT := WPR_SimpleSingleComponentHintsSecondPhase(hintsForT, simpleGroupFamily, gens, L, m); + return rec(origGensS := gens, hintsForT := hintsForT); end); InstallGlobalFunction( WPR_SimpleSingleComponentHintsFirstPhase, -function(simpleGroupFamily, A, L, m) +function(simpleGroupFamily, gens, L, m) local hintsForT; if simpleGroupFamily = "Alt" then # TODO: compute some orders of random elms @@ -213,20 +212,20 @@ function(simpleGroupFamily, A, L, m) end); InstallGlobalFunction( WPR_SimpleSingleComponentBaseStep, -function(A, L, delta) +function(gens, L, delta) local y, ord, z, n; # TODO: how to generate random elements? - y := PseudoRandom(Group(A)); + y := PseudoRandom(Group(gens)); # TODO: use upper bounds for order for iterative computation ord := Order(StripMemory(y)); if IsEvenInt(ord) then z := y ^ (ord / 2); # TODO: how to choose n with respect to L and delta? n := 10; - return FastNormalClosure(A, [z], n); + return FastNormalClosure(gens, [z], n); else # TODO: return fail and count fails in main function - return A; + return gens; fi; end); @@ -238,20 +237,13 @@ function(simpleGroupFamily) return fail; end); -InstallGlobalFunction( WPR_StandardGensAlmostSimple, -function(simpleGroupFamily, lambda, slpFuncForT, stdGensS) - local n, t, s; +InstallGlobalFunction( WPR_RecogniseAlmostSimple, +function(origGensS, simpleGroupFamily, hintsForT, eps) if simpleGroupFamily = "Alt" then - n := NrMovedPoints(Image(lambda)); - t := ResultOfStraightLineProgram(slpFuncForT((1,2,3)), stdGensS); - if IsEvenInt(n) then - s := ResultOfStraightLineProgram(slpFuncForT((1,2)*CycleFromList([3 .. n])), stdGensS); - else - s := ResultOfStraightLineProgram(slpFuncForT(CycleFromList([3 .. n])), stdGensS); - fi; - return [t, s]; + return WPR_RecogniseAlt(origGensS, simpleGroupFamily, hintsForT, eps); + else + ErrorNoReturn("TODO"); fi; - return fail; end); InstallGlobalFunction( WPR_TopGroupDomain, @@ -332,70 +324,6 @@ function(g, ri, simpleGroupFamily, stdGensS, t, projFunc, lambda) return ErrorNoReturn("TODO"); end); -InstallGlobalFunction(WPR_ImageAltGeneric, -function(g, ri, stdGensS, t, projFunc, lambda) - local n, m, top, base, i, j, k, a, b, aCycles, bCycles, aPoints, bPoints, abPoints, 3Point, 3PosInA, 3PosInB, images; - n := NrMovedPoints(Image(lambda)); - m := Length(t); - top := projFunc(g); - if top = fail then - return TemporaryFailure; - fi; - base := EmptyPlist(m); - for i in [1 .. m] do - j := i ^ top; - images := EmptyPlist(n); - a := (stdGensS[1] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; - if a = fail then - return TemporaryFailure; - fi; - b := (stdGensS[2] ^ (t[i] * g * t[j] ^ -1)) ^ lambda; - if b = fail then - return TemporaryFailure; - fi; - # aPoints contains images of [1 .. 3] up to cyclic shifting - aCycles := Cycles(a, [1 .. n]); - if Set(aCycles, Length) <> [1, 3] then - return TemporaryFailure; - fi; - aPoints := First(aCycles, c -> Length(c) = 3); - # bPoints contains images of [3 .. n] up to cyclic shifting - bCycles := Cycles(b, [1 .. n]); - if IsEvenInt(n) and Set(bCycles, Length) <> [2, n - 2] then - return TemporaryFailure; - elif not IsEvenInt(n) and Set(bCycles, Length) <> [1, n -2] then - return TemporaryFailure; - fi; - bPoints := First(bCycles, c -> Length(c) = n - 2); - # the image of 3 is the unique intersection point of aPoints and bPoints - abPoints := Intersection(aPoints, bPoints); - if Length(abPoints) <> 1 then - return TemporaryFailure; - fi; - 3Point := abPoints[1]; - images[3] := 3Point; - 3PosInA := Position(aPoints, 3Point); - images[1] := aPoints[(3PosInA + 1 - 1) mod 3 + 1]; - images[2] := aPoints[(3PosInA + 2 - 1) mod 3 + 1]; - 3PosInB := Position(bPoints, 3Point); - for k in [1 .. n - 3] do - images[3 + k] := bPoints[(3PosInB + k - 1) mod (n - 2) + 1]; - od; - base[i] := PermList(images); - od; - return Concatenation(base, [top]); -end); - -InstallGlobalFunction(WPR_ImageAltFilter, -function(g, ri, stdGensS, t, projFunc, lambda) - return ErrorNoReturn("TODO"); -end); - -InstallGlobalFunction(WPR_SLPforElement, -function(wList, slpFuncForK, riH) - ErrorNoReturn("TODO"); -end); - InstallGlobalFunction(WPR_StandardGensSingleComponent, function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) if simpleGroupFamily = "Alt" then @@ -404,112 +332,41 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag return ErrorNoReturn("TODO"); end); -InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, -function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) - local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData, stdGensT, gens; - H := Grp(riH); - m := NrMovedPoints(H); - n := NrMovedPoints(Image(lambda)); - if ForAll(imagesG, g -> ForAll([1 .. m], i -> SignPerm(g[i]) = 1)) then - stdGens := stdGensS; - groupData := rec(family := "Alt", degree := n); - return rec(stdGens := stdGens, groupData := groupData); - fi; - if IsEvenInt(n) then - stdGensT := [(1,2,3), (1,2)*CycleFromList([3 .. n])]; - else - stdGensT := [(1,2,3), CycleFromList([3 .. n])]; - fi; - stdGensW := List(imagesG, g -> WreathProductElementList(W, g)); - stdGensSW := List([1 .. m], i -> List(stdGensT, g -> g ^ Embedding(W, i))); - stdGensH := CalcNiceGens(riH, stdGensW); - # elms with mem in W - gens := GeneratorsWithMemory(Concatenation(stdGensW, Concatenation(stdGensSW), stdGensH)); - stdGensW := gens{[1 .. Length(stdGensW)]}; - stdGensSW := List([1 .. m], i -> gens{[1 + Length(stdGensW) + Length(stdGensT) * (i - 1) .. Length(stdGensW) + Length(stdGensT) * i]}); - stdGensH := gens{[1 + Length(stdGensW) + Length(stdGensT) * m .. Length(gens)]}; - Wmem := Group(stdGensW); - b := EmptyPlist(m); - repeats := 0; - while repeats < m + Int(Ceil(Log2(Float(1/eps)))) do - repeats := repeats + 1; - wMem := PseudoRandom(Wmem); - wList := ListWreathProductElement(W, StripMemory(wMem)); - pi := wList[m + 1]; - if pi <> One(H) then - slpToPi := SLPforElement(riH, pi); - vMem := ResultOfStraightLineProgram(slpToPi, stdGensH); - wMem := vMem ^ -1 * wMem; - wList := ListWreathProductElement(W, StripMemory(wMem)); - fi; - for i in Reversed([1 .. m]) do - g := wList[i]; - if SignPerm(g) = 1 then - slpToG := slpFuncForT(g); - else - slpToG := slpFuncForT(g * (1,2)); - fi; - vMem := ResultOfStraightLineProgram(slpToG, stdGensSW[i]); - wMem := vMem ^ -1 * wMem; - if SignPerm(g) = -1 then - if IsBound(b[i]) then - wMem := b[i] ^ -1 * wMem; - else - b[i] := wMem; - break; - fi; - fi; - wList := ListWreathProductElement(W, StripMemory(wMem)); - od; - if IsBound(b[1]) then - break; - fi; - od; - if IsBound(b[1]) then - c := stdGensSW[1,2] * stdGensSW[1,1]; - if IsEvenInt(n) then - c := b[1] * c; - fi; - gens := Concatenation(ri!.gensHmem, Concatenation(List([1 .. m], i -> OnTuples(stdGensS, t[i]))), CalcNiceGens(riH, ri!.gensHmem)); - stdGens := List([b[1], c], x -> ResultOfStraightLineProgram(SLPOfElm(x), gens)); - groupData := rec(family := "Sym", degree := n); - return rec(stdGens := stdGens, groupData := groupData); - fi; - return TemporaryFailure; -end); - -InstallGlobalFunction(WPR_Verification, -function(ri, simpleGroupFamily, riS, riH, imagesG, SLPforElementFunc) - return ErrorNoReturn("TODO"); -end); - InstallGlobalFunction(WPR_StandardGensTopGroup, function(ri, stdGensBase, imagesG, slpFuncForK, riH) - local H, m, l, k, baseElm, g, gList, gensH; + local H, m, l, k, baseElm, g, gList, origGensH; H := Grp(riH); m := NrMovedPoints(H); l := Length(imagesG); - gensH := EmptyPlist(l); + origGensH := EmptyPlist(l); for k in [1 .. l] do g := ri!.gensHmem[k]; gList := imagesG[k]; baseElm := Product([1 .. m], i -> ResultOfStraightLineProgram(slpFuncForK(gList[i]), stdGensBase[i])); - gensH[k] := baseElm ^ -1 * g; + origGensH[k] := baseElm ^ -1 * g; od; - return CalcNiceGens(riH, gensH); + return CalcNiceGens(riH, origGensH); end); InstallGlobalFunction(WPR_SLPforAlmostSimple, function(groupData) if groupData.family = "Alt" then return function(x) + # slp from (1,2,3), (1,2)(3,..,n) if n even + # slp from (1,2,3), (3,..,n) if n odd. return RECOG.SLPforAn(groupData.degree, x); end; elif groupData.family = "Sym" then return function(x) + # slp from (1,2), (1,2,3,..,n). return RECOG.SLPforSn(groupData.degree, x); end; else return ErrorNoReturn("TODO"); fi; +end); + +InstallGlobalFunction(WPR_Verification, +function(TODO) + return ErrorNoReturn("TODO"); end); \ No newline at end of file diff --git a/read.g b/read.g index 072b5a8..6d67e32 100644 --- a/read.g +++ b/read.g @@ -4,3 +4,5 @@ # Reading the implementation part of the package. # ReadPackage( "WPR", "gap/WPR.gi"); + +ReadPackage( "WPR", "gap/Alt.gi"); From 9bcba52723d264dfe5b7bede8f151a8f91a31b23 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Thu, 30 Sep 2021 11:49:19 +0200 Subject: [PATCH 08/14] Add Upper Bound for m for Product Action Type. --- gap/WPR.gi | 28 +++++++++++++++++++++++----- 1 file changed, 23 insertions(+), 5 deletions(-) diff --git a/gap/WPR.gi b/gap/WPR.gi index 8604734..391c659 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -170,7 +170,7 @@ end); InstallGlobalFunction( WPR_SimpleSingleComponent, function(ri, simpleGroupFamily, L, m, eps) - local gens, P, logEps, l1, l2, delta, i, hints, hintsForT; + local gens, gensB, P, logEps, l1, l2, delta, i, hints, hintsForT; gens := ri!.gensHmem; P := WPR_SimpleSingleComponentSuccessProb(simpleGroupFamily); if P = fail then @@ -179,20 +179,25 @@ function(ri, simpleGroupFamily, L, m, eps) logEps := Log(Float(1 / eps)); l1 := Int(Ceil(logEps/Log(Float(1 / (1 - P[1]))))); # TODO: we make bound m tighter after l1 steps. Thus delta could be much smaller. + # TODO: the contant factors in l2 are too large! l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); delta := eps / (l1 + l2); # go down into base group for i in [1 .. l1] do gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); od; + # Change: Compute Normal Closure in a subgroup of the base group + # instead of the preceeding group in the chain. + # This leads to the same complexity analysis, but we have fewer generators. # TODO: better hints system - hints := WPR_SimpleSingleComponentHintsFirstPhase(simpleGroupFamily, gens, L, m); + gensB := gens; + hints := WPR_SimpleSingleComponentHintsFirstPhase(ri, simpleGroupFamily, gensB, L, m); m := hints.m; hintsForT := hints.hintsForT; l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); # go down into single component group for i in [1 .. l2] do - gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); + gens := WPR_SimpleSingleComponentBaseStep(gensB, L, delta); od; # TODO: adjust hints after getting to a single component group # hintsForT := WPR_SimpleSingleComponentHintsSecondPhase(hintsForT, simpleGroupFamily, gens, L, m); @@ -200,8 +205,21 @@ function(ri, simpleGroupFamily, L, m, eps) end); InstallGlobalFunction( WPR_SimpleSingleComponentHintsFirstPhase, -function(simpleGroupFamily, gens, L, m) - local hintsForT; +function(ri, simpleGroupFamily, gens, L, m) + local G, S, orbs, n, M, hintsForT; + G := ri!.Grp; + S := Group(gens); + if IsPrimitive(G) then + # TODO: if G is primitive use O'Nan Scott Type for bounds. + # Suppose this is in product action + orbs := OrbitsDomain(S); + n := Minimum(List(orbs, Length)); + M := Log(NrMovedPoints(G), n); + if n^M <> NrMovedPoints(G) then + Error("TODO: this cannot be a wreath product in product action"); + fi; + m := Minimum(m, M); + fi; if simpleGroupFamily = "Alt" then # TODO: compute some orders of random elms hintsForT := rec(upperDegreeBound := L); From 268eceaacc21a82932f5048042ea2ab6d8af424a Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Fri, 1 Oct 2021 13:25:18 +0200 Subject: [PATCH 09/14] Add Info Printer --- gap/Alt.gi | 9 ++++++++ gap/WPR.gi | 62 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 71 insertions(+) diff --git a/gap/Alt.gi b/gap/Alt.gi index c8d4941..d9ac4b7 100644 --- a/gap/Alt.gi +++ b/gap/Alt.gi @@ -94,17 +94,21 @@ function(g, ri, stdGensS, t, projFunc, lambda) return ErrorNoReturn("TODO"); end); +# TODO: Do we need to take care of SLP failures? InstallGlobalFunction(WPR_StandardGensSingleComponentAlt, function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W) local Wmem, stdGensW, H, m, n, stdGensH, stdGensSW1, stdGensSW, wMem, wList, vMem, vList, pi, b, c, g, i, slpToPi, slpToG, repeats, stdGens, groupData, stdGensT, gens; H := Grp(riH); m := NrMovedPoints(H); n := NrMovedPoints(Image(lambda)); + Info(WPR_Info, 2, "base component K has socle Alt(", n, ")"); if ForAll(imagesG, g -> ForAll([1 .. m], i -> SignPerm(g[i]) = 1)) then + Info(WPR_Info, 2, "\tK = Alt(", n, ")"); stdGens := stdGensS; groupData := rec(family := "Alt", degree := n); return rec(stdGens := stdGens, groupData := groupData); fi; + Info(WPR_Info, 2, "K = Sym(", n, ")"); if IsEvenInt(n) then stdGensT := [(1,2,3), (1,2)*CycleFromList([3 .. n])]; else @@ -121,8 +125,10 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag Wmem := Group(stdGensW); b := EmptyPlist(m); repeats := 0; + Info(WPR_Info, 3, "Start Iteration:"); while repeats < m + Int(Ceil(Log2(Float(1/eps)))) do repeats := repeats + 1; + Info(WPR_Info, 3, "\tStep ", repeats); wMem := PseudoRandom(Wmem); wList := ListWreathProductElement(W, StripMemory(wMem)); pi := wList[m + 1]; @@ -146,6 +152,7 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag wMem := b[i] ^ -1 * wMem; else b[i] := wMem; + Info(WPR_Info, 3, "\tSet b_i for i = ", i); break; fi; fi; @@ -155,6 +162,7 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag break; fi; od; + Info(WPR_Info, 3, "Finished Iteration"); if IsBound(b[1]) then c := stdGensSW[1,2] * stdGensSW[1,1]; if IsEvenInt(n) then @@ -165,5 +173,6 @@ function(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imag groupData := rec(family := "Sym", degree := n); return rec(stdGens := stdGens, groupData := groupData); fi; + Info(WPR_Info, 2, "Couldn't find standard generators!"); return TemporaryFailure; end); \ No newline at end of file diff --git a/gap/WPR.gi b/gap/WPR.gi index 391c659..dc7f4c4 100644 --- a/gap/WPR.gi +++ b/gap/WPR.gi @@ -4,6 +4,11 @@ # Implementations # +# Level 1: Show Current Step in Main Recognition Method +# Level 2: Show Important Bounds in Submethods +# Level 3: Show Progress of Iterations +BindGlobal("WPR_Info", NewInfoClass("WPR_Info")); + InstallGlobalFunction( WreathProductRecognition, function(ri, G, simpleGroupFamily...) local N, L, m, eps, simpleCompData, origGensS, hintsForT, @@ -18,6 +23,8 @@ function(ri, G, simpleGroupFamily...) #### ------------------------ #### #################################### + Info(WPR_Info, 1, "Step 0: Initialize bounds for wreath product recognition"); + Info(WPR_Info, 2, "--------------------------------------------------------"); if Length(simpleGroupFamily) = 0 then # TODO: try to deduce simple group family or set this to unknown. simpleGroupFamily := "Alt"; @@ -36,6 +43,7 @@ function(ri, G, simpleGroupFamily...) ErrorNoReturn("TODO: Implement matrix and projective representation"); fi; eps := 1/100; + Info(WPR_Info, 2, "eps = ", eps); # TODO: maybe call subprocedures with smaller error bound? ################################## @@ -48,6 +56,9 @@ function(ri, G, simpleGroupFamily...) # Step 1 : Compute a single-component group S isomorphic to T # # ------------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 1 : ", "Compute a single-component group S isomorphic to T"); + Info(WPR_Info, 2, "---------------------------------------------------------------"); # TODO: if G is primitive, we could compute a single component group as a socle factor directly. simpleCompData := WPR_SimpleSingleComponent(ri, simpleGroupFamily, L, m, eps); # elms with memory in G @@ -61,6 +72,9 @@ function(ri, G, simpleGroupFamily...) # Step 2 : Compute standard generators in S isomorphic to T # # ----------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 2 : ", "Compute standard generators in S isomorphic to T"); + Info(WPR_Info, 2, "-------------------------------------------------------------"); # TODO: give hints to recog node (G is almost simple, etc.) and abort if assumptions do not hold. # TODO: we need an isomorphism from S to T or maybe an embedding from S to the standard copy of Aut(T) > T. # TODO: we need very special nice generators. @@ -71,6 +85,7 @@ function(ri, G, simpleGroupFamily...) # elms with memory in G stdGensS := recogData.stdGensS; lambda := recogData.lambda; + Info(WPR_Info, 2, "T = ", simpleGroupFamily); ####################################### #### --------------------------- #### @@ -82,15 +97,22 @@ function(ri, G, simpleGroupFamily...) # Step 3 : Compute a faithful H-set { S ^ {t_1}, ..., S ^ {t_m} } # # ----------------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 3 : ", "Compute a faithful H-set { S ^ {t_1}, ..., S ^ {t_m} }"); + Info(WPR_Info, 2, "-------------------------------------------------------------------"); domainData := WPR_TopGroupDomain(ri, stdGensS); t := domainData.t; domain := domainData.domain; + Info(WPR_Info, 2, "m = ", Length(t)); m := Length(domain); # ------------------------------------------------ # # Step 4 : Compute projection onto top component # # ------------------------------------------------ # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 4 : ", "Compute projection onto top component"); + Info(WPR_Info, 2, "--------------------------------------------------"); projFunc := function(g) return WPR_TopComponentImage(StripMemory(g), ri, StripMemory(domain)); end; @@ -105,9 +127,16 @@ function(ri, G, simpleGroupFamily...) # Step 5 : theoretically define single-component group Shat > S isomorphic to K # # ------------------------------------------------------------------------------ # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 5 : ", "theoretically define single-component group Shat > S isomorphic to K"); + Info(WPR_Info, 2, "---------------------------------------------------------------------------------"); + # --------------------------------------------------------------- # # Step 6 : theoretically define isomorphism phi from G to K wr H # # --------------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 6 : ", "theoretically define isomorphism phi from G to K wr H"); + Info(WPR_Info, 2, "------------------------------------------------------------------"); ############################# #### ----------------- #### @@ -119,6 +148,9 @@ function(ri, G, simpleGroupFamily...) # Step 7 : Compute images of all generators of G under isomorphism phi # # ---------------------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 7 : ", "Compute images of all generators of G under isomorphism phi"); + Info(WPR_Info, 2, "------------------------------------------------------------------------"); W := WreathProduct(AutT, SymmetricGroup(m)); phiImageFunc := function(g) return WPR_Image(StripMemory(g), ri, simpleGroupFamily, StripMemory(stdGensS), StripMemory(t), projFunc, lambda); @@ -135,6 +167,9 @@ function(ri, G, simpleGroupFamily...) # Step 8 : Recognise top group H # # -------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 8 : ", "Recognise top group H"); + Info(WPR_Info, 2, "----------------------------------"); # TODO: take care of trivial generators H := Group(List(ri!.gensHmem, g -> projFunc(g))); # TODO: give hints to recog node (H is transitive, etc.) and abort if assumptions do not hold. @@ -144,6 +179,9 @@ function(ri, G, simpleGroupFamily...) # Step 9 : Compute standard generators of base component # # -------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 9 : ", "Compute standard generators of base component"); + Info(WPR_Info, 2, "----------------------------------------------------------"); stdGensData := WPR_StandardGensSingleComponent(ri, eps, simpleGroupFamily, lambda, stdGensS, slpFuncForT, t, riH, imagesG, W); stdGensBaseComponent := stdGensData.stdGens; groupDataBaseComponent := stdGensData.groupData; @@ -154,6 +192,9 @@ function(ri, G, simpleGroupFamily...) # Step 10 : Compute standard generators of top component # # ------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 10 : ", "Compute standard generators of top component"); + Info(WPR_Info, 2, "----------------------------------------------------------"); stdGensTop := WPR_StandardGensTopGroup(ri, stdGensBase, imagesG, slpFuncForK, riH); ############################# @@ -176,16 +217,26 @@ function(ri, simpleGroupFamily, L, m, eps) if P = fail then return NeverApplicable; fi; + Info(WPR_Info, 2, "Success Probabilities for a step in each phase:"); + Info(WPR_Info, 2, "\tP_1 = ", P[1]); + Info(WPR_Info, 2, "\tP_2 = ", P[2]); logEps := Log(Float(1 / eps)); l1 := Int(Ceil(logEps/Log(Float(1 / (1 - P[1]))))); # TODO: we make bound m tighter after l1 steps. Thus delta could be much smaller. # TODO: the contant factors in l2 are too large! l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); delta := eps / (l1 + l2); + Info(WPR_Info, 2, "Bounds for first phase:"); + Info(WPR_Info, 2, "\tm = ", m); + Info(WPR_Info, 2, "\tl_1 = ", l1); + Info(WPR_Info, 2, "\tdelta = ", delta); # go down into base group + Info(WPR_Info, 3, "Start Iteration for Phase 1:"); for i in [1 .. l1] do + Info(WPR_Info, 3, "\tStep ", i); gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); od; + Info(WPR_Info, 3, "Finished Iteration"); # Change: Compute Normal Closure in a subgroup of the base group # instead of the preceeding group in the chain. # This leads to the same complexity analysis, but we have fewer generators. @@ -195,10 +246,17 @@ function(ri, simpleGroupFamily, L, m, eps) m := hints.m; hintsForT := hints.hintsForT; l2 := Int(Ceil(Maximum(Float(2 / P[2] * m), logEps * 8 / P[2]))); + Info(WPR_Info, 2, "Bounds for second phase:"); + Info(WPR_Info, 2, "\tm = ", m); + Info(WPR_Info, 2, "\tl_2 = ", l2); + Info(WPR_Info, 2, "\tdelta = ", delta); # go down into single component group + Info(WPR_Info, 3, "Start Iteration for Phase 2:"); for i in [1 .. l2] do + Info(WPR_Info, 3, "\tStep ", i); gens := WPR_SimpleSingleComponentBaseStep(gensB, L, delta); od; + Info(WPR_Info, 3, "Finished Iteration"); # TODO: adjust hints after getting to a single component group # hintsForT := WPR_SimpleSingleComponentHintsSecondPhase(hintsForT, simpleGroupFamily, gens, L, m); return rec(origGensS := gens, hintsForT := hintsForT); @@ -357,12 +415,16 @@ function(ri, stdGensBase, imagesG, slpFuncForK, riH) m := NrMovedPoints(H); l := Length(imagesG); origGensH := EmptyPlist(l); + Info(WPR_Info, 3, "Start Iteration:"); for k in [1 .. l] do + Info(WPR_Info, 3, "\tStep ", k); g := ri!.gensHmem[k]; gList := imagesG[k]; + # TODO: do we need to take care of failures? baseElm := Product([1 .. m], i -> ResultOfStraightLineProgram(slpFuncForK(gList[i]), stdGensBase[i])); origGensH[k] := baseElm ^ -1 * g; od; + Info(WPR_Info, 3, "Finished Iteration"); return CalcNiceGens(riH, origGensH); end); From 0eaa60b60618a906fd529d2546d27ad1e8b0a2aa Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Wed, 6 Oct 2021 11:39:52 +0200 Subject: [PATCH 10/14] Change LongTitle --- PackageInfo.g | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/PackageInfo.g b/PackageInfo.g index 9fa34dc..d8d83b3 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -60,7 +60,7 @@ PackageDoc := rec( HTMLStart := "doc/chap0.html", PDFFile := "doc/manual.pdf", SixFile := "doc/manual.six", - LongTitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component", + LongTitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with an almost simple base component", ), Dependencies := rec( From dbb6262a4441dcdf3934b44bb9c39d6fd4f7db20 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Sat, 12 Apr 2025 17:16:42 +0200 Subject: [PATCH 11/14] Stash rework on algorithm --- 2*m*k^2 | 0 LICENSE | 4 +- PackageInfo.g | 10 +- README.md | 6 +- _dev/aut.g | 142 + examples/MatImprimitive.gi | 61 + examples/MatImprimitive.mag | 27 + examples/PermImprimitive.gi | 30 + examples/PermPrimitive.gi | 35 + examples/difficultMat.mag | 13728 ++++++++++++++++++++++++++++++++++ examples/difficultMatG.mag | 13623 +++++++++++++++++++++++++++++++++ gap/Alt.gi | 2 +- gap/Experiment.gi | 353 + gap/Random.gi | 44 + gap/Recog.gi | 72 + gap/RecogSubroutines.gi | 103 + gap/SingleComponentGroup.gi | 200 + gap/TopGroupAction.gi | 239 + gap/WPR.gd | 35 - gap/WPrecog.gd | 30 + gap/{WPR.gi => WPrecog.gi} | 2 +- init.g | 4 +- makedoc.g | 2 +- read.g | 15 +- tst/files/Alt.tst | 42 + tst/testall.g | 6 +- 26 files changed, 28759 insertions(+), 56 deletions(-) create mode 100644 2*m*k^2 create mode 100644 _dev/aut.g create mode 100644 examples/MatImprimitive.gi create mode 100644 examples/MatImprimitive.mag create mode 100644 examples/PermImprimitive.gi create mode 100644 examples/PermPrimitive.gi create mode 100644 examples/difficultMat.mag create mode 100644 examples/difficultMatG.mag create mode 100644 gap/Experiment.gi create mode 100644 gap/Random.gi create mode 100644 gap/Recog.gi create mode 100644 gap/RecogSubroutines.gi create mode 100644 gap/SingleComponentGroup.gi create mode 100644 gap/TopGroupAction.gi delete mode 100644 gap/WPR.gd create mode 100644 gap/WPrecog.gd rename gap/{WPR.gi => WPrecog.gi} (99%) create mode 100644 tst/files/Alt.tst diff --git a/2*m*k^2 b/2*m*k^2 new file mode 100644 index 0000000..e69de29 diff --git a/LICENSE b/LICENSE index d196bd3..de984af 100644 --- a/LICENSE +++ b/LICENSE @@ -1,9 +1,9 @@ -WPR is free software; you can redistribute and/or modify +WPrecog is free software; you can redistribute and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your opinion) any later version. -WPR is distributed in the hope that it will be useful, +WPrecog is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. diff --git a/PackageInfo.g b/PackageInfo.g index d8d83b3..6d00b31 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -1,5 +1,5 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # This file contains package meta data. For additional information on # the meaning and correct usage of these fields, please consult the @@ -8,7 +8,7 @@ # SetPackageInfo( rec( -PackageName := "WPR", +PackageName := "WPrecog", Subtitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component", Version := "0.1", Date := "09/06/2021", # dd/mm/yyyy format @@ -30,10 +30,10 @@ Persons := [ SourceRepository := rec( Type := "git", - URL := "https://github.com/FriedrichRober/WPR", + URL := "https://github.com/FriedrichRober/WPrecog", ), IssueTrackerURL := Concatenation( ~.SourceRepository.URL, "/issues" ), -PackageWWWHome := "https://FriedrichRober.github.io/WPR/", +PackageWWWHome := "https://FriedrichRober.github.io/WPrecog/", PackageInfoURL := Concatenation( ~.PackageWWWHome, "PackageInfo.g" ), README_URL := Concatenation( ~.PackageWWWHome, "README.md" ), ArchiveURL := Concatenation( ~.SourceRepository.URL, @@ -55,7 +55,7 @@ Status := "dev", AbstractHTML := "", PackageDoc := rec( - BookName := "WPR", + BookName := "WPrecog", ArchiveURLSubset := ["doc"], HTMLStart := "doc/chap0.html", PDFFile := "doc/manual.pdf", diff --git a/README.md b/README.md index 9932f36..f2aed7e 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,7 @@ -[![CI](https://github.com/FriedrichRober/WPR/workflows/CI/badge.svg)](https://github.com/FriedrichRober/WPR/actions?query=workflow%3ACI+branch%3Amaster) -[![Code Coverage](https://codecov.io/gh/FriedrichRober/WPR/coverage.svg?branch=master&token=)](https://codecov.io/gh/FriedrichRober/WPR) +[![CI](https://github.com/FriedrichRober/WPrecog/workflows/CI/badge.svg)](https://github.com/FriedrichRober/WPrecog/actions?query=workflow%3ACI+branch%3Amaster) +[![Code Coverage](https://codecov.io/gh/FriedrichRober/WPrecog/coverage.svg?branch=master&token=)](https://codecov.io/gh/FriedrichRober/WPrecog) -# The GAP package WPR +# The GAP package WPrecog TODO: add a description of your package; perhaps also instructions how how to install and use it, resp. where to find out more diff --git a/_dev/aut.g b/_dev/aut.g new file mode 100644 index 0000000..7955835 --- /dev/null +++ b/_dev/aut.g @@ -0,0 +1,142 @@ + +################################ +## ## +## SL(n, q) ## +## ## +################################ + +# parameters of classical group +n := 4; +p := 3; +e := 2; +q := p ^ e; + +# classical groups +P := GL(n,q); # parent +M := SL(n,q); # matrix group in parent + +# simple group, factoring scalar matrices out +ZP := Centre(P); +ZM := Centre(M); +quo := NaturalHomomorphismByNormalSubgroup(P, ZP); +T := Image(quo, M); + +# automorphism group +# A = = I ><| ( x F) +# I = T and F = C_e +# D = C_d, d = (n, q - 1) +# if n > 2 => G = C_2 and = D_{2 d} +# if n = 2 => G = C_1 and = C_{d} +A := AutomorphismGroup(T); +nice := NiceMonomorphism(A); + +# inner automorphisms +Print("-------------------------------------------", "\n"); +Print(" I : Inner Automorphisms", "\n"); +Print("|I| = ", Order(T), "\n"); +emb_I := GroupHomomorphismByFunction(T, A, x -> ConjugatorAutomorphism(T, x));; +I := Image(emb_I); # = T + +# diagonal automorphism +Print("-------------------------------------------", "\n"); +Print(" D : Diagonal Automorphisms", "\n"); +d := Gcd(n, q - 1); +Print("|D| = ", d, "\n"); +psi := NaturalHomomorphismByNormalSubgroup(Image(quo), T); +x := First(GeneratorsOfGroup(Image(psi)), x -> Order(x) = d); +y := PreImagesRepresentative(psi, x); +diag := y ^ (Order(y) / d); +diag_aut := ConjugatorAutomorphism(T, diag); +D := Group(diag_aut); # = C_d = F_q^* / F_q^{*n} = PGL(n, q) / PSL(n, q) +# C := Group(Z(q)); +# lambda := GroupHomomorphismByFunction(C, C, c -> c ^ n); +# Cn := Image(lambda); +# rho := NaturalHomomorphismByNormalSubgroup(C, Cn); + +# graph automorphisms +Print("-------------------------------------------", "\n"); +Print(" G : Graph Automorphisms", "\n"); +# trivial +if n = 2 then + Print("|G| = ", 1, "\n"); + G := Group(One(A)); # = C_1 +# duality automorphism +else + Print("|G| = ", 2, "\n"); + duality_aut := GroupHomomorphismByFunction(T, T, x -> (TransposedMat(PreImagesRepresentative(quo, x) ^ -1)) ^ quo); + G := Group(duality_aut); # = C_2 +fi; + +# field automorphisms +Print("-------------------------------------------", "\n"); +Print(" F : Field Automorphisms", "\n"); +Print("|F| = ", e, "\n"); +frobenius := FrobeniusAutomorphism(GF(q)); +frobenius_aut := GroupHomomorphismByFunction(T, T, x -> (PreImagesRepresentative(quo, x) ^ frobenius) ^ quo); +F := Group(frobenius_aut); # = C_e + +# random element generator in A +sample_size := 100; +data := rec( + emb_I := emb_I, + frobenius_aut := frobenius_aut, + diag_aut := diag_aut, + G := G, +);; +opts := rec( + +);; +RandomA := function(data, opts) + local emb_I, frobenius_aut, diag_aut, G, T, + elm_I, elm_F, elm_D, elm_G, exp_F, exp_D, exp_G, gen_G; + emb_I := data.emb_I; + frobenius_aut := data.frobenius_aut; + diag_aut := data.diag_aut; + G := data.G; + # I + T := Source(emb_I); + elm_I := PseudoRandom(T) ^ emb_I; + # F + if IsBound(opts.exp_F) then + exp_F := opts.exp_F; + else + exp_F := PseudoRandom([0 .. e - 1]); + fi; + elm_F := frobenius_aut ^ exp_F; + # D + if IsBound(opts.exp_D) then + exp_D := opts.exp_D; + else + exp_D := PseudoRandom([0 .. d - 1]); + fi; + elm_D := diag_aut ^ exp_D; + # G + gen_G := GeneratorsOfGroup(G)[1]; + if IsBound(opts.exp_G) then + exp_G := opts.exp_G; + elif n = 2 then + exp_G := 0; + else + exp_G := PseudoRandom([0, 1]); + fi; + elm_G := gen_G ^ exp_G; + + return rec( + elm := elm_I * elm_F * elm_D * elm_G, + elm_I := elm_I, + exp_F := exp_F, + elm_F := elm_F, + exp_D := exp_D, + elm_D := elm_D, + exp_G := exp_G, + elm_G := elm_G, + ); +end;; + +sample := EmptyPlist(sample_size); +for i in [1 .. sample_size] do + r := RandomA(data, opts); + r.order := Order(r.elm); + Add(sample, r); + Print(r.order, ", "); +od; \ No newline at end of file diff --git a/examples/MatImprimitive.gi b/examples/MatImprimitive.gi new file mode 100644 index 0000000..cc9cbd0 --- /dev/null +++ b/examples/MatImprimitive.gi @@ -0,0 +1,61 @@ +Read("gap/Experiment.gi"); + +EmbedGenerator := function(mat, m, q) + local n, big, i, j; + n := Length(mat); + big := IdentityMat(m, GF(q)); + for i in [1..n] do + for j in [1..n] do + big[i][j] := mat[i][j]; + od; + od; + return big; +end; + +# Matrix Groups : Imprimitive +d := 9; +q := 5; +K := GL(d,q); +m := 12; +H := SymmetricGroup(m); +# H := Random(AllTransitiveGroups(NrMovedPoints, m)); +W := WreathProduct(K, H); +# isoWreath := IsomorphismWreathProduct(W); +D := d*m + 2; +P := GL(D, q); +W2 := Group(List(GeneratorsOfGroup(W), g -> EmbedGenerator(g, D, q))); +c := PseudoRandom(P); +G := W2^(c^(-1)); +# conj := GroupHomomorphismByFunction(G, W, g -> g^c); +# iso := conj * isoWreath;; + +BlocksMat := function(G) + S := BlindDescend(G); + # IsSingleComponent(S, iso); + + # S acts on W + U + # W invariant space, dim(W) = d + # U fixed space, dim(U) = (m-1)*d + M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); + v1 := RandomVector(D,q); + v2 := RandomVector(D,q); + # basis of W + < [v]\rho_U > + L1 := MTX.SubmoduleGModule(M, v1);; + L2 := MTX.SubmoduleGModule(M, v2);; + # Length(L1) = d + 1; + # Length(L2) = d + 1; + W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); + # Dimension(W) = d; + tmp := TopGroupDomainVectorSpace(G, W); + return tmp; +end; + +tmp := BlocksMat(G); time; +domain := tmp.domain; +transversal := tmp.transversal; +B := Concatenation(List(domain, Basis)); +# B1 := Concatenation(List(domain, Basis)); +# B2 := SemiEchelonBasis(VectorSpace(GF(q), B1)); +# B3 := Subspace(GF(q)^D, List(Basis(GF(q)^D), v->SiftedVector(B2,v))); +# B := Concatenation(B1, Basis(B3)); +Display(G.3^(B^(-1))); \ No newline at end of file diff --git a/examples/MatImprimitive.mag b/examples/MatImprimitive.mag new file mode 100644 index 0000000..f12a13a --- /dev/null +++ b/examples/MatImprimitive.mag @@ -0,0 +1,27 @@ + +EmbedGenerator := function(g, m) + // Embed g ∈ GL(n, F) into GL(m, F) as top-left block + n := Nrows(g); + I := IdentityMatrix(BaseRing(g), m); + for i in [1..n] do + for j in [1..n] do + I[i][j] := g[i][j]; + end for; + end for; + return I; +end function; + +d := 4; +q := 7; +K := GL(d, q); +m := 5; +H := SymmetricGroup(m); +W := WreathProduct(K, H); +D := d*m + 2; +P := GL(D, q); +W2 := MatrixGroup; +c := Random(GL(D, q)); +G := MatrixGroup^(c^(-1)); + +time IsPrimitive(G); +time Blocks(G); \ No newline at end of file diff --git a/examples/PermImprimitive.gi b/examples/PermImprimitive.gi new file mode 100644 index 0000000..9d724de --- /dev/null +++ b/examples/PermImprimitive.gi @@ -0,0 +1,30 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Permutation Group : Imprimitive +n := 9; +m := 12; +K := AlternatingGroup(n); +H := SymmetricGroup(m); + +# Construct wreath product +PP := SymmetricGroup(n*m); +P := WreathProduct(SymmetricGroup(n), SymmetricGroup(m)); +W := Group(Concatenation( + List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), + List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) +)); + +# Random conjugation +c := PseudoRandom(PP); +G := W^(c^(-1)); + +# # Nice isomorphism +# isoWreath := IsomorphismWreathProduct(W);; +# isoConj := GroupHomomorphismByFunction(G, W, g -> g^c); +# isoNice := isoConj * isoWreath;; + +# Recognition +data := RecogniseWreathProduct(RecogNode(G), rec( + simpleBaseComp := false, +)); diff --git a/examples/PermPrimitive.gi b/examples/PermPrimitive.gi new file mode 100644 index 0000000..b7416b2 --- /dev/null +++ b/examples/PermPrimitive.gi @@ -0,0 +1,35 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Permutation Group : Product Action +m := 5; +l := 15; +k := 1; +n := k * l; +l > 2*m*k^2; # Is Large Base? +K := Action(AlternatingGroup(n), Combinations([1..n],k), OnSets); +H := Random(AllTransitiveGroups(NrMovedPoints, m)); + +# Construct wreath product +PP := SymmetricGroup(n^m); +P := WreathProductProductAction(SymmetricGroup(n), SymmetricGroup(m)); +W := Group(Concatenation( + List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), + List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) +)); + +# Random conjugation +c := PseudoRandom(PP); +G := W^(c^(-1)); + +# # Nice isomorphism +# isoWreath := IsomorphismWreathProduct(W);; +# isoConj := GroupHomomorphismByFunction(G, W, g -> g^c); +# isoNice := isoConj * isoWreath;; + +# Recognition +data := RecogniseWreathProduct(RecogNode(G), rec( + action := "product action", +)); + +RecogniseGroup(G); \ No newline at end of file diff --git a/examples/difficultMat.mag b/examples/difficultMat.mag new file mode 100644 index 0000000..253880d --- /dev/null +++ b/examples/difficultMat.mag @@ -0,0 +1,13728 @@ +K := MatrixGroup<51, GF(3) | + Matrix(GF(3), 51, 51, \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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2, 1, 0, 2, 2, 1, 2, 2, 0, 0, 1, + 0, 2, 0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1, 2, 0, 2, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 1, 2, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, + 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 1, 0, 2, 2, 0, 1, 0, 2, 2, 1, 1, 0, 0, 2, 0, 2, 0, 0, + 0, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 0, 2, 1, 2, 1, 2, 2, 1, 1, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 2, + 1, 1, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 1, 1, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 2, 2, 1, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, + 1, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 0, 1, 2, + 2, 0, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 2, 0, 1, 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0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, + 1, 0, 2, 0, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 0, 2, 0, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 2, + 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 1, 2, 0, 2, 0, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, + 1, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 2, 0, 0, 0 ]) >; +H :=PermutationGroup<12 | + \[ 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3 ], + \[ 10, 5, 3, 4, 2, 9, 7, 8, 6, 1, 11, 12 ], + \[ 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4 ], + \[ 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12 ] >; +d := 51; +q := 3; +m := 12; +G := MatrixGroup<612, GF(3) | + Matrix(GF(3), 612, 612, \[ 0, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 1, + 2, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, + 0, 0, 0, 2, 0, 2, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, + 1, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 1, 0, + 0, 2, 2, 1, 1, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, + 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, + 2, 2, 1, 0, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 2, 1, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 1, 1, 2, 0, 0, + 2, 2, 2, 0, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 2, 2, 1, 1, 1, 1, + 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 1, 0, 0, 2, 1, 1, 2, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, + 0, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 0, 0, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 2, + 1, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0, 2, 1, 2, 2, 1, 1, 2, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 0, 2, 2, 0, + 1, 2, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2, 0, 2, 1, 2, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, + 1, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 2, 2, 2, 1, 0, 1, 1, 0, 2, 1, 2, + 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, + 1, 2, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 0, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 2, + 1, 0, 0, 1, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2, 1, + 0, 2, 1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 1, 2, 2, 0, 1, 0, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 1, + 1, 2, 2, 1, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, + 1, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 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0, 2, 0, 0, + 1, 1, 2, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 1, 0, 2, 0, + 2, 0, 1, 0, 2, 2, 1, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 2, 1, 1, 0, 1, 1, 2, 0, + 2, 2, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 1, 0, + 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 1, 1, 0, 2, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 1, + 0, 0, 1 ]) >; diff --git a/examples/difficultMatG.mag b/examples/difficultMatG.mag new file mode 100644 index 0000000..4b273a7 --- /dev/null +++ b/examples/difficultMatG.mag @@ -0,0 +1,13623 @@ +G := MatrixGroup<612, GF(3) | + Matrix(GF(3), 612, 612, \[ 0, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 1, + 2, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, + 0, 0, 0, 2, 0, 2, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, + 1, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 1, 0, + 0, 2, 2, 1, 1, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, + 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, + 2, 2, 1, 0, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 2, 1, 0, 2, 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2, + 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 1, 0, + 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 1, 0, 2, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 2, 2, 1, 0, 2, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 2, + 2, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, + 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2, 1, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 1, + 0, 2, 0, 2, 1, 0, 0, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 2, 0, 2, 1, 2, + 2, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 1, 2, 1, 1, + 0, 1, 1, 0, 2, 2, 2, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 1, 1, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 0, + 2, 1, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 2, + 0, 2, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 1, 2, 0, 2, 2, 0, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 0, 2, 1, 0, 0, + 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 1, 2, 2, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 1, 2, + 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 1, 1, 0, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, + 0, 1, 1, 1, 2, 2, 0, 0, 1, 1, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2, 1, 0, 0, 2, 1, 2, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, + 0, 1, 0, 0, 1, 2, 0, 2, 1, 1, 2, 1, 2, 1, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 1, + 0, 2, 0, 0, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 0, 2, 2, 2, 0, 0, + 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 2, 1, 0, 2, 0, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 1, 0, 1, 0, 2, 2, 0, + 1, 0, 2, 1, 1, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 1, 2, 0, 0, 1, 1, 2, 0, 2, 1, 0, 0, 2, 0, 2, 1, 0, 1, 0, + 2, 1, 1, 0, 2, 0, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 0, 2, 1, 1, 2, 1, 2, 2, + 0, 2, 2, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 0, 0, 0, 1, 1, 2, 1, 0, 2, 0, 0, 1, 2, 2, 1, 2, 1, 0, 2, 1, 2, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 2, 2, 2, 1, 1, 0, 0, 1, 1, + 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 0, 2, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 1, 2, 1, 2, 0, 2, 1, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, + 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 2, 2, 0, 1, 0, 1, 1, 1, 2, 2, 0, 0, 2, 1, 2, 1, 2, 2, 2, 0, 0, 2, 2, 2, 1, 1, 2, 1, 0, 2, 1, 0, 1, 2, 1, 2, 0, + 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 1, 2, 2, 1, 2, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, + 0, 1, 1, 0, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 1, 2, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 0, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 0, 1, 0, 2, 1, + 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 2, 0, 2, 2, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 2, + 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 0, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 1, + 2, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, + 1, 2, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 2, 2, 1, 1, 2, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 2, 1, 0, 1, 1, + 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 0, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 2, 1, 1, 2, 1, + 0, 0, 2, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 1, 1, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, + 0, 0, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 1, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 1, 0, 0, 2, 2, 1, 1, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 2, 1, 2, 2, 1, 1, 1, 0, 1, 1, 0, 0, + 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2, 1, 2, 2, 2, 1, 1, 2, 0, 1, 1, 1, 0, 1, 1, + 1, 0, 1, 1, 0, 2, 0, 1, 2, 1, 0, 1, 1, 2, 0, 2, 2, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 1, 1, 0, 2, 0, 0, 0, 2, + 0, 1, 2, 2, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 2, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 0, + 1, 2, 1, 2, 2, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 1, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, + 2, 1, 0, 2, 0, 0, 2, 2, 0, 1, 1, 2, 0, 1, 2, 2, 1, 0, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 1, 2, 2, 2, 1, 0, 0, 2, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 1, 0, 0, + 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, + 2, 1, 2, 1, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 2, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 1, 1, 2, 1, 0, 2, 0, 2, 0, 2, + 1, 2, 1, 1, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 1, 1, 2, 1, 1, 0, 2, 2, 0, 2, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0, 2, 2, 2, 1, 1, + 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 2, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 0, + 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 2, 2, 1, 2, 1, 0, 0, 2, 1, 0, 0, 2, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 2, 2, 2, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, + 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0, 2, 1, + 0, 0, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 0, 1, 2, 0, 1, 2, 2, 1, 2, 1, 2, 1, 1, 0, 2, 2, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 1, 0, + 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 1, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 0, 2, 0, 0, 2, 2, 1, 2, 1, 0, 0, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 1, 0, 1, 0, 1, 1, + 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, + 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 1, 2, 2, 2, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, + 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 2, 2, 0, 1, 1, 2, 2, 2, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 1, 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 2, 0, + 2, 1, 1, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 0, 2, 2, 0, 1, 1, 2, 1, 0, 0, 2, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 2, 2, 0, + 0, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 0, 2, 1, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, + 1, 1, 2, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 1, 0, 2, 0, + 2, 0, 1, 0, 2, 2, 1, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 2, 1, 1, 0, 1, 1, 2, 0, + 2, 2, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 1, 0, + 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 1, 1, 0, 2, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 1, + 0, 0, 1 ]) >; \ No newline at end of file diff --git a/gap/Alt.gi b/gap/Alt.gi index d9ac4b7..bb44d36 100644 --- a/gap/Alt.gi +++ b/gap/Alt.gi @@ -3,7 +3,7 @@ function(origGensS, simpleGroupFamily, hintsForT, eps) local S, riS, recogData, isoData, degree, T, AutT, slpFuncForT, swapSLP, slpToStdGensS, stdGensS, lambdaImageFunc, lambdaPreImageFunc, lambda; S := Group(StripMemory(origGensS)); - riS := EmptyRecognitionInfoRecord(rec(), S, false); + riS := RecogNode(S); recogData := RECOG.RecogniseSnAn(riS, eps, hintsForT.upperDegreeBound); if not IsRecord(recogData) then return TemporaryFailure; diff --git a/gap/Experiment.gi b/gap/Experiment.gi new file mode 100644 index 0000000..3e1dec2 --- /dev/null +++ b/gap/Experiment.gi @@ -0,0 +1,353 @@ +LoadPackage("recog", false); +LoadPackage("WPE", false); + +DeclareGlobalFunction("BlindDescend"); +DeclareGlobalFunction("QuickRandomList"); +DeclareGlobalFunction("QuickRandom"); +DeclareGlobalFunction("BlindDescend_Step"); + +InstallGlobalFunction("QuickRandomList", function(n) + local lst, i, j, tmp; + lst := [1..n]; + for i in [n, n-1..2] do + j := Random([1..i]); + tmp := lst[i]; + lst[i] := lst[j]; + lst[j] := tmp; + od; + return lst; +end); + +InstallGlobalFunction("QuickRandom", function(gens) + local n, A, B; + n := Length(gens); + A := List([1 .. n], i -> Random([-1,0,1])); + B := QuickRandomList(n); + return Product([1 .. n], i -> gens[B[i]]^A[i]); +end); + +InstallGlobalFunction("BlindDescend_Step", function(gens, P, n) + local y, ord, z; + y := QuickRandom(gens); + ord := Order(y); + if IsEvenInt(ord) then + z := y ^ (ord / 2); + return FastNormalClosure(P, [z], n); + else + return gens; + fi; +end); + +InstallGlobalFunction("BlindDescend", function(args...) + local G, l1, l2, n, n2, S, gens, i, B; + + if Length(args) < 1 then + Error("Argument G is required."); + fi; + + G := args[1]; + + if Length(args) >= 2 then + l1 := args[2]; + else + l1 := 5; + fi; + + if Length(args) >= 3 then + l2 := args[3]; + else + l2 := 35; + fi; + + if Length(args) >= 4 then + n1 := args[4]; + else + n1 := 5; # roughly 30 generators + fi; + + if Length(args) >= 5 then + n2 := args[5]; + else + n2 := 2; + fi; + + S := G; + gens := List(GeneratorsOfGroup(S)); + for i in [1 .. l1] do + gens := BlindDescend_Step(gens, S, n1); + S := Group(gens); + od; + B := S; # inside base group + for i in [1 .. l2] do + gens := BlindDescend_Step(gens, S, n1); + S := Group(gens); + od; + # As a pre-caution, take normal closure in base group, if we descended too far + S := Group(FastNormalClosure(B, gens, n2)); + return S; +end); + +BindGlobal("IsSingleComponent", function(G, iso) + local T, g, t; + T := fail; + for g in GeneratorsOfGroup(G) do + t := Territory(g^iso); + if Length(t) > 1 then + return false; + fi; + if T = fail then + T := t; + elif T <> t then + return false; + fi; + od; + return true; +end); + +# TODO, make faster for matrix group, by checking component-wise +DeclareGlobalFunction("DoCommuteElms"); +InstallGlobalFunction(DoCommuteElms, function(x, y) + return x * y = y * x; +end); + +DeclareGlobalFunction("DoCommuteGroups"); +InstallGlobalFunction(DoCommuteGroups, function(A, B) + local a, b; + for a in GeneratorsOfGroup(A) do + for b in GeneratorsOfGroup(B) do + if not DoCommuteElms(a, b) then + return false; + fi; + od; + od; + return true; +end); + +MergeGroups := function(Sig, Sj, Sk) + return Group(Concatenation( + GeneratorsOfGroup(Sk), + GeneratorsOfGroup(Sig), + GeneratorsOfGroup(Sj) + )); +end; + +MergeVectorSpaces := function(A, B, q) + return VectorSpace(GF(q), + Concatenation( + Basis(A), + Basis(B) + )); +end; + +AreVectorSpacesDisjoint := function(A, B) + for a in Basis(A) do + if a in B then + return false; + fi; + od; + return true; +end; + +DeclareGlobalFunction("TopGroupDomain"); +InstallGlobalFunction(TopGroupDomain, function(args...) + local G, S, isDisjoint, merge, recursionDepth, recursionMaxDepth, maximalBoundOnTopDegree, t, domain, i, g, Si, Sig, Sj, foundNew, Sk, SS; + + if Length(args) < 2 then + Error("Arguments G and S are required."); + fi; + + G := args[1]; + S := args[2]; + + if Length(args) >= 3 then + recursionDepth := args[3]; + else + recursionDepth := 1; + fi; + + if Length(args) >= 4 then + recursionMaxDepth := args[4]; + else + recursionMaxDepth := 5; + fi; + + if Length(args) >= 5 then + maximalBoundOnTopDegree := args[5]; + else + maximalBoundOnTopDegree := 50; + fi; + + if recursionMaxDepth <= recursionDepth then + return fail; + fi; + + t := [One(G)]; + domain := [S]; + i := 1; + + while i <= Length(domain) do + Si := domain[i]; + for g in GeneratorsOfGroup(G) do + Sig := OnPoints(Si, g); + foundNew := true; + Sk := fail; + for Sj in domain do + if not DoCommuteGroups(Sig, Sj) then + foundNew := false; + if Sk = fail then + Sk := Sj; + else + SS := MergeGroups(Sig, Sj, Sk); + return TopGroupDomain(G, SS, recursionDepth + 1, recursionMaxDepth); + fi; + fi; + od; + if foundNew then + if Length(domain) >= maximalBoundOnTopDegree then + return fail; + fi; + Add(t, t[i] * g); + Add(domain, Sig); + fi; + od; + i := i + 1; + od; + + return rec(domain := domain, transversal := t); +end); + +DeclareGlobalFunction("TopGroupDomainVectorSpace"); +InstallGlobalFunction(TopGroupDomainVectorSpace, function(args...) + local G, S, q, recursionDepth, recursionMaxDepth, maximalBoundOnTopDegree, t, domain, i, g, Si, Sig, Sj, foundNew, Sk, SS; + + if Length(args) < 2 then + Error("Arguments G and S are required."); + fi; + + G := args[1]; + q := Size(DefaultFieldOfMatrixGroup(G)); + S := args[2]; + + if Length(args) >= 3 then + recursionDepth := args[3]; + else + recursionDepth := 1; + fi; + + if Length(args) >= 4 then + recursionMaxDepth := args[4]; + else + recursionMaxDepth := 5; + fi; + + if Length(args) >= 5 then + maximalBoundOnTopDegree := args[5]; + else + maximalBoundOnTopDegree := 50; + fi; + + if recursionMaxDepth <= recursionDepth then + return fail; + fi; + + t := [One(G)]; + domain := [S]; + i := 1; + + while i <= Length(domain) do + Si := domain[i]; + for g in GeneratorsOfGroup(G) do + Sig := OnPoints(Si, g); + foundNew := true; + for Sj in domain do + if Sig = Sj then + foundNew := false; + break; + elif not IsTrivial(Intersection(Sig, Sj)) then + SS := MergeVectorSpaces(Sig, Sj, q); + Basis(SS); + Dimension(SS); + return TopGroupDomainVectorSpace(G, SS, recursionDepth + 1, recursionMaxDepth); + fi; + od; + if foundNew then + if Length(domain) >= maximalBoundOnTopDegree then + return fail; + fi; + Add(t, t[i] * g); + Add(domain, Sig); + fi; + od; + i := i + 1; + od; + + return rec(domain := domain, transversal := t); +end); + +BindGlobal("TopComponentImage", function(g, domain) + local m, images, i, j, Si, Sj, Sig; + m := Length(domain); + images := EmptyPlist(m); + for i in [1 .. m] do + Si := domain[i]; + Sig := OnPoints(Si, g); + for j in [1 .. m] do + if j in images then + continue; + fi; + Sj := domain[j]; + if not DoCommuteGroups(Sig, Sj) then + images[i] := j; + break; + fi; + od; + if not IsBound(images[i]) then + return fail; + fi; + od; + return PermList(images); +end); + + +BindGlobal("RandomVector", function(d, q) + local F; + F := GF(q); + return List([1..d], i -> PseudoRandom(F)); +end); + +BindGlobal("StandardVector", function(d, q, i) + local F, v; + F := GF(q); + v := ListWithIdenticalEntries(d, Zero(F)); + v[i] := One(F); + return v; +end); + +BindGlobal("NormaliseVector", function(d, q, b, I) + local F, v, i; + F := GF(q); + v := ListWithIdenticalEntries(d, Zero(F)); + for i in I do + v[i] := b[i]; + od; + return v; +end); + +BindGlobal("ExtendAndNormaliseBasis", function(d, q, L) + local B, I, j, i; + B := []; + I := []; + for j in [1 .. Length(L)] do + Add(I, First([1 .. d], i -> L[j][i] = One(GF(q)))); + od; + j := 1; + for i in [1 .. d] do + if j <= Length(L) and L[j][i] = One(GF(q)) then + Add(B, L[j]); + j := j + 1; + else + Add(B, StandardVector(d, q, i)); + fi; + od; + return B; +end); \ No newline at end of file diff --git a/gap/Random.gi b/gap/Random.gi new file mode 100644 index 0000000..068fca8 --- /dev/null +++ b/gap/Random.gi @@ -0,0 +1,44 @@ + +# Returns a random permutation on n as a list +InstallGlobalFunction("QuickRandomPermList", function(n) + local lst, i, j, tmp; + lst := [1..n]; + for i in [n, n-1..2] do + j := Random([1..i]); + tmp := lst[i]; + lst[i] := lst[j]; + lst[j] := tmp; + od; + return lst; +end); + +# Returns a random subproduct of G +InstallGlobalFunction("QuickRandomSubproduct", function(G) + local gens, n, A, B; + if IsGroup(G) then + gens := GeneratorsOfGroup(G); + else # G is a list of group elements + gens := G; + fi; + n := Length(gens); + A := List([1 .. n], i -> Random([-1,0,1])); + B := QuickRandomPermList(n); + return Product([1 .. n], i -> gens[B[i]]^A[i]); +end); + +# normal closure of H in G, i.e. +InstallGlobalFunction("QuickNormalClosure", function(H, G, n) + local gens; + if IsGroup(H) then + gens := GeneratorsOfGroup(H); + else + gens := H; + fi; + return Group(FastNormalClosure(G, gens, n)); +end); + +BindGlobal("QuickRandomVector", function(d, q) + local F; + F := GF(q); + return List([1..d], i -> PseudoRandom(F)); +end); \ No newline at end of file diff --git a/gap/Recog.gi b/gap/Recog.gi new file mode 100644 index 0000000..b3bd760 --- /dev/null +++ b/gap/Recog.gi @@ -0,0 +1,72 @@ + +BindGlobal( "RecogniseWreathProduct", function(args...) + local ri, userOptions, options, name, data, res, output; + + # ================================================== + # Input extraction + # ================================================== + if Length(args) = 0 or Length(args) > 2 then + Error("Usage: RecogniseWreathProduct(ri[, options])"); + fi; + + ri := args[1]; + userOptions := rec(); + if Length(args) = 2 then + userOptions := args[2]; + fi; + + # ================================================== + # Default options + # ================================================== + options := rec( + ForSingleComponentGroup := rec(), + ForTopGroupDomain := rec(), + action := fail, + checkPrimitivity := false, + simpleBaseComp := true, + ); + + # ================================================== + # Input validation + # ================================================== + + # Check recog node + if not IsRecogNode(ri) then + Error("First argument must be a recog node"); + fi; + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ================================================== + # Algorithm + # ================================================== + data := rec(); + output := rec(res := fail, data := data, options := options); + + # Init options + res := WPR_InitOptions(ri, data, options); + if res = fail then + return output; + fi; + + # Single Component Group + res := WPR_SingleComponentGroup(ri, data, options); + if res = fail then + return output; + fi; + + # Top Group Domain + res := WPR_TopGroupDomain(ri, data, options); + if res = fail then + return output; + fi; + + output.res := true; + return output; +end); diff --git a/gap/RecogSubroutines.gi b/gap/RecogSubroutines.gi new file mode 100644 index 0000000..cc670eb --- /dev/null +++ b/gap/RecogSubroutines.gi @@ -0,0 +1,103 @@ +BindGlobal("WPR_InitOptions", function(ri, data, options) + local timer, name, G, isPrim, N, F, M, d; + G := Grp(ri); + Info(WPR_Info, 1, "Step 0: Initialize bounds for wreath product recognition"); + Info(WPR_Info, 2, "--------------------------------------------------------"); + if IsPermGroup(G) then + isPrim := fail; + if options.action = fail and options.checkPrimitivity then + isPrim := IsPrimitive(G); + elif options.action = "product action" then + isPrim := true; + elif options.action = "imprimitive action" then + isPrim := false; + fi; + if isPrim = true or isPrim = fail then + # assume product action + N := NrMovedPoints(G); + F := Collected(PartialFactorization(N, 0)); + M := F[1][2]; # upper bound for top degree + if ForAll(F, f -> f[2] = M) then + options.action := "product action"; + isPrim := true; + fi; + fi; + if isPrim = false or isPrim = fail then + N := NrMovedPoints(G); + M := N / First(Primes, p -> RemInt(N, p) = 0); # upper bound for top degree + options.action := "imprimitive action"; + isPrim := false; + fi; + elif IsMatrixGroup(G) then + d := DimensionOfMatrixGroup(G); + M := d / First(Primes, p -> RemInt(d, p) = 0); # upper bound for top degree + options.action := "imprimitive action"; + else + Error("todo"); + fi; + + options.ForSingleComponentGroup.M := Minimum(options.ForSingleComponentGroup.M, M); + return true; +end); + +BindGlobal("WPR_SingleComponentGroup", function(ri, data, options) + local timer, name, S; + # ------------------------------------------------------------- # + # Step 1 : Compute a single-component group S isomorphic to T # + # ------------------------------------------------------------- # + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 1 : ", "Compute a single-component group S"); + Info(WPR_Info, 2, "---------------------------------------------------------------"); + timer := Runtime(); + S := SingleComponentGroup(ri, options.ForSingleComponentGroup); # with memory + timer := Runtime() - timer; + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + data.S := S; + return true; +end); + +BindGlobal("WPR_TopGroupDomain", function(ri, data, options) + local timer, name, G, S, S_withoutMem, domainData, W; + G := Grp(ri); + S := data.S; + S_withoutMem := Group(List(GeneratorsOfGroup(S), StripMemory)); + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step 3 : ", "Compute a faithful H-set"); + Info(WPR_Info, 2, "-------------------------------------------------------------------"); + timer := Runtime(); + # exploit representations + if IsPermGroup(G) then + if options.action = "product action" then + domainData := TopGroupDomainViaProductAction(ri, S_withoutMem, options.ForTopGroupDomain); + elif options.action = "imprimitive action" then + # TODO + fi; + elif IsMatrixGroup(G) then + if options.action = "imprimitive action" then + W := TopGroupPointViaLinearAction(S); + data.invariantSubspace := W; + domainData := TopGroupDomainViaLinearAction(ri, W, options.ForTopGroupDomain); + fi; + fi; + # generic fallback + if not IsBound(domainData) then + if options.simpleBaseComp then + domainData := TopGroupDomainViaSimpleSubgroup(ri, S_withoutMem, options.ForTopGroupDomain); + else + domainData := TopGroupDomainViaGenericSubgroup(ri, S_withoutMem, options.ForTopGroupDomain); + fi; + fi; + timer := Runtime() - timer; + if domainData = fail then + Info(WPR_Info, 1, "Failure: invalid domain"); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return fail; + fi; + for name in RecNames(domainData) do + data.(name) := domainData.(name); + data.m := Length(domainData.domain); + od; + Info(WPR_Info, 2, "m = ", data.m); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return true; +end); \ No newline at end of file diff --git a/gap/SingleComponentGroup.gi b/gap/SingleComponentGroup.gi new file mode 100644 index 0000000..f6a5b3d --- /dev/null +++ b/gap/SingleComponentGroup.gi @@ -0,0 +1,200 @@ +# args: ri[, options] +# - ri is recog node +# - options are user options, see in code +# Returns single-component group +InstallGlobalFunction("SingleComponentGroup", function(args...) + local ri, userOptions, options, name, S, l1, l2, P, R, B, i, descendOptions, logEps; + + # ================================================== + # Input extraction + # ================================================== + if Length(args) = 0 or Length(args) > 2 then + Error("Usage: SingleComponentGroup(ri[, options])"); + fi; + + ri := args[1]; + userOptions := rec(); + if Length(args) = 2 then + userOptions := args[2]; + fi; + + # ================================================== + # Default options + # ================================================== + options := rec( + # -- Error control ------------------------------------------- + heuristic := true, # whether to use heuristic values instead of explicit ones + eps := 1/100, # error probability + M := 20, # upper bound for degree of top group + + # -- Strategy flags ------------------------------------------- + P := [2, 3, 5, 7], # prime numbers to use in a step + randomElementGenerator # function to generate random elements + := QuickRandomSubproduct, + useMemory := true, # whether to use memory for group elements + useBaseGroupInPhase2 := false, # use base group instead of previous group in phase 2 + useBaseGroupAtEnd := true, # use base group at end (ignored if useBaseGroupInPhase2) + socleType := fail, # socleType + updateParameters := false, # whether to update parameters after phase 1 + + # -- Phase iteration counts ------------------------------------------- + l1 := 5, # number of iterations in phase 1 + l2 := 35, # number of iterations in phase 2 + + # -- Normal closure effort parameters --------------------------------- + n1 := 5, # effort per step in phase 1 + n2 := 5, # effort per step in phase 2 + n0 := 2, # effort at final step (used only if useBaseGroupAtEnd) + ); + + # ================================================== + # Input validation + # ================================================== + + # Check recog node + if not IsRecogNode(ri) then + Error("First argument must be a recog node"); + fi; + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ================================================== + # Algorithm + # ================================================== + + if options.useMemory then + S := Group(ri!.gensHmem); + else + S := Grp(ri); + fi; + R := SingleComponentGroup_ReductionRate(options.socleType); + if not options.heuristic then + P := [2]; + Info(WPR_Info, 2, "Reduction rate probabilities for a step in each phase:"); + Info(WPR_Info, 2, "\tP_1 = ", R[1]); + Info(WPR_Info, 2, "\tP_2 = ", R[2]); + else + P := options.P; + fi; + + # -- Phase 1 ------------------------------------------- + l1 := SingleComponentGroup_NrIterations1(R[1], options.eps/2); + if options.heuristic then + l1 := Minimum(l1, options.l1); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n1, + P := P, + ); + Info(WPR_Info, 2, "Bounds for Phase 1:"); + Info(WPR_Info, 2, "\tl_1 = ", l1); + Info(WPR_Info, 3, "Start Iteration for Phase 1..."); + for i in [1 .. l1] do + S := SingleComponentGroup_Descend(S, S, descendOptions); + od; + Info(WPR_Info, 3, "...Finished Iteration for Phase 1"); + + # -- Update Parameters --------------------------------- + B := S; # supposedly inside base group + if options.updateParameters then + SingleComponentGroup_UpdateParameters(options, B); + fi; + + # -- Phase 2 ------------------------------------------- + l2 := SingleComponentGroup_NrIterations2(R[2], options.M, options.eps/2); + if options.heuristic then + l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M)))), options.l2); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n2, + P := P, + ); + Info(WPR_Info, 2, "Bounds for Phase 2:"); + Info(WPR_Info, 2, "\tl_2 = ", l2); + Info(WPR_Info, 3, "Start Iteration for Phase 2..."); + for i in [1 .. l2] do + if options.useBaseGroupInPhase2 then + S := SingleComponentGroup_Descend(S, B, descendOptions); + else + S := SingleComponentGroup_Descend(S, S, descendOptions); + fi; + od; + Info(WPR_Info, 3, "...Finished Iteration for Phase 2"); + + # -- Post ------------------------------------------- + # As a pre-caution, take normal closure in base group, if we descended too far + if not options.useBaseGroupInPhase2 and options.useBaseGroupAtEnd then + Info(WPR_Info, 3, "Start computing normal closure in base group..."); + S := QuickNormalClosure(S, B, options.n0); + Info(WPR_Info, 3, "... Finished computing normal closure in base group"); + fi; + return S; + +end); + +# args: H, G, options +# - for options, see SingleComponentGroup. +# - H is current group in iteration step +# - computes normal closure in G +# Returns next group in iteration step +InstallGlobalFunction("SingleComponentGroup_Descend", function(H, G, options) + local y, ord, P, p, z; + y := options.randomElementGenerator(H); + ord := Order(y); + P := options.P{QuickRandomPermList(Length(options.P))}; + for p in P do + if (p = 2 and IsEvenInt(ord)) + or RemInt(ord, p) = 0 then + z := y ^ (ord / p); + return QuickNormalClosure([z], G, options.n); + fi; + od; + return H; +end); + +InstallGlobalFunction( "SingleComponentGroup_ReductionRate", function(socleType) + if socleType = fail then + socleType := "Alt"; + fi; + if socleType = "Alt" then + return [1/2, 1/3]; + fi; + Error("Invalid socle type: ", socleType); +end); + +InstallGlobalFunction( "SingleComponentGroup_NrIterations1", function(p1, eps) + local logEps; + logEps := Log(Float(1 / eps)); + return Int(Ceil(logEps/Log(Float(1 / (1 - p1))))); +end); + +InstallGlobalFunction( "SingleComponentGroup_NrIterations2", function(p2, M, eps) + local delta, c, r, k, m, logDelta, l_lin, l_log, l2; + delta := eps/2; + logDelta := Log(Float(1 / delta)); + c := 2 * (1 + 1/p2); + r := 1 - p2/2; + m := 2*c; + if m < M then + k := Int(Ceil(Log(Float(M/c))/Log(Float(1/r)))); + l_log := Int(Ceil(Maximum(Float(4 * k), 16 * logDelta))); + else + l_log := 0; + fi; + l_lin := Int(Ceil(Maximum(Float(2 / p2 * m), 8 / p2 * logDelta))); + l2 := Int(Ceil(Maximum(Float(2 / p2 * M), 8 / p2 * logDelta))); + return Minimum(l2, l_log + l_lin); +end); + +InstallGlobalFunction("SingleComponentGroup_UpdateParameters", function(options, B) + return; # TODO +end); + diff --git a/gap/TopGroupAction.gi b/gap/TopGroupAction.gi new file mode 100644 index 0000000..a266cd9 --- /dev/null +++ b/gap/TopGroupAction.gi @@ -0,0 +1,239 @@ +BindGlobal("DoCommuteElms", function(x, y) + return x * y = y * x; +end); + +BindGlobal("DoCommuteGroups", function(A, B) + local a, b; + for a in GeneratorsOfGroup(A) do + for b in GeneratorsOfGroup(B) do + if not DoCommuteElms(a, b) then + return false; + fi; + od; + od; + return true; +end); + +BindGlobal("TopGroupDomainViaSimpleSubgroup", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: TopGroupDomainViaSimpleSubgroup(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> not DoCommuteGroups(a,b); # if groups do not commute, groups must be equal + userOptions.isDistinguishable := {a, b} -> true; # if groups commute, groups must be disjoint + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("TopGroupDomainViaGenericSubgroup", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: TopGroupDomainViaGenericSubgroup(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> false; # we cannot check for equality without further assumptions + userOptions.isDistinguishable := {a, b} -> DoCommuteGroups(a,b); # if groups commute, then they might lie in different components + userOptions.isConflict := {p, P} -> Length(P) >= 2; # we found two groups with which p does not commute + userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); # we merge these groups and hope that we now cover the socle in the component + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("TopGroupPointViaLinearAction", function(S) + local d, q, M, v1, v2, L1, L2, W; + d := DimensionOfMatrixGroup(S); + q := Size(DefaultFieldOfMatrixGroup(S)); + # S acts on W + U + # W invariant space, dim(W) = d + # U fixed space, dim(U) = (m-1)*d + M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); + v1 := QuickRandomVector(d,q); + v2 := QuickRandomVector(d,q); + # basis of W + < [v]\rho_U > + L1 := MTX.SubmoduleGModule(M, v1);; + L2 := MTX.SubmoduleGModule(M, v2);; + W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); + return W; +end); + +BindGlobal("TopGroupDomainViaLinearAction", function(args...) + local ri, s, q, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: TopGroupDomainViaLinearAction(ri, s[, options])"); + fi; + + ri := args[1]; + q := Size(DefaultFieldOfMatrixGroup(Grp(ri))); + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> a = b; + userOptions.isDistinguishable := {a, b} -> IsTrivial(Intersection(a, b)); + userOptions.isConflict := {p, P} -> Length(P) >= 1; + userOptions.resolveConflict := function(p1, P) + local p2, pNew; + p2 := P[1]; + pNew := VectorSpace(GF(q), Concatenation(Basis(p1),Basis(p2))); + Basis(pNew); + Dimension(pNew); + return pNew; + end; + + return BlackBoxOrbit(ri, s, userOptions); + +end); + +BindGlobal("TopGroupDomainViaProductAction", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: TopGroupDomainViaProductAction(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> Set(Orbit(a, 1)) = Set(Orbit(b, 1)); + userOptions.isDistinguishable := {a, b} -> Size(Intersection(Orbit(a, 1), Orbit(b, 1))) = 1; + userOptions.isConflict := {p, P} -> Length(P) >= 1; + userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); + + return BlackBoxOrbit(ri, s, userOptions); +end); + +InstallGlobalFunction("BlackBoxOrbit", function(args...) + local ri, s, userOptions, options, name, G, t, domain, i, a, b, g, p, isEq, foundNew, indistinguishablePoints, j; + + # ================================================== + # Input extraction + # ================================================== + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: BlackBoxOrbit(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + + # ================================================== + # Default options + # ================================================== + options := rec( + # -- Strategy flags ------------------------------------------- + recursionDepth := 1, + recursionMaxDepth := 5, + maximalBoundOnTopDegree := 50, + useMemory := true, # whether to use memory for group elements + # -- Action oracles ------------------------------------------- + act := OnPoints, + isEqual := \=, # isEqual returns true if p and b are equal + # returns false if we cannot determine whether p and b are equal + isDistinguishable := {a, b} -> true, # if IsEqual returns false (so a = b could not be proven, but might be true), + # this returns true if we can distinguish between a and b. + # If points are not distinguishable, we assume they are equal for the moment + isConflict := {p, indistinguishablePoints} -> false, # return true if domain might not be invariant under the action + resolveConflict := {p, indistinguishablePoints} -> fail, # try to find different domain or return fail, + ); + + # ================================================== + # Input validation + # ================================================== + + # Check recog node + if not IsRecogNode(ri) then + Error("First argument must be a recog node"); + fi; + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ================================================== + # Algorithm + # ================================================== + + if options.recursionDepth > options.recursionMaxDepth then + return fail; + fi; + Info(WPR_Info, 2, "Recursion Depth: ", options.recursionDepth); + if options.useMemory then + G := Group(ri!.gensHmem); + else + G := Grp(ri); + fi; + t := [One(G)]; + domain := [s]; + i := 1; + + # -- Iteration ------------------------------------- + while i <= Length(domain) do + a := domain[i]; + for g in GeneratorsOfGroup(G) do + p := options.act(a, StripMemory(g)); + foundNew := true; + indistinguishablePoints := []; + for j in [1 .. Length(domain)] do + b := domain[j]; + isEq := options.isEqual(p, b); + if isEq then + foundNew := false; + break; + # can we distinguish between p and b via our action? + elif not options.isDistinguishable(p, b) then + Add(indistinguishablePoints, b); + # We cannot distinguish between these points, + # so we need to assume for now that they are equal. + foundNew := false; + # If we can prove a conflict, we need to adjust the domain + if options.isConflict(p, indistinguishablePoints) then + Info(WPR_Info, 2, "Found conflict"); + # The domain is not invariant under the action, + # thus we try compute a new point to resolve the conflict + s := options.resolveConflict(p, indistinguishablePoints); + if s = fail then + Info(WPR_Info, 2, "Could not resolve conflict"); + return fail; + fi; + Error("Examine Me!"); + options.recursionDepth := options.recursionDepth + 1; + return BlackBoxOrbit(ri, s, options); + fi; + fi; + od; + if foundNew then + if Length(domain) >= options.maximalBoundOnTopDegree then + Info(WPR_Info, 2, "Domain too large, abort now"); + return fail; + fi; + Add(t, t[i] * g); + Add(domain, p); + fi; + od; + i := i + 1; + od; + return rec(domain := domain, transversal := t); +end); \ No newline at end of file diff --git a/gap/WPR.gd b/gap/WPR.gd deleted file mode 100644 index af8180e..0000000 --- a/gap/WPR.gd +++ /dev/null @@ -1,35 +0,0 @@ -# -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component -# -#! @Chapter Introduction -#! -#! WPR is a package which does some -#! interesting and cool things -#! -#! @Chapter Functionality -#! -#! -#! @Section Example Methods -#! -#! This section will describe the example -#! methods of WPR - -DeclareGlobalFunction( "WreathProductRecognition" ); -DeclareGlobalFunction( "WPR_SimpleSingleComponent" ); -DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsFirstPhase" ); -DeclareGlobalFunction( "WPR_SimpleSingleComponentHintsSecondPhase" ); -DeclareGlobalFunction( "WPR_SimpleSingleComponentBaseStep" ); -DeclareGlobalFunction( "WPR_SimpleSingleComponentSuccessProb" ); -DeclareGlobalFunction( "WPR_TopGroupDomain" ); -DeclareGlobalFunction( "WPR_TopComponentImage" ); -DeclareGlobalFunction( "WPR_Image" ); -DeclareGlobalFunction( "WPR_ImageAltGeneric" ); -DeclareGlobalFunction( "WPR_ImageAltFilter" ); -DeclareGlobalFunction( "WPR_StandardGensSingleComponent" ); -DeclareGlobalFunction( "WPR_StandardGensSingleComponentAlt" ); -DeclareGlobalFunction( "WPR_SLPforAlmostSimple" ); -DeclareGlobalFunction( "WPR_StandardGensTopGroup" ); -DeclareGlobalFunction( "WPR_Verification" ); -DeclareGlobalFunction( "WPR_RecogniseAlmostSimple" ); -DeclareGlobalFunction( "WPR_RecogniseAlt" ); - diff --git a/gap/WPrecog.gd b/gap/WPrecog.gd new file mode 100644 index 0000000..7c9400e --- /dev/null +++ b/gap/WPrecog.gd @@ -0,0 +1,30 @@ +# +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# +#! @Chapter Introduction +#! +#! WPrecog is a package which does some +#! interesting and cool things +#! +#! @Chapter Functionality +#! +#! +#! @Section Example Methods +#! +#! This section will describe the example +#! methods of WPrecog + +DeclareGlobalFunction("QuickRandomPermList"); +DeclareGlobalFunction("QuickRandomSubproduct"); +DeclareGlobalFunction("QuickNormalClosure"); +DeclareGlobalFunction("SingleComponentGroup"); +DeclareGlobalFunction("SingleComponentGroup_Descend"); +DeclareGlobalFunction("SingleComponentGroup_ReductionRate"); +DeclareGlobalFunction("SingleComponentGroup_NrIterations1"); +DeclareGlobalFunction("SingleComponentGroup_NrIterations2"); +DeclareGlobalFunction("SingleComponentGroup_UpdateParameters"); + +DeclareGlobalFunction("BlackBoxOrbit"); + + + diff --git a/gap/WPR.gi b/gap/WPrecog.gi similarity index 99% rename from gap/WPR.gi rename to gap/WPrecog.gi index dc7f4c4..6eaafd8 100644 --- a/gap/WPR.gi +++ b/gap/WPrecog.gi @@ -1,5 +1,5 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # Implementations # diff --git a/init.g b/init.g index 23635b7..d902504 100644 --- a/init.g +++ b/init.g @@ -1,7 +1,7 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # Reading the declaration part of the package. # -ReadPackage( "WPR", "gap/WPR.gd"); +ReadPackage( "WPrecog", "gap/WPrecog.gd"); diff --git a/makedoc.g b/makedoc.g index 0dc1670..1364304 100644 --- a/makedoc.g +++ b/makedoc.g @@ -1,5 +1,5 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # This file is a script which compiles the package manual. # diff --git a/read.g b/read.g index 6d67e32..33101ef 100644 --- a/read.g +++ b/read.g @@ -1,8 +1,17 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # Reading the implementation part of the package. # -ReadPackage( "WPR", "gap/WPR.gi"); -ReadPackage( "WPR", "gap/Alt.gi"); +# Level 1: Show Current Step in Main Recognition Method +# Level 2: Show Important Bounds in Submethods +# Level 3: Show Progress of Iterations +BindGlobal("WPR_Info", NewInfoClass("WPR_Info")); +SetInfoLevel(WPR_Info, 3); + +ReadPackage( "WPrecog", "gap/Random.gi"); +ReadPackage( "WPrecog", "gap/SingleComponentGroup.gi"); +ReadPackage( "WPrecog", "gap/TopGroupAction.gi"); +ReadPackage( "WPrecog", "gap/RecogSubroutines.gi"); +ReadPackage( "WPrecog", "gap/Recog.gi"); diff --git a/tst/files/Alt.tst b/tst/files/Alt.tst new file mode 100644 index 0000000..ec1e1c5 --- /dev/null +++ b/tst/files/Alt.tst @@ -0,0 +1,42 @@ +gap> LoadPackage("WPrecog"); +gap> n := 11;; +gap> G := WreathProduct(SymmetricGroup(n), DihedralGroup(IsPermGroup, 8));; +gap> ri := RecogNode(G);; +gap> simpleGroupFamily := "Alt";; +gap> SetInfoLevel(WPR_Info, 3); +gap> WreathProductRecognition(ri, G, simpleGroupFamily); + + +# Example for slow GAP Socle but fast WPrecog Socle (Factor) + +gap> LoadPackage("WPrecog"); +gap> K := SymmetricGroup(10);; +gap> H := DihedralGroup(IsPermGroup, 10);; +gap> G := WreathProductProductAction(K, H);; +gap> ri := RecogNode(G);; +gap> G := ri!.Grp; +gap> gens := GeneratorsOfGroup(G);; +gap> L := NrMovedPoints(G);; +gap> delta := 1/10;; +gap> l := 3;; +gap> for i in [1 .. l] do +> gens := WPR_SimpleSingleComponentBaseStep(gens, L, delta); +> od; time; +gap> S := Group(gens);; +gap> StructureDescription(S); +gap> Socle(G);; time; + +gap> simpleGroupFamily := "Alt";; +gap> origGensS := gens; +gap> hintsForT := rec(upperDegreeBound := 10); +gap> eps := 1/10; +gap> recogData := WPR_RecogniseAlmostSimple(origGensS, simpleGroupFamily, hintsForT, eps);; time; +gap> T := recogData.T; +gap> AutT := recogData.AutT; +gap> slpFuncForT := recogData.slpFuncForT; +gap> stdGensS := recogData.stdGensS; +gap> lambda := recogData.lambda; + +gap> domainData := WPR_TopGroupDomain(ri, stdGensS);; time; +gap> t := domainData.t; +gap> domain := domainData.domain; \ No newline at end of file diff --git a/tst/testall.g b/tst/testall.g index 9066c3b..d67f98e 100644 --- a/tst/testall.g +++ b/tst/testall.g @@ -1,12 +1,12 @@ # -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component # # This file runs package tests. It is also referenced in the package # metadata in PackageInfo.g. # -LoadPackage( "WPR" ); +LoadPackage( "WPrecog" ); -TestDirectory(DirectoriesPackageLibrary( "WPR", "tst/files" ), +TestDirectory(DirectoriesPackageLibrary( "WPrecog", "tst/files" ), rec(exitGAP := true)); FORCE_QUIT_GAP(1); # if we ever get here, there was an error From 202cbc67296674183fbecea227b66b9d844beb90 Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Sun, 13 Apr 2025 13:36:41 +0200 Subject: [PATCH 12/14] Stash progress --- examples/PermImprimitive.gi | 15 +- examples/PermPrimitive.gi | 32 +- examples/PermPrimitiveLargeBase.gi | 36 +++ gap/Quick.gi | 107 +++++++ gap/Random.gi | 44 --- gap/Recog.gi | 77 ++++- gap/RecogSubroutines.gi | 103 ------ gap/SingleComponentGroup.gi | 200 ------------ gap/TopGroupAction.gi | 239 -------------- gap/WPrecog.gd | 10 +- gap/subroutines/Image.gi | 84 +++++ gap/subroutines/Image/ViaConjugationAction.gi | 8 + gap/subroutines/Image/ViaLinearAction.gi | 8 + gap/subroutines/Image/ViaProductAction.gi | 86 +++++ gap/subroutines/Init.gi | 54 ++++ gap/subroutines/RecogniseBaseComponent.gi | 35 ++ gap/subroutines/RecogniseTopComponent.gi | 0 gap/subroutines/SingleComponentGroup.gi | 204 ++++++++++++ .../SingleComponentGroup/Helpers.gi | 111 +++++++ gap/subroutines/TopGroupDomainAndAction.gi | 303 ++++++++++++++++++ .../ViaLinearAction.gi | 90 ++++++ .../ViaProductAction.gi | 66 ++++ .../TopGroupDomainAndAction/ViaSubgroup.gi | 99 ++++++ read.g | 25 +- 24 files changed, 1401 insertions(+), 635 deletions(-) create mode 100644 examples/PermPrimitiveLargeBase.gi create mode 100644 gap/Quick.gi delete mode 100644 gap/Random.gi delete mode 100644 gap/RecogSubroutines.gi delete mode 100644 gap/SingleComponentGroup.gi delete mode 100644 gap/TopGroupAction.gi create mode 100644 gap/subroutines/Image.gi create mode 100644 gap/subroutines/Image/ViaConjugationAction.gi create mode 100644 gap/subroutines/Image/ViaLinearAction.gi create mode 100644 gap/subroutines/Image/ViaProductAction.gi create mode 100644 gap/subroutines/Init.gi create mode 100644 gap/subroutines/RecogniseBaseComponent.gi create mode 100644 gap/subroutines/RecogniseTopComponent.gi create mode 100644 gap/subroutines/SingleComponentGroup.gi create mode 100644 gap/subroutines/SingleComponentGroup/Helpers.gi create mode 100644 gap/subroutines/TopGroupDomainAndAction.gi create mode 100644 gap/subroutines/TopGroupDomainAndAction/ViaLinearAction.gi create mode 100644 gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi create mode 100644 gap/subroutines/TopGroupDomainAndAction/ViaSubgroup.gi diff --git a/examples/PermImprimitive.gi b/examples/PermImprimitive.gi index 9d724de..eab30d0 100644 --- a/examples/PermImprimitive.gi +++ b/examples/PermImprimitive.gi @@ -9,15 +9,15 @@ H := SymmetricGroup(m); # Construct wreath product PP := SymmetricGroup(n*m); -P := WreathProduct(SymmetricGroup(n), SymmetricGroup(m)); +P := WreathProduct(SymmetricGroup(n), SymmetricGroup(m));; W := Group(Concatenation( List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) -)); +));; # Random conjugation -c := PseudoRandom(PP); -G := W^(c^(-1)); +c := PseudoRandom(PP);; +G := W^(c^(-1));; # # Nice isomorphism # isoWreath := IsomorphismWreathProduct(W);; @@ -25,6 +25,7 @@ G := W^(c^(-1)); # isoNice := isoConj * isoWreath;; # Recognition -data := RecogniseWreathProduct(RecogNode(G), rec( - simpleBaseComp := false, -)); +output := RecogniseWreathProduct(RecogNode(G), rec( + assumeSimpleBaseComponent := true, +));; +output.res; \ No newline at end of file diff --git a/examples/PermPrimitive.gi b/examples/PermPrimitive.gi index b7416b2..e6b6c13 100644 --- a/examples/PermPrimitive.gi +++ b/examples/PermPrimitive.gi @@ -2,34 +2,32 @@ LoadPackage("WPE", false); LoadPackage("WPrecog", false); # Permutation Group : Product Action -m := 5; -l := 15; -k := 1; -n := k * l; -l > 2*m*k^2; # Is Large Base? -K := Action(AlternatingGroup(n), Combinations([1..n],k), OnSets); +m := 3; +d := 3; +q := 5; +K := PSL(d,q); +n := NrMovedPoints(K); +n^m; H := Random(AllTransitiveGroups(NrMovedPoints, m)); # Construct wreath product PP := SymmetricGroup(n^m); -P := WreathProductProductAction(SymmetricGroup(n), SymmetricGroup(m)); -W := Group(Concatenation( - List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), - List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) -)); +P := WreathProductProductAction(K, H);; +W := P;; # Random conjugation -c := PseudoRandom(PP); -G := W^(c^(-1)); +c := PermList(QuickRandomPermutedList(NrMovedPoints(PP)));; +G := W^(c^(-1));; # # Nice isomorphism -# isoWreath := IsomorphismWreathProduct(W);; -# isoConj := GroupHomomorphismByFunction(G, W, g -> g^c); +# isoWreath := IsomorphismWreathProduct(P);; +# isoConj := GroupHomomorphismByFunction(G, P, g -> g^c); # isoNice := isoConj * isoWreath;; # Recognition -data := RecogniseWreathProduct(RecogNode(G), rec( +output := RecogniseWreathProduct(RecogNode(G), rec( action := "product action", -)); +));; +res := output.res; RecogniseGroup(G); \ No newline at end of file diff --git a/examples/PermPrimitiveLargeBase.gi b/examples/PermPrimitiveLargeBase.gi new file mode 100644 index 0000000..712f0fd --- /dev/null +++ b/examples/PermPrimitiveLargeBase.gi @@ -0,0 +1,36 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Permutation Group : Product Action +m := 5; +l := 15; +k := 1; +n := k * l; +l > 2*m*k^2; # Is Large Base? +K := Action(AlternatingGroup(n), Combinations([1..n],k), OnSets); +H := Random(AllTransitiveGroups(NrMovedPoints, m)); + +# Construct wreath product +PP := SymmetricGroup(n^m); +P := WreathProductProductAction(SymmetricGroup(n), SymmetricGroup(m));; +W := Group(Concatenation( + List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), + List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) +));; + +# Random conjugation +c := PseudoRandom(PP);; +G := W^(c^(-1));; + +# # Nice isomorphism +isoWreath := IsomorphismWreathProduct(P);; +isoConj := GroupHomomorphismByFunction(G, P, g -> g^c); +isoNice := isoConj * isoWreath;; + +# Recognition +output := RecogniseWreathProduct(RecogNode(G), rec( + action := "product action", +));; +res := output.res; + +RecogniseGroup(G); \ No newline at end of file diff --git a/gap/Quick.gi b/gap/Quick.gi new file mode 100644 index 0000000..974962a --- /dev/null +++ b/gap/Quick.gi @@ -0,0 +1,107 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## Quick.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains code for generating quickly pseudo-random objects. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Random permuted list of [1 .. n]. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("QuickRandomPermutedList", function(n) + local lst, i, j, tmp; + lst := [1..n]; + for i in [n, n-1..2] do + j := Random([1..i]); + tmp := lst[i]; + lst[i] := lst[j]; + lst[j] := tmp; + od; + return lst; +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: G +## - G is either a group or list of group elements. +## +## Returns a random subproduct of G. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("QuickRandomSubproduct", function(G) + local gens, n, A, B; + if IsGroup(G) then + gens := GeneratorsOfGroup(G); + else # G is a list of group elements + gens := G; + fi; + n := Length(gens); + A := List([1 .. n], i -> Random([-1,0,1])); + B := QuickRandomPermutedList(n); + return Product([1 .. n], i -> gens[B[i]]^A[i]); +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: H, G, n +## - n is an integer, the effort parameter for FastNormalClosure. +## +## Returns the normal closure of H in G, i.e. . +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("QuickNormalClosure", function(H, G, n) + local gens; + if IsGroup(H) then + gens := GeneratorsOfGroup(H); + else + gens := H; + fi; + return Group(FastNormalClosure(G, gens, n)); +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Random vector in GF(q)^d. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("QuickRandomVector", function(d, q) + local F; + F := GF(q); + return List([1..d], i -> PseudoRandom(F)); +end); diff --git a/gap/Random.gi b/gap/Random.gi deleted file mode 100644 index 068fca8..0000000 --- a/gap/Random.gi +++ /dev/null @@ -1,44 +0,0 @@ - -# Returns a random permutation on n as a list -InstallGlobalFunction("QuickRandomPermList", function(n) - local lst, i, j, tmp; - lst := [1..n]; - for i in [n, n-1..2] do - j := Random([1..i]); - tmp := lst[i]; - lst[i] := lst[j]; - lst[j] := tmp; - od; - return lst; -end); - -# Returns a random subproduct of G -InstallGlobalFunction("QuickRandomSubproduct", function(G) - local gens, n, A, B; - if IsGroup(G) then - gens := GeneratorsOfGroup(G); - else # G is a list of group elements - gens := G; - fi; - n := Length(gens); - A := List([1 .. n], i -> Random([-1,0,1])); - B := QuickRandomPermList(n); - return Product([1 .. n], i -> gens[B[i]]^A[i]); -end); - -# normal closure of H in G, i.e. -InstallGlobalFunction("QuickNormalClosure", function(H, G, n) - local gens; - if IsGroup(H) then - gens := GeneratorsOfGroup(H); - else - gens := H; - fi; - return Group(FastNormalClosure(G, gens, n)); -end); - -BindGlobal("QuickRandomVector", function(d, q) - local F; - F := GF(q); - return List([1..d], i -> PseudoRandom(F)); -end); \ No newline at end of file diff --git a/gap/Recog.gi b/gap/Recog.gi index b3bd760..b647f95 100644 --- a/gap/Recog.gi +++ b/gap/Recog.gi @@ -1,10 +1,38 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## Recog.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains the main function for recognising wreath products. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# BindGlobal( "RecogniseWreathProduct", function(args...) local ri, userOptions, options, name, data, res, output; - # ================================================== + # ======================================================================= # Input extraction - # ================================================== + # ======================================================================= + if Length(args) = 0 or Length(args) > 2 then Error("Usage: RecogniseWreathProduct(ri[, options])"); fi; @@ -15,20 +43,24 @@ BindGlobal( "RecogniseWreathProduct", function(args...) userOptions := args[2]; fi; - # ================================================== + # ======================================================================= # Default options - # ================================================== + # ======================================================================= + options := rec( - ForSingleComponentGroup := rec(), - ForTopGroupDomain := rec(), + forSingleComponentGroup := rec(), + forTopGroupDomain := rec(), action := fail, checkPrimitivity := false, - simpleBaseComp := true, + assumeSimpleBaseComponent := true, + recogniseComponents := true, + recogniseBaseComponentBeforeDomain := true, + recogniseBaseComponentViaIsomorphism := false, ); - # ================================================== + # ======================================================================= # Input validation - # ================================================== + # ======================================================================= # Check recog node if not IsRecogNode(ri) then @@ -43,10 +75,11 @@ BindGlobal( "RecogniseWreathProduct", function(args...) options.(name) := userOptions.(name); od; - # ================================================== + # ======================================================================= # Algorithm - # ================================================== - data := rec(); + # ======================================================================= + + data := rec(currentStep := 0); output := rec(res := fail, data := data, options := options); # Init options @@ -61,12 +94,32 @@ BindGlobal( "RecogniseWreathProduct", function(args...) return output; fi; + # Recognise Base Component? + if options.recogniseComponents + and options.recogniseBaseComponentBeforeDomain + then + WPR_RecogniseBaseComponent(ri, data, options); + fi; + # Top Group Domain res := WPR_TopGroupDomain(ri, data, options); if res = fail then return output; fi; + # Recognise Base Component? + if options.recogniseComponents + and not options.recogniseBaseComponentBeforeDomain + then + WPR_RecogniseBaseComponent(ri, data, options); + fi; + + # Embedding + res := WPR_Embedding(ri, data, options); + if res = fail then + return output; + fi; + output.res := true; return output; end); diff --git a/gap/RecogSubroutines.gi b/gap/RecogSubroutines.gi deleted file mode 100644 index cc670eb..0000000 --- a/gap/RecogSubroutines.gi +++ /dev/null @@ -1,103 +0,0 @@ -BindGlobal("WPR_InitOptions", function(ri, data, options) - local timer, name, G, isPrim, N, F, M, d; - G := Grp(ri); - Info(WPR_Info, 1, "Step 0: Initialize bounds for wreath product recognition"); - Info(WPR_Info, 2, "--------------------------------------------------------"); - if IsPermGroup(G) then - isPrim := fail; - if options.action = fail and options.checkPrimitivity then - isPrim := IsPrimitive(G); - elif options.action = "product action" then - isPrim := true; - elif options.action = "imprimitive action" then - isPrim := false; - fi; - if isPrim = true or isPrim = fail then - # assume product action - N := NrMovedPoints(G); - F := Collected(PartialFactorization(N, 0)); - M := F[1][2]; # upper bound for top degree - if ForAll(F, f -> f[2] = M) then - options.action := "product action"; - isPrim := true; - fi; - fi; - if isPrim = false or isPrim = fail then - N := NrMovedPoints(G); - M := N / First(Primes, p -> RemInt(N, p) = 0); # upper bound for top degree - options.action := "imprimitive action"; - isPrim := false; - fi; - elif IsMatrixGroup(G) then - d := DimensionOfMatrixGroup(G); - M := d / First(Primes, p -> RemInt(d, p) = 0); # upper bound for top degree - options.action := "imprimitive action"; - else - Error("todo"); - fi; - - options.ForSingleComponentGroup.M := Minimum(options.ForSingleComponentGroup.M, M); - return true; -end); - -BindGlobal("WPR_SingleComponentGroup", function(ri, data, options) - local timer, name, S; - # ------------------------------------------------------------- # - # Step 1 : Compute a single-component group S isomorphic to T # - # ------------------------------------------------------------- # - Info(WPR_Info, 2, "\n"); - Info(WPR_Info, 1, "Step 1 : ", "Compute a single-component group S"); - Info(WPR_Info, 2, "---------------------------------------------------------------"); - timer := Runtime(); - S := SingleComponentGroup(ri, options.ForSingleComponentGroup); # with memory - timer := Runtime() - timer; - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); - data.S := S; - return true; -end); - -BindGlobal("WPR_TopGroupDomain", function(ri, data, options) - local timer, name, G, S, S_withoutMem, domainData, W; - G := Grp(ri); - S := data.S; - S_withoutMem := Group(List(GeneratorsOfGroup(S), StripMemory)); - Info(WPR_Info, 2, "\n"); - Info(WPR_Info, 1, "Step 3 : ", "Compute a faithful H-set"); - Info(WPR_Info, 2, "-------------------------------------------------------------------"); - timer := Runtime(); - # exploit representations - if IsPermGroup(G) then - if options.action = "product action" then - domainData := TopGroupDomainViaProductAction(ri, S_withoutMem, options.ForTopGroupDomain); - elif options.action = "imprimitive action" then - # TODO - fi; - elif IsMatrixGroup(G) then - if options.action = "imprimitive action" then - W := TopGroupPointViaLinearAction(S); - data.invariantSubspace := W; - domainData := TopGroupDomainViaLinearAction(ri, W, options.ForTopGroupDomain); - fi; - fi; - # generic fallback - if not IsBound(domainData) then - if options.simpleBaseComp then - domainData := TopGroupDomainViaSimpleSubgroup(ri, S_withoutMem, options.ForTopGroupDomain); - else - domainData := TopGroupDomainViaGenericSubgroup(ri, S_withoutMem, options.ForTopGroupDomain); - fi; - fi; - timer := Runtime() - timer; - if domainData = fail then - Info(WPR_Info, 1, "Failure: invalid domain"); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); - return fail; - fi; - for name in RecNames(domainData) do - data.(name) := domainData.(name); - data.m := Length(domainData.domain); - od; - Info(WPR_Info, 2, "m = ", data.m); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); - return true; -end); \ No newline at end of file diff --git a/gap/SingleComponentGroup.gi b/gap/SingleComponentGroup.gi deleted file mode 100644 index f6a5b3d..0000000 --- a/gap/SingleComponentGroup.gi +++ /dev/null @@ -1,200 +0,0 @@ -# args: ri[, options] -# - ri is recog node -# - options are user options, see in code -# Returns single-component group -InstallGlobalFunction("SingleComponentGroup", function(args...) - local ri, userOptions, options, name, S, l1, l2, P, R, B, i, descendOptions, logEps; - - # ================================================== - # Input extraction - # ================================================== - if Length(args) = 0 or Length(args) > 2 then - Error("Usage: SingleComponentGroup(ri[, options])"); - fi; - - ri := args[1]; - userOptions := rec(); - if Length(args) = 2 then - userOptions := args[2]; - fi; - - # ================================================== - # Default options - # ================================================== - options := rec( - # -- Error control ------------------------------------------- - heuristic := true, # whether to use heuristic values instead of explicit ones - eps := 1/100, # error probability - M := 20, # upper bound for degree of top group - - # -- Strategy flags ------------------------------------------- - P := [2, 3, 5, 7], # prime numbers to use in a step - randomElementGenerator # function to generate random elements - := QuickRandomSubproduct, - useMemory := true, # whether to use memory for group elements - useBaseGroupInPhase2 := false, # use base group instead of previous group in phase 2 - useBaseGroupAtEnd := true, # use base group at end (ignored if useBaseGroupInPhase2) - socleType := fail, # socleType - updateParameters := false, # whether to update parameters after phase 1 - - # -- Phase iteration counts ------------------------------------------- - l1 := 5, # number of iterations in phase 1 - l2 := 35, # number of iterations in phase 2 - - # -- Normal closure effort parameters --------------------------------- - n1 := 5, # effort per step in phase 1 - n2 := 5, # effort per step in phase 2 - n0 := 2, # effort at final step (used only if useBaseGroupAtEnd) - ); - - # ================================================== - # Input validation - # ================================================== - - # Check recog node - if not IsRecogNode(ri) then - Error("First argument must be a recog node"); - fi; - - # Validate and apply user-provided options - for name in RecNames(userOptions) do - if not name in RecNames(options) then - Error("Invalid option name: ", name); - fi; - options.(name) := userOptions.(name); - od; - - # ================================================== - # Algorithm - # ================================================== - - if options.useMemory then - S := Group(ri!.gensHmem); - else - S := Grp(ri); - fi; - R := SingleComponentGroup_ReductionRate(options.socleType); - if not options.heuristic then - P := [2]; - Info(WPR_Info, 2, "Reduction rate probabilities for a step in each phase:"); - Info(WPR_Info, 2, "\tP_1 = ", R[1]); - Info(WPR_Info, 2, "\tP_2 = ", R[2]); - else - P := options.P; - fi; - - # -- Phase 1 ------------------------------------------- - l1 := SingleComponentGroup_NrIterations1(R[1], options.eps/2); - if options.heuristic then - l1 := Minimum(l1, options.l1); - fi; - descendOptions := rec( - randomElementGenerator := options.randomElementGenerator, - n := options.n1, - P := P, - ); - Info(WPR_Info, 2, "Bounds for Phase 1:"); - Info(WPR_Info, 2, "\tl_1 = ", l1); - Info(WPR_Info, 3, "Start Iteration for Phase 1..."); - for i in [1 .. l1] do - S := SingleComponentGroup_Descend(S, S, descendOptions); - od; - Info(WPR_Info, 3, "...Finished Iteration for Phase 1"); - - # -- Update Parameters --------------------------------- - B := S; # supposedly inside base group - if options.updateParameters then - SingleComponentGroup_UpdateParameters(options, B); - fi; - - # -- Phase 2 ------------------------------------------- - l2 := SingleComponentGroup_NrIterations2(R[2], options.M, options.eps/2); - if options.heuristic then - l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M)))), options.l2); - fi; - descendOptions := rec( - randomElementGenerator := options.randomElementGenerator, - n := options.n2, - P := P, - ); - Info(WPR_Info, 2, "Bounds for Phase 2:"); - Info(WPR_Info, 2, "\tl_2 = ", l2); - Info(WPR_Info, 3, "Start Iteration for Phase 2..."); - for i in [1 .. l2] do - if options.useBaseGroupInPhase2 then - S := SingleComponentGroup_Descend(S, B, descendOptions); - else - S := SingleComponentGroup_Descend(S, S, descendOptions); - fi; - od; - Info(WPR_Info, 3, "...Finished Iteration for Phase 2"); - - # -- Post ------------------------------------------- - # As a pre-caution, take normal closure in base group, if we descended too far - if not options.useBaseGroupInPhase2 and options.useBaseGroupAtEnd then - Info(WPR_Info, 3, "Start computing normal closure in base group..."); - S := QuickNormalClosure(S, B, options.n0); - Info(WPR_Info, 3, "... Finished computing normal closure in base group"); - fi; - return S; - -end); - -# args: H, G, options -# - for options, see SingleComponentGroup. -# - H is current group in iteration step -# - computes normal closure in G -# Returns next group in iteration step -InstallGlobalFunction("SingleComponentGroup_Descend", function(H, G, options) - local y, ord, P, p, z; - y := options.randomElementGenerator(H); - ord := Order(y); - P := options.P{QuickRandomPermList(Length(options.P))}; - for p in P do - if (p = 2 and IsEvenInt(ord)) - or RemInt(ord, p) = 0 then - z := y ^ (ord / p); - return QuickNormalClosure([z], G, options.n); - fi; - od; - return H; -end); - -InstallGlobalFunction( "SingleComponentGroup_ReductionRate", function(socleType) - if socleType = fail then - socleType := "Alt"; - fi; - if socleType = "Alt" then - return [1/2, 1/3]; - fi; - Error("Invalid socle type: ", socleType); -end); - -InstallGlobalFunction( "SingleComponentGroup_NrIterations1", function(p1, eps) - local logEps; - logEps := Log(Float(1 / eps)); - return Int(Ceil(logEps/Log(Float(1 / (1 - p1))))); -end); - -InstallGlobalFunction( "SingleComponentGroup_NrIterations2", function(p2, M, eps) - local delta, c, r, k, m, logDelta, l_lin, l_log, l2; - delta := eps/2; - logDelta := Log(Float(1 / delta)); - c := 2 * (1 + 1/p2); - r := 1 - p2/2; - m := 2*c; - if m < M then - k := Int(Ceil(Log(Float(M/c))/Log(Float(1/r)))); - l_log := Int(Ceil(Maximum(Float(4 * k), 16 * logDelta))); - else - l_log := 0; - fi; - l_lin := Int(Ceil(Maximum(Float(2 / p2 * m), 8 / p2 * logDelta))); - l2 := Int(Ceil(Maximum(Float(2 / p2 * M), 8 / p2 * logDelta))); - return Minimum(l2, l_log + l_lin); -end); - -InstallGlobalFunction("SingleComponentGroup_UpdateParameters", function(options, B) - return; # TODO -end); - diff --git a/gap/TopGroupAction.gi b/gap/TopGroupAction.gi deleted file mode 100644 index a266cd9..0000000 --- a/gap/TopGroupAction.gi +++ /dev/null @@ -1,239 +0,0 @@ -BindGlobal("DoCommuteElms", function(x, y) - return x * y = y * x; -end); - -BindGlobal("DoCommuteGroups", function(A, B) - local a, b; - for a in GeneratorsOfGroup(A) do - for b in GeneratorsOfGroup(B) do - if not DoCommuteElms(a, b) then - return false; - fi; - od; - od; - return true; -end); - -BindGlobal("TopGroupDomainViaSimpleSubgroup", function(args...) - local ri, s, userOptions; - if Length(args) < 2 or Length(args) > 3 then - Error("Usage: TopGroupDomainViaSimpleSubgroup(ri, s[, options])"); - fi; - - ri := args[1]; - s := args[2]; - userOptions := rec(); - if Length(args) = 3 then - userOptions := args[3]; - fi; - userOptions.isEqual := {a, b} -> not DoCommuteGroups(a,b); # if groups do not commute, groups must be equal - userOptions.isDistinguishable := {a, b} -> true; # if groups commute, groups must be disjoint - - return BlackBoxOrbit(ri, s, userOptions); -end); - -BindGlobal("TopGroupDomainViaGenericSubgroup", function(args...) - local ri, s, userOptions; - if Length(args) < 2 or Length(args) > 3 then - Error("Usage: TopGroupDomainViaGenericSubgroup(ri, s[, options])"); - fi; - - ri := args[1]; - s := args[2]; - userOptions := rec(); - if Length(args) = 3 then - userOptions := args[3]; - fi; - userOptions.isEqual := {a, b} -> false; # we cannot check for equality without further assumptions - userOptions.isDistinguishable := {a, b} -> DoCommuteGroups(a,b); # if groups commute, then they might lie in different components - userOptions.isConflict := {p, P} -> Length(P) >= 2; # we found two groups with which p does not commute - userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); # we merge these groups and hope that we now cover the socle in the component - - return BlackBoxOrbit(ri, s, userOptions); -end); - -BindGlobal("TopGroupPointViaLinearAction", function(S) - local d, q, M, v1, v2, L1, L2, W; - d := DimensionOfMatrixGroup(S); - q := Size(DefaultFieldOfMatrixGroup(S)); - # S acts on W + U - # W invariant space, dim(W) = d - # U fixed space, dim(U) = (m-1)*d - M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); - v1 := QuickRandomVector(d,q); - v2 := QuickRandomVector(d,q); - # basis of W + < [v]\rho_U > - L1 := MTX.SubmoduleGModule(M, v1);; - L2 := MTX.SubmoduleGModule(M, v2);; - W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); - return W; -end); - -BindGlobal("TopGroupDomainViaLinearAction", function(args...) - local ri, s, q, userOptions; - if Length(args) < 2 or Length(args) > 3 then - Error("Usage: TopGroupDomainViaLinearAction(ri, s[, options])"); - fi; - - ri := args[1]; - q := Size(DefaultFieldOfMatrixGroup(Grp(ri))); - s := args[2]; - userOptions := rec(); - if Length(args) = 3 then - userOptions := args[3]; - fi; - userOptions.isEqual := {a, b} -> a = b; - userOptions.isDistinguishable := {a, b} -> IsTrivial(Intersection(a, b)); - userOptions.isConflict := {p, P} -> Length(P) >= 1; - userOptions.resolveConflict := function(p1, P) - local p2, pNew; - p2 := P[1]; - pNew := VectorSpace(GF(q), Concatenation(Basis(p1),Basis(p2))); - Basis(pNew); - Dimension(pNew); - return pNew; - end; - - return BlackBoxOrbit(ri, s, userOptions); - -end); - -BindGlobal("TopGroupDomainViaProductAction", function(args...) - local ri, s, userOptions; - if Length(args) < 2 or Length(args) > 3 then - Error("Usage: TopGroupDomainViaProductAction(ri, s[, options])"); - fi; - - ri := args[1]; - s := args[2]; - userOptions := rec(); - if Length(args) = 3 then - userOptions := args[3]; - fi; - userOptions.isEqual := {a, b} -> Set(Orbit(a, 1)) = Set(Orbit(b, 1)); - userOptions.isDistinguishable := {a, b} -> Size(Intersection(Orbit(a, 1), Orbit(b, 1))) = 1; - userOptions.isConflict := {p, P} -> Length(P) >= 1; - userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); - - return BlackBoxOrbit(ri, s, userOptions); -end); - -InstallGlobalFunction("BlackBoxOrbit", function(args...) - local ri, s, userOptions, options, name, G, t, domain, i, a, b, g, p, isEq, foundNew, indistinguishablePoints, j; - - # ================================================== - # Input extraction - # ================================================== - if Length(args) < 2 or Length(args) > 3 then - Error("Usage: BlackBoxOrbit(ri, s[, options])"); - fi; - - ri := args[1]; - s := args[2]; - userOptions := rec(); - if Length(args) = 3 then - userOptions := args[3]; - fi; - - # ================================================== - # Default options - # ================================================== - options := rec( - # -- Strategy flags ------------------------------------------- - recursionDepth := 1, - recursionMaxDepth := 5, - maximalBoundOnTopDegree := 50, - useMemory := true, # whether to use memory for group elements - # -- Action oracles ------------------------------------------- - act := OnPoints, - isEqual := \=, # isEqual returns true if p and b are equal - # returns false if we cannot determine whether p and b are equal - isDistinguishable := {a, b} -> true, # if IsEqual returns false (so a = b could not be proven, but might be true), - # this returns true if we can distinguish between a and b. - # If points are not distinguishable, we assume they are equal for the moment - isConflict := {p, indistinguishablePoints} -> false, # return true if domain might not be invariant under the action - resolveConflict := {p, indistinguishablePoints} -> fail, # try to find different domain or return fail, - ); - - # ================================================== - # Input validation - # ================================================== - - # Check recog node - if not IsRecogNode(ri) then - Error("First argument must be a recog node"); - fi; - - # Validate and apply user-provided options - for name in RecNames(userOptions) do - if not name in RecNames(options) then - Error("Invalid option name: ", name); - fi; - options.(name) := userOptions.(name); - od; - - # ================================================== - # Algorithm - # ================================================== - - if options.recursionDepth > options.recursionMaxDepth then - return fail; - fi; - Info(WPR_Info, 2, "Recursion Depth: ", options.recursionDepth); - if options.useMemory then - G := Group(ri!.gensHmem); - else - G := Grp(ri); - fi; - t := [One(G)]; - domain := [s]; - i := 1; - - # -- Iteration ------------------------------------- - while i <= Length(domain) do - a := domain[i]; - for g in GeneratorsOfGroup(G) do - p := options.act(a, StripMemory(g)); - foundNew := true; - indistinguishablePoints := []; - for j in [1 .. Length(domain)] do - b := domain[j]; - isEq := options.isEqual(p, b); - if isEq then - foundNew := false; - break; - # can we distinguish between p and b via our action? - elif not options.isDistinguishable(p, b) then - Add(indistinguishablePoints, b); - # We cannot distinguish between these points, - # so we need to assume for now that they are equal. - foundNew := false; - # If we can prove a conflict, we need to adjust the domain - if options.isConflict(p, indistinguishablePoints) then - Info(WPR_Info, 2, "Found conflict"); - # The domain is not invariant under the action, - # thus we try compute a new point to resolve the conflict - s := options.resolveConflict(p, indistinguishablePoints); - if s = fail then - Info(WPR_Info, 2, "Could not resolve conflict"); - return fail; - fi; - Error("Examine Me!"); - options.recursionDepth := options.recursionDepth + 1; - return BlackBoxOrbit(ri, s, options); - fi; - fi; - od; - if foundNew then - if Length(domain) >= options.maximalBoundOnTopDegree then - Info(WPR_Info, 2, "Domain too large, abort now"); - return fail; - fi; - Add(t, t[i] * g); - Add(domain, p); - fi; - od; - i := i + 1; - od; - return rec(domain := domain, transversal := t); -end); \ No newline at end of file diff --git a/gap/WPrecog.gd b/gap/WPrecog.gd index 7c9400e..305a45e 100644 --- a/gap/WPrecog.gd +++ b/gap/WPrecog.gd @@ -14,17 +14,9 @@ #! This section will describe the example #! methods of WPrecog -DeclareGlobalFunction("QuickRandomPermList"); -DeclareGlobalFunction("QuickRandomSubproduct"); -DeclareGlobalFunction("QuickNormalClosure"); DeclareGlobalFunction("SingleComponentGroup"); -DeclareGlobalFunction("SingleComponentGroup_Descend"); -DeclareGlobalFunction("SingleComponentGroup_ReductionRate"); -DeclareGlobalFunction("SingleComponentGroup_NrIterations1"); -DeclareGlobalFunction("SingleComponentGroup_NrIterations2"); -DeclareGlobalFunction("SingleComponentGroup_UpdateParameters"); - DeclareGlobalFunction("BlackBoxOrbit"); +DeclareGlobalFunction("BlackBoxAction"); diff --git a/gap/subroutines/Image.gi b/gap/subroutines/Image.gi new file mode 100644 index 0000000..00e3e30 --- /dev/null +++ b/gap/subroutines/Image.gi @@ -0,0 +1,84 @@ + +BindGlobal("WPR_SetupImage", function(ri, data, options) + local G; + G := Grp(ri); + # exploit representations + if IsPermGroup(G) then + if options.action = "product action" then + return SetupImageViaProductAction(ri, data, options); + elif options.action = "imprimitive action" then + # TODO + fi; + elif IsMatrixGroup(G) then + if options.action = "imprimitive action" then + return SetupImageViaLinearAction(ri, data, options); + fi; + fi; + # generic fallback + return SetupImageViaConjugationAction(ri, data, options); +end); + + +BindGlobal("WPR_Image", function(g, ri, data, options) + local G; + G := Grp(ri); + # exploit representations + if IsPermGroup(G) then + if options.action = "product action" then + return ImageViaProductAction(g, ri, data, options); + elif options.action = "imprimitive action" then + # TODO + fi; + elif IsMatrixGroup(G) then + if options.action = "imprimitive action" then + return ImageViaLinearAction(g, ri, data, options); + fi; + fi; + # generic fallback + return ImageViaConjugationAction(g, ri, data, options); +end); + +BindGlobal("WPR_Projection", function(g, ri, data, options) + local G; + G := Grp(ri); + # exploit representations + if IsPermGroup(G) then + if options.action = "product action" then + return WPR_TopGroupActionViaProductAction(g, data.domain); + elif options.action = "imprimitive action" then + # TODO + fi; + elif IsMatrixGroup(G) then + if options.action = "imprimitive action" then + return WPR_TopGroupActionViaLinearAction(g, data.domain); + fi; + fi; + # generic fallback + return TopGroupActionViaSubgroup(g, data.domain); +end); + +BindGlobal("WPR_Embedding", function(ri, data, options) + local W, embedding; + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step ", data.currentStep, ": Compute embedding function"); + Info(WPR_Info, 2, "--------------------------------------------------"); + data.currentStep := data.currentStep + 1; + data.projectionFunction := function(g) + return WPR_Projection(StripMemory(g), ri, data, options); + end; + + WPR_SetupImage(ri, data, options); + data.imageFunc := function(g) + return WPR_Image(StripMemory(g), ri, data, options); + end; + + W := data.parentWreathProduct; + embedding := MappingByFunction(Grp(ri), W, data.imageFunc); + if embedding = fail then + return fail; + fi; + + data.embedding := embedding; + + return true; +end); diff --git a/gap/subroutines/Image/ViaConjugationAction.gi b/gap/subroutines/Image/ViaConjugationAction.gi new file mode 100644 index 0000000..c76fbc8 --- /dev/null +++ b/gap/subroutines/Image/ViaConjugationAction.gi @@ -0,0 +1,8 @@ + +BindGlobal("SetupImageViaConjugationAction", function(ri, data, options) + # TODO +end); + +BindGlobal("ImageViaConjugationAction", function(g, ri, data, options) + # TODO +end); \ No newline at end of file diff --git a/gap/subroutines/Image/ViaLinearAction.gi b/gap/subroutines/Image/ViaLinearAction.gi new file mode 100644 index 0000000..968dbc3 --- /dev/null +++ b/gap/subroutines/Image/ViaLinearAction.gi @@ -0,0 +1,8 @@ + +BindGlobal("SetupImageViaLinearAction", function(ri, data, options) + # TODO +end); + +BindGlobal("ImageViaLinearAction", function(g, ri, data, options) + # TODO +end); \ No newline at end of file diff --git a/gap/subroutines/Image/ViaProductAction.gi b/gap/subroutines/Image/ViaProductAction.gi new file mode 100644 index 0000000..841d912 --- /dev/null +++ b/gap/subroutines/Image/ViaProductAction.gi @@ -0,0 +1,86 @@ + +BindGlobal("SetupImageViaProductAction", function(ri, data, options) + local riS, domainDataS, n, m; + m := data.m; + n := RootInt(NrMovedPoints(Grp(ri)), m); + riS := RecogNode(Group(List(GeneratorsOfGroup(data.S), StripMemory))); + domainDataS := BlackBoxOrbit(riS, 1, rec( + useMemory := false, + maximalBoundOnTopDegree := n)); + data.domainS := domainDataS.domain; + data.transversalS := domainDataS.transversal; + if n <> Length(data.transversalS) then + return fail; + fi; + data.translationS := MappingPermListList(data.domainS, [1..n]); + data.parentWreathProduct := WreathProduct(SymmetricGroup(n), SymmetricGroup(m)); + return true; +end); + +BindGlobal("ImageViaProductAction", function(g, ri, data, options) + local pi, m, domain, t, riS, domainDataS, orb, s, n, W, sigma, w, i, j, k, points, p, candidates1, x, L, l, candidates2, images; + pi := data.projectionFunction(g); + if pi = fail then + return fail; + fi; + m := data.m; + t := List(data.transversal, StripMemory); + orb := data.domainS; + s := data.transversalS; + n := Length(s); + W := data.parentWreathProduct; + sigma := data.translationS; + w := EmptyPlist(m + 1); + # now t_i*g*t_j^(-1) acts on O1 like z_i*g*z_j^(-1), + # hence like the image under phi that we want to define. + for i in [1 .. m] do + j := i^pi; + points := []; + for k in [1 .. n] do + p := s[k]^(t[i] * g * t[j]^(-1)); + points[k] := RestrictedPerm(p, orb)^sigma; + od; + # try to find x = 1^w_i + # Frequency Analysis: check that x has n distinct image points + candidates1 := []; + for x in [1 .. n] do + L := []; + for k in [1 .. n] do + l := x^points[k]; + if l in L then + break; + else + Add(L, l); + fi; + od; + if Length(L) = n then + Add(candidates1, x); + fi; + od; + if Length(candidates1) = 0 then + return fail; + elif Length(candidates1) = 1 then + x := candidates1[1]; + else + candidates2 := []; + for x in candidates2 do + if ForAll([1..n], k -> CycleLength(points[k], [1..n], x) = CycleLength(s[k], [1..n], 1)) then + Add(candidates2, x); + fi; + od; + if Length(candidates2) = 1 then + x := candidates2[1]; + else + return fail; + fi; + fi; + # now we found x = 1^w_i. Thus x^points[k] = k^w_i. + images := []; + for k in [1 .. n] do + images[k] := x^points[k]; + od; + w[i] := PermList(images); + od; + Add(w, pi); + return WreathProductElementList(W, w); +end); diff --git a/gap/subroutines/Init.gi b/gap/subroutines/Init.gi new file mode 100644 index 0000000..3e614e4 --- /dev/null +++ b/gap/subroutines/Init.gi @@ -0,0 +1,54 @@ +BindGlobal("WPR_InitOptions", function(ri, data, options) + local timer, name, G, isPrim, N, F, M, d, q; + G := Grp(ri); + Info(WPR_Info, 1, "Step ", data.currentStep, ": Initialize bounds for wreath product recognition"); + Info(WPR_Info, 2, "--------------------------------------------------------"); + data.currentStep := data.currentStep + 1; + if IsPermGroup(G) then + Info(WPR_Info, 2, "G is permutation group on ", NrMovedPoints(G), " points"); + isPrim := fail; + if options.action = fail and options.checkPrimitivity then + isPrim := IsPrimitive(G); + elif options.action = "product action" then + isPrim := true; + elif options.action = "imprimitive action" then + isPrim := false; + fi; + if isPrim = true or isPrim = fail then + # assume product action + N := NrMovedPoints(G); + F := Collected(PartialFactorization(N, 0)); + M := F[1][2]; # upper bound for top degree + if ForAll(F, f -> f[2] = M) then + options.action := "product action"; + isPrim := true; + Info(WPR_Info, 2, "Assume product action on n^m points with m <= ", M); + fi; + fi; + if isPrim = false or isPrim = fail then + N := NrMovedPoints(G); + M := N / First(Primes, p -> RemInt(N, p) = 0); # upper bound for top degree + options.action := "imprimitive action"; + isPrim := false; + Info(WPR_Info, 2, "Assume imprimitive action on n*m points with m <= ", M); + fi; + elif IsMatrixGroup(G) then + d := DimensionOfMatrixGroup(G); + q := Size(FieldOfMatrixGroup(G)); + Info(WPR_Info, 2, "G is matrix group of dimension ", d, " over GF(", q, ")"); + M := d / First(Primes, p -> RemInt(d, p) = 0); # upper bound for top degree + options.action := "imprimitive action"; + Info(WPR_Info, 2, "Assume imprimitve action on n*m points with m <= ", M); + else + Error("todo"); + fi; + + if IsBound(options.forSingleComponentGroup.M) then + Info(WPR_Info, 2, "User specified an upper bound for m"); + options.forSingleComponentGroup.M := Minimum(options.forSingleComponentGroup.M, M); + Info(WPR_Info, 2, "Assume m <= ", M); + else + options.forSingleComponentGroup.M := M; + fi; + return true; +end); diff --git a/gap/subroutines/RecogniseBaseComponent.gi b/gap/subroutines/RecogniseBaseComponent.gi new file mode 100644 index 0000000..fe510e6 --- /dev/null +++ b/gap/subroutines/RecogniseBaseComponent.gi @@ -0,0 +1,35 @@ +BindGlobal("WPR_RecogniseBaseComponent", function(ri, data, options) + local timer, name, G, gensS, S_withoutMem, isoReductionForS, S_reduced, riS_reduced, orb; + G := Grp(ri); + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step ", data.currentStep, ": Recognise base component"); + Info(WPR_Info, 2, "-------------------------------------------------------------------"); + data.currentStep := data.currentStep + 1; + timer := Runtime(); + gensS := List(GeneratorsOfGroup(data.S), StripMemory); + S_withoutMem := Group(gensS); + isoReductionForS := GroupHomomorphismByFunction(S_withoutMem, S_withoutMem, x -> x); + if IsPermGroup(G) then + if options.action = "product action" then + orb := Orbit(S_withoutMem, 1); + isoReductionForS := ActionHomomorphism(S_withoutMem, orb, OnPoints); + fi; + fi; + data.isoReductionForS := isoReductionForS; + S_reduced := Image(data.isoReductionForS); + if options.recogniseBaseComponentViaIsomorphism then + Error("TODO"); + else + riS_reduced := RecogniseGroup(S_reduced); + fi; + timer := Runtime() - timer; + if riS_reduced = fail then + Info(WPR_Info, 1, "Failure: could not recognise base component"); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return fail; + fi; + data.riS_reduced := riS_reduced; + data.niceGensForS := ResultOfStraightLineProgram(slptonice(data.riS_reduced), gensS); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return true; +end); \ No newline at end of file diff --git a/gap/subroutines/RecogniseTopComponent.gi b/gap/subroutines/RecogniseTopComponent.gi new file mode 100644 index 0000000..e69de29 diff --git a/gap/subroutines/SingleComponentGroup.gi b/gap/subroutines/SingleComponentGroup.gi new file mode 100644 index 0000000..213368e --- /dev/null +++ b/gap/subroutines/SingleComponentGroup.gi @@ -0,0 +1,204 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## SingleComponentGroup.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains the functions to blindly descend into +## a single-component group. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Called by RecogniseWreathProduct. +## Wrapper for SingleComponentGroup. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_SingleComponentGroup", function(ri, data, options) + local timer, name, S; + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step ", data.currentStep, ": Compute a single-component group S"); + Info(WPR_Info, 2, "---------------------------------------------------------------"); + data.currentStep := data.currentStep + 1; + timer := Runtime(); + S := SingleComponentGroup(ri, options.forSingleComponentGroup); # with memory + timer := Runtime() - timer; + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + data.S := S; + return true; +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: ri[, options] +## - ri is recog node +## - options are user options, see in code +## +## Returns a supposedly single-component group. +## The backbone of WPR_SingleComponentGroup. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +InstallGlobalFunction("SingleComponentGroup", function(args...) + local ri, userOptions, options, name, S, l1, l2, primes, R, B, i, descendOptions, logEps; + + # ======================================================================= + # Input extraction + # ======================================================================= + + if Length(args) = 0 or Length(args) > 2 then + Error("Usage: SingleComponentGroup(ri[, options])"); + fi; + + ri := args[1]; + userOptions := rec(); + if Length(args) = 2 then + userOptions := args[2]; + fi; + + # ======================================================================= + # Default options + # ======================================================================= + options := rec( + # -- Error control ------------------------------------------------------------------------- + heuristic := true, # whether to use heuristic values instead of explicit ones + eps := 1/100, # error probability + M := 20, # upper bound for degree of top group + + # -- Strategy flags ------------------------------------------------------------------------ + primes := [2, 3, 5, 7], # prime numbers to use in a step + randomElementGenerator # function to generate random elements + := QuickRandomSubproduct, + useMemory := true, # whether to use memory for group elements + useBaseGroupInPhase2 := false, # use base group instead of previous group in phase 2 + useBaseGroupAtEnd := true, # use base group at end (ignored if useBaseGroupInPhase2) + socleType := fail, # socleType + updateParameters := false, # whether to update parameters after phase 1 + + # -- Phase iteration counts ---------------------------------------------------------------- + l1 := 5, # number of iterations in phase 1 + l2 := 35, # number of iterations in phase 2 + + # -- Normal closure effort parameters ------------------------------------------------------ + n1 := 5, # effort per step in phase 1 + n2 := 5, # effort per step in phase 2 + n0 := 2, # effort at final step (used only if useBaseGroupAtEnd) + ); + + # ======================================================================= + # Input validation + # ======================================================================= + + # Check recog node + if not IsRecogNode(ri) then + Error("First argument must be a recog node"); + fi; + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ======================================================================= + # Algorithm + # ======================================================================= + + if options.useMemory then + S := Group(ri!.gensHmem); + else + S := Grp(ri); + fi; + R := WPR_SCG_ReductionRate(options.socleType); + if not options.heuristic then + primes := [2]; + Info(WPR_Info, 2, "Reduction rate probabilities for a step in each phase:"); + Info(WPR_Info, 2, "\tP_1 = ", R[1]); + Info(WPR_Info, 2, "\tP_2 = ", R[2]); + else + primes := options.primes; + fi; + + # -- Phase 1 ------------------------------------------------------------ + l1 := WPR_SCG_NrIterations1(R[1], options.eps/2); + if options.heuristic then + l1 := Minimum(l1, options.l1); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n1, + primes := primes, + ); + Info(WPR_Info, 2, "Bounds for Phase 1:"); + Info(WPR_Info, 2, "\tl_1 = ", l1); + Info(WPR_Info, 3, "Start Iteration for Phase 1..."); + for i in [1 .. l1] do + S := WPR_SCG_Descend(S, S, descendOptions); + od; + Info(WPR_Info, 3, "...Finished Iteration for Phase 1"); + + # -- Update Parameters -------------------------------------------------- + B := S; # supposedly inside base group + if options.updateParameters then + WPR_SCG_UpdateParameters(options, B); + fi; + + # -- Phase 2 ------------------------------------------------------------ + l2 := WPR_SCG_NrIterations2(R[2], options.M, options.eps/2); + if options.heuristic then + l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M)))), options.l2); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n2, + primes := primes, + ); + Info(WPR_Info, 2, "Bounds for Phase 2:"); + Info(WPR_Info, 2, "\tl_2 = ", l2); + Info(WPR_Info, 3, "Start Iteration for Phase 2..."); + for i in [1 .. l2] do + if options.useBaseGroupInPhase2 then + S := WPR_SCG_Descend(S, B, descendOptions); + else + S := WPR_SCG_Descend(S, S, descendOptions); + fi; + od; + Info(WPR_Info, 3, "...Finished Iteration for Phase 2"); + + # -- Post --------------------------------------------------------------- + # As a pre-caution, take normal closure in base group, if we descended too far + if not options.useBaseGroupInPhase2 and options.useBaseGroupAtEnd then + Info(WPR_Info, 3, "Start computing normal closure in base group..."); + S := QuickNormalClosure(S, B, options.n0); + Info(WPR_Info, 3, "... Finished computing normal closure in base group"); + fi; + return S; + +end); diff --git a/gap/subroutines/SingleComponentGroup/Helpers.gi b/gap/subroutines/SingleComponentGroup/Helpers.gi new file mode 100644 index 0000000..3b489c9 --- /dev/null +++ b/gap/subroutines/SingleComponentGroup/Helpers.gi @@ -0,0 +1,111 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## SingleComponentGroup/Helpers.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains helper functions for SingleComponentGroup. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: H, G, options +## - H is current group in iteration step +## - computes normal closure in G +## - for options, see SingleComponentGroup. +## +## Returns next group in iteration step. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_SCG_Descend", function(H, G, options) + local y, ord, primes, p, z; + y := options.randomElementGenerator(H); + ord := Order(y); + primes := options.primes{QuickRandomPermutedList(Length(options.primes))}; + for p in primes do + if (p = 2 and IsEvenInt(ord)) + or RemInt(ord, p) = 0 then + z := y ^ (ord / p); + return QuickNormalClosure([z], G, options.n); + fi; + od; + return H; +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Explicit probability estimations. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal( "WPR_SCG_ReductionRate", function(socleType) + if socleType = fail then + socleType := "Alt"; + fi; + if socleType = "Alt" then + return [1/2, 1/3]; + fi; + Error("Invalid socle type: ", socleType); +end); + +BindGlobal( "WPR_SCG_NrIterations1", function(p1, eps) + local logEps; + logEps := Log(Float(1 / eps)); + return Int(Ceil(logEps/Log(Float(1 / (1 - p1))))); +end); + +BindGlobal( "WPR_SCG_NrIterations2", function(p2, M, eps) + local delta, c, r, k, m, logDelta, l_lin, l_log, l2; + delta := eps/2; + logDelta := Log(Float(1 / delta)); + c := 2 * (1 + 1/p2); + r := 1 - p2/2; + m := 2*c; + if m < M then + k := Int(Ceil(Log(Float(M/c))/Log(Float(1/r)))); + l_log := Int(Ceil(Maximum(Float(4 * k), 16 * logDelta))); + else + l_log := 0; + fi; + l_lin := Int(Ceil(Maximum(Float(2 / p2 * m), 8 / p2 * logDelta))); + l2 := Int(Ceil(Maximum(Float(2 / p2 * M), 8 / p2 * logDelta))); + return Minimum(l2, l_log + l_lin); +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Returns updated parameters after Phase 1, +## assuming that B is a subgroup of the base group. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_SCG_UpdateParameters", function(options, B) + return; # TODO +end); diff --git a/gap/subroutines/TopGroupDomainAndAction.gi b/gap/subroutines/TopGroupDomainAndAction.gi new file mode 100644 index 0000000..5419fd9 --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction.gi @@ -0,0 +1,303 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## TopGroupDomainAndAction.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains the black box functions to compute +## a top group domain and the induced action. +## Specialized functions are in the respective directory. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Called by RecogniseWreathProduct. +## Wrapper for WPR_TopGroupDomainVia___. +## These use BlackBoxOrbit under the hood. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_TopGroupDomain", function(ri, data, options) + local timer, name, G, gensS, S_withoutMem, domainData, W; + G := Grp(ri); + if IsBound(data.niceGensForS) then + gensS := data.niceGensForS; + else + gensS := List(GeneratorsOfGroup(data.S), StripMemory); + fi; + S_withoutMem := Group(gensS); + Info(WPR_Info, 2, "\n"); + Info(WPR_Info, 1, "Step ", data.currentStep, ": Compute a faithful H-set"); + Info(WPR_Info, 2, "-------------------------------------------------------------------"); + data.currentStep := data.currentStep + 1; + timer := Runtime(); + # exploit representations + if IsPermGroup(G) then + if options.action = "product action" then + domainData := WPR_TopGroupDomainViaProductAction(ri, S_withoutMem, options.forTopGroupDomain); + elif options.action = "imprimitive action" then + # TODO + fi; + elif IsMatrixGroup(G) then + if options.action = "imprimitive action" then + W := WPR_TopGroupPointViaLinearAction(S_withoutMem); + data.invariantSubspace := W; + domainData := WPR_TopGroupDomainViaLinearAction(ri, W, options.forTopGroupDomain); + fi; + fi; + # generic fallback + if not IsBound(domainData) then + if options.assumeSimpleBaseComponent then + domainData := WPR_TopGroupDomainViaSimpleSubgroup(ri, S_withoutMem, options.forTopGroupDomain); + else + domainData := WPR_TopGroupDomainViaGenericSubgroup(ri, S_withoutMem, options.forTopGroupDomain); + fi; + fi; + timer := Runtime() - timer; + if domainData = fail then + Info(WPR_Info, 1, "Failure: invalid domain"); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return fail; + fi; + for name in RecNames(domainData) do + data.(name) := domainData.(name); + data.m := Length(domainData.domain); + od; + Info(WPR_Info, 2, "m = ", data.m); + Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + return true; +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: ri, s[, options] +## - ri is recog node with G = Grp(ri) +## - s is a single point on which G acts on +## - options are user options, see in code +## +## Returns a supposedly orbit of s under G. +## The backbone of TopGroupDomainVia___. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +InstallGlobalFunction("BlackBoxOrbit", function(args...) + local ri, s, userOptions, options, name, G, t, domain, i, a, b, g, p, isEq, foundNew, indistinguishablePoints, j; + + # ================================================== + # Input extraction + # ================================================== + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: BlackBoxOrbit(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + + # ================================================== + # Default options + # ================================================== + options := rec( + # -- Strategy flags ------------------------------------------- + recursionDepth := 1, + recursionMaxDepth := 5, + maximalBoundOnTopDegree := 50, + useMemory := true, # whether to use memory for group elements + # -- Action oracles ------------------------------------------- + act := OnPoints, + isEqual := \=, # isEqual returns true if p and b are equal + # returns false if we cannot determine whether p and b are equal + isDistinguishable := {a, b} -> true, # if IsEqual returns false (so a = b could not be proven, but might be true), + # this returns true if we can distinguish between a and b. + # If points are not distinguishable, we assume they are equal for the moment + isConflict := {p, indistinguishablePoints} -> false, # return true if domain might not be invariant under the action + resolveConflict := {p, indistinguishablePoints} -> fail, # try to find different domain or return fail, + ); + + # ================================================== + # Input validation + # ================================================== + + # Check recog node + if not IsRecogNode(ri) then + Error("First argument must be a recog node"); + fi; + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ================================================== + # Algorithm + # ================================================== + + if options.recursionDepth > options.recursionMaxDepth then + return fail; + fi; + Info(WPR_Info, 2, "Recursion Depth: ", options.recursionDepth); + if options.useMemory then + G := Group(ri!.gensHmem); + else + G := Grp(ri); + fi; + t := [One(G)]; + domain := [s]; + i := 1; + + # -- Iteration ------------------------------------- + while i <= Length(domain) do + a := domain[i]; + for g in GeneratorsOfGroup(G) do + p := options.act(a, StripMemory(g)); + foundNew := true; + indistinguishablePoints := []; + for j in [1 .. Length(domain)] do + b := domain[j]; + isEq := options.isEqual(p, b); + if isEq then + foundNew := false; + break; + # can we distinguish between p and b via our action? + elif not options.isDistinguishable(p, b) then + Add(indistinguishablePoints, b); + # We cannot distinguish between these points, + # so we need to assume for now that they are equal. + foundNew := false; + # If we can prove a conflict, we need to adjust the domain + if options.isConflict(p, indistinguishablePoints) then + Info(WPR_Info, 2, "Found conflict"); + # The domain is not invariant under the action, + # thus we try compute a new point to resolve the conflict + s := options.resolveConflict(p, indistinguishablePoints); + if s = fail then + Info(WPR_Info, 2, "Could not resolve conflict"); + return fail; + fi; + Error("Examine Me!"); + options.recursionDepth := options.recursionDepth + 1; + return BlackBoxOrbit(ri, s, options); + fi; + fi; + od; + if foundNew then + if Length(domain) >= options.maximalBoundOnTopDegree then + Info(WPR_Info, 2, "Domain too large, abort now"); + return fail; + fi; + Add(t, t[i] * g); + Add(domain, p); + fi; + od; + i := i + 1; + od; + return rec(domain := domain, transversal := t); +end); + +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## +## Args: g, domain[, options] +## - g is a group element +## - domain is a supposedly action domain of g +## - options are user options, see in code +## +## Returns a supposedly action of g on domain. +## The backbone of TopGroupActionVia___. +## Similar to BlackBoxOrbit. +## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +InstallGlobalFunction("BlackBoxAction", function(args...) + local g, domain, s, userOptions, options, name, m, images, i, j, a, b, p; + + # ================================================== + # Input extraction + # ================================================== + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: BlackBoxAction(g, domain[, options])"); + fi; + + g := args[1]; + domain := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + + # ================================================== + # Default options + # ================================================== + options := rec( + # -- Action oracles ------------------------------------------- + act := OnPoints, + isEqual := \=, # isEqual returns true if p and b are assumed to be equal + ); + + # ================================================== + # Input validation + # ================================================== + + # Validate and apply user-provided options + for name in RecNames(userOptions) do + if not name in RecNames(options) then + Error("Invalid option name: ", name); + fi; + options.(name) := userOptions.(name); + od; + + # ================================================== + # Algorithm + # ================================================== + m := Length(domain); + images := EmptyPlist(m); + for i in [1 .. m] do + a := domain[i]; + p := options.act(a, g); + for j in [1 .. m] do + if j in images then + continue; + fi; + b := domain[j]; + if options.isEqual(p, b) then + images[i] := j; + break; + fi; + od; + if not IsBound(images[i]) then + return fail; + fi; + od; + return PermList(images); +end); diff --git a/gap/subroutines/TopGroupDomainAndAction/ViaLinearAction.gi b/gap/subroutines/TopGroupDomainAndAction/ViaLinearAction.gi new file mode 100644 index 0000000..e25480a --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction/ViaLinearAction.gi @@ -0,0 +1,90 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## TopGroupDomainAndAction/ViaLinearAction.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains functions to compute a top group domain +## and the induced action considering subgroups and their linear actions. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_TopGroupPointViaLinearAction", function(S) + local d, q, M, v1, v2, L1, L2, W; + d := DimensionOfMatrixGroup(S); + q := Size(DefaultFieldOfMatrixGroup(S)); + # S acts on W + U + # W invariant space, dim(W) = d + # U fixed space, dim(U) = (m-1)*d + M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); + v1 := QuickRandomVector(d,q); + v2 := QuickRandomVector(d,q); + # basis of W + < [v]\rho_U > + L1 := MTX.SubmoduleGModule(M, v1);; + L2 := MTX.SubmoduleGModule(M, v2);; + W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); + return W; +end); + +BindGlobal("WPR_TopGroupDomainViaLinearAction", function(args...) + local ri, s, q, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupDomainViaLinearAction(ri, s[, options])"); + fi; + + ri := args[1]; + q := Size(DefaultFieldOfMatrixGroup(Grp(ri))); + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> a = b; + userOptions.isDistinguishable := {a, b} -> IsTrivial(Intersection(a, b)); + userOptions.isConflict := {p, P} -> Length(P) >= 1; + userOptions.resolveConflict := function(p1, P) + local p2, pNew; + p2 := P[1]; + pNew := VectorSpace(GF(q), Concatenation(Basis(p1),Basis(p2))); + Basis(pNew); + Dimension(pNew); + return pNew; + end; + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("WPR_TopGroupActionViaLinearAction", function(args...) + local g, domain, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupActionViaLinearAction(g, domain[, options])"); + fi; + + g := args[1]; + domain := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> a = b; + + return BlackBoxAction(g, domain, userOptions); +end); \ No newline at end of file diff --git a/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi b/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi new file mode 100644 index 0000000..de7b8f1 --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi @@ -0,0 +1,66 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## TopGroupDomainAndAction/ViaLinearAction.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains functions to compute a top group domain +## and the induced action considering subgroups in product action +## and their orbits under 1. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("WPR_TopGroupDomainViaProductAction", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupDomainViaProductAction(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> Set(Orbit(a, 1)) = Set(Orbit(b, 1)); + userOptions.isDistinguishable := {a, b} -> Size(Intersection(Orbit(a, 1), Orbit(b, 1))) = 1; + userOptions.isConflict := {p, P} -> Length(P) >= 1; + userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("WPR_TopGroupActionViaProductAction", function(args...) + local g, domain, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupActionViaProductAction(g, domain[, options])"); + fi; + + g := args[1]; + domain := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> Set(Orbit(a, 1)) = Set(Orbit(b, 1)); + + return BlackBoxAction(g, domain, userOptions); +end); \ No newline at end of file diff --git a/gap/subroutines/TopGroupDomainAndAction/ViaSubgroup.gi b/gap/subroutines/TopGroupDomainAndAction/ViaSubgroup.gi new file mode 100644 index 0000000..cb28a43 --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction/ViaSubgroup.gi @@ -0,0 +1,99 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## TopGroupDomainAndAction/ViaSubgroup.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains functions to compute a top group domain +## and the induced action considering subgroups. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + +BindGlobal("DoCommuteElms", function(x, y) + return x * y = y * x; +end); + +BindGlobal("DoCommuteGroups", function(A, B) + local a, b; + for a in GeneratorsOfGroup(A) do + for b in GeneratorsOfGroup(B) do + if not DoCommuteElms(a, b) then + return false; + fi; + od; + od; + return true; +end); + +BindGlobal("WPR_TopGroupDomainViaSimpleSubgroup", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupDomainViaSimpleSubgroup(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> not DoCommuteGroups(a,b); # if groups do not commute, groups must be equal + userOptions.isDistinguishable := {a, b} -> true; # if groups commute, groups must be disjoint + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("WPR_TopGroupDomainViaGenericSubgroup", function(args...) + local ri, s, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupDomainViaGenericSubgroup(ri, s[, options])"); + fi; + + ri := args[1]; + s := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> false; # we cannot check for equality without further assumptions + userOptions.isDistinguishable := {a, b} -> DoCommuteGroups(a,b); # if groups commute, then they might lie in different components + userOptions.isConflict := {p, P} -> Length(P) >= 2; # we found two groups with which p does not commute + userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); # we merge these groups and hope that we now cover the socle in the component + + return BlackBoxOrbit(ri, s, userOptions); +end); + +BindGlobal("TopGroupActionViaSubgroup", function(args...) + local g, domain, userOptions; + if Length(args) < 2 or Length(args) > 3 then + Error("Usage: WPR_TopGroupActionViaLinearAction(g, domain[, options])"); + fi; + + g := args[1]; + domain := args[2]; + userOptions := rec(); + if Length(args) = 3 then + userOptions := args[3]; + fi; + userOptions.isEqual := {a, b} -> not DoCommuteGroups(a,b); + + return BlackBoxAction(g, domain, userOptions); +end); diff --git a/read.g b/read.g index 33101ef..62503e5 100644 --- a/read.g +++ b/read.g @@ -10,8 +10,25 @@ BindGlobal("WPR_Info", NewInfoClass("WPR_Info")); SetInfoLevel(WPR_Info, 3); -ReadPackage( "WPrecog", "gap/Random.gi"); -ReadPackage( "WPrecog", "gap/SingleComponentGroup.gi"); -ReadPackage( "WPrecog", "gap/TopGroupAction.gi"); -ReadPackage( "WPrecog", "gap/RecogSubroutines.gi"); +ReadPackage( "WPrecog", "gap/Quick.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/Init.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/SingleComponentGroup/Helpers.gi"); +ReadPackage( "WPrecog", "gap/subroutines/SingleComponentGroup.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/RecogniseBaseComponent.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/RecogniseTopComponent.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/TopGroupDomainAndAction/ViaLinearAction.gi"); +ReadPackage( "WPrecog", "gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi"); +ReadPackage( "WPrecog", "gap/subroutines/TopGroupDomainAndAction/ViaSubgroup.gi"); +ReadPackage( "WPrecog", "gap/subroutines/TopGroupDomainAndAction.gi"); + +ReadPackage( "WPrecog", "gap/subroutines/Image/ViaConjugationAction.gi"); +ReadPackage( "WPrecog", "gap/subroutines/Image/ViaLinearAction.gi"); +ReadPackage( "WPrecog", "gap/subroutines/Image/ViaProductAction.gi"); +ReadPackage( "WPrecog", "gap/subroutines/Image.gi"); + ReadPackage( "WPrecog", "gap/Recog.gi"); From 98d011c939c4b069006736af7664bf68bb92e60a Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Sun, 13 Apr 2025 19:43:20 +0200 Subject: [PATCH 13/14] Stash progress --- 2*m*k^2 | 0 archive/MatImprimitive.gi | 61 +++++++++++++++++++ {examples => archive}/MatImprimitive.mag | 0 {examples => archive}/difficultMat.mag | 0 {examples => archive}/difficultMatG.mag | 0 examples/CreateExample.gi | 10 +++ examples/LoadExample.gi | 16 +++++ examples/LoadExample.mag | 4 ++ examples/MatImprimitive.gi | 71 ++++++---------------- examples/PermImprimitive.gi | 15 +---- examples/PermPrimitive.gi | 26 ++++---- examples/PermPrimitiveLargeBase.gi | 25 +++----- gap/Recog.gi | 19 +++++- gap/Utils.gi | 55 +++++++++++++++++ gap/subroutines/Image.gi | 7 ++- gap/subroutines/Init.gi | 4 +- gap/subroutines/RecogniseBaseComponent.gi | 8 ++- gap/subroutines/SingleComponentGroup.gi | 22 ++++--- gap/subroutines/TopGroupDomainAndAction.gi | 51 ++++++++-------- read.g | 1 + 20 files changed, 262 insertions(+), 133 deletions(-) delete mode 100644 2*m*k^2 create mode 100644 archive/MatImprimitive.gi rename {examples => archive}/MatImprimitive.mag (100%) rename {examples => archive}/difficultMat.mag (100%) rename {examples => archive}/difficultMatG.mag (100%) create mode 100644 examples/CreateExample.gi create mode 100644 examples/LoadExample.gi create mode 100644 examples/LoadExample.mag create mode 100644 gap/Utils.gi diff --git a/2*m*k^2 b/2*m*k^2 deleted file mode 100644 index e69de29..0000000 diff --git a/archive/MatImprimitive.gi b/archive/MatImprimitive.gi new file mode 100644 index 0000000..cc9cbd0 --- /dev/null +++ b/archive/MatImprimitive.gi @@ -0,0 +1,61 @@ +Read("gap/Experiment.gi"); + +EmbedGenerator := function(mat, m, q) + local n, big, i, j; + n := Length(mat); + big := IdentityMat(m, GF(q)); + for i in [1..n] do + for j in [1..n] do + big[i][j] := mat[i][j]; + od; + od; + return big; +end; + +# Matrix Groups : Imprimitive +d := 9; +q := 5; +K := GL(d,q); +m := 12; +H := SymmetricGroup(m); +# H := Random(AllTransitiveGroups(NrMovedPoints, m)); +W := WreathProduct(K, H); +# isoWreath := IsomorphismWreathProduct(W); +D := d*m + 2; +P := GL(D, q); +W2 := Group(List(GeneratorsOfGroup(W), g -> EmbedGenerator(g, D, q))); +c := PseudoRandom(P); +G := W2^(c^(-1)); +# conj := GroupHomomorphismByFunction(G, W, g -> g^c); +# iso := conj * isoWreath;; + +BlocksMat := function(G) + S := BlindDescend(G); + # IsSingleComponent(S, iso); + + # S acts on W + U + # W invariant space, dim(W) = d + # U fixed space, dim(U) = (m-1)*d + M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); + v1 := RandomVector(D,q); + v2 := RandomVector(D,q); + # basis of W + < [v]\rho_U > + L1 := MTX.SubmoduleGModule(M, v1);; + L2 := MTX.SubmoduleGModule(M, v2);; + # Length(L1) = d + 1; + # Length(L2) = d + 1; + W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); + # Dimension(W) = d; + tmp := TopGroupDomainVectorSpace(G, W); + return tmp; +end; + +tmp := BlocksMat(G); time; +domain := tmp.domain; +transversal := tmp.transversal; +B := Concatenation(List(domain, Basis)); +# B1 := Concatenation(List(domain, Basis)); +# B2 := SemiEchelonBasis(VectorSpace(GF(q), B1)); +# B3 := Subspace(GF(q)^D, List(Basis(GF(q)^D), v->SiftedVector(B2,v))); +# B := Concatenation(B1, Basis(B3)); +Display(G.3^(B^(-1))); \ No newline at end of file diff --git a/examples/MatImprimitive.mag b/archive/MatImprimitive.mag similarity index 100% rename from examples/MatImprimitive.mag rename to archive/MatImprimitive.mag diff --git a/examples/difficultMat.mag b/archive/difficultMat.mag similarity index 100% rename from examples/difficultMat.mag rename to archive/difficultMat.mag diff --git a/examples/difficultMatG.mag b/archive/difficultMatG.mag similarity index 100% rename from examples/difficultMatG.mag rename to archive/difficultMatG.mag diff --git a/examples/CreateExample.gi b/examples/CreateExample.gi new file mode 100644 index 0000000..348ba96 --- /dev/null +++ b/examples/CreateExample.gi @@ -0,0 +1,10 @@ + +outputStream := OutputTextFile("examples/difficultExample.gi", false); +SetPrintFormattingStatus(outputStream, false); +AppendTo(outputStream, "G := ", String(G), ";;"); +CloseStream(outputStream); + +outputStream := OutputTextFile("examples/difficultExample.mag", false); +SetPrintFormattingStatus(outputStream, false); +AppendTo(outputStream, "G := ", ConvertToMagmaInputString(G)); +CloseStream(outputStream); \ No newline at end of file diff --git a/examples/LoadExample.gi b/examples/LoadExample.gi new file mode 100644 index 0000000..6fcd0d0 --- /dev/null +++ b/examples/LoadExample.gi @@ -0,0 +1,16 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Permutation Group : Product Action +Read("examples/difficultPermPrimitiveLargeBase.gi");; + +# Recognition +output := RecogniseWreathProduct(RecogNode(G), rec( + action := "product action", +));; +res := output.res; + +timer := Runtime();; +riG := RecogniseGroup(G);; +timer := Runtime() - timer;; +Print("Total Time: ", FormatFloat(timer / 1000.0), " seconds"); \ No newline at end of file diff --git a/examples/LoadExample.mag b/examples/LoadExample.mag new file mode 100644 index 0000000..590b418 --- /dev/null +++ b/examples/LoadExample.mag @@ -0,0 +1,4 @@ + +load "difficultPermPrimitiveLargeBase.mag"; + +time riG := CompositionTree(G); \ No newline at end of file diff --git a/examples/MatImprimitive.gi b/examples/MatImprimitive.gi index cc9cbd0..4582ab3 100644 --- a/examples/MatImprimitive.gi +++ b/examples/MatImprimitive.gi @@ -1,61 +1,28 @@ -Read("gap/Experiment.gi"); +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); -EmbedGenerator := function(mat, m, q) - local n, big, i, j; - n := Length(mat); - big := IdentityMat(m, GF(q)); - for i in [1..n] do - for j in [1..n] do - big[i][j] := mat[i][j]; - od; - od; - return big; -end; - -# Matrix Groups : Imprimitive +# Matrix Group : Imprimitive d := 9; q := 5; K := GL(d,q); m := 12; -H := SymmetricGroup(m); -# H := Random(AllTransitiveGroups(NrMovedPoints, m)); -W := WreathProduct(K, H); -# isoWreath := IsomorphismWreathProduct(W); -D := d*m + 2; +H := Random(AllTransitiveGroups(NrMovedPoints, m)); +D := d*m; + +# Construct wreath product P := GL(D, q); -W2 := Group(List(GeneratorsOfGroup(W), g -> EmbedGenerator(g, D, q))); -c := PseudoRandom(P); -G := W2^(c^(-1)); -# conj := GroupHomomorphismByFunction(G, W, g -> g^c); -# iso := conj * isoWreath;; +W := WreathProduct(K, H); -BlocksMat := function(G) - S := BlindDescend(G); - # IsSingleComponent(S, iso); +# Random conjugation +c := PseudoRandom(P);; +G := W^(c^(-1));; - # S acts on W + U - # W invariant space, dim(W) = d - # U fixed space, dim(U) = (m-1)*d - M := GModuleByMats(GeneratorsOfGroup(S), GF(q)); - v1 := RandomVector(D,q); - v2 := RandomVector(D,q); - # basis of W + < [v]\rho_U > - L1 := MTX.SubmoduleGModule(M, v1);; - L2 := MTX.SubmoduleGModule(M, v2);; - # Length(L1) = d + 1; - # Length(L2) = d + 1; - W := Intersection(VectorSpace(GF(q), L1), VectorSpace(GF(q), L2)); - # Dimension(W) = d; - tmp := TopGroupDomainVectorSpace(G, W); - return tmp; -end; +# Recognition +output := RecogniseWreathProduct(RecogNode(G), rec( + assumeSimpleBaseComponent := false, + recogniseBaseComponentBeforeDomain := false, +));; +output.res; -tmp := BlocksMat(G); time; -domain := tmp.domain; -transversal := tmp.transversal; -B := Concatenation(List(domain, Basis)); -# B1 := Concatenation(List(domain, Basis)); -# B2 := SemiEchelonBasis(VectorSpace(GF(q), B1)); -# B3 := Subspace(GF(q)^D, List(Basis(GF(q)^D), v->SiftedVector(B2,v))); -# B := Concatenation(B1, Basis(B3)); -Display(G.3^(B^(-1))); \ No newline at end of file +B := output.data.B; +Display(G.1^B); \ No newline at end of file diff --git a/examples/PermImprimitive.gi b/examples/PermImprimitive.gi index eab30d0..ae291de 100644 --- a/examples/PermImprimitive.gi +++ b/examples/PermImprimitive.gi @@ -8,22 +8,13 @@ K := AlternatingGroup(n); H := SymmetricGroup(m); # Construct wreath product -PP := SymmetricGroup(n*m); -P := WreathProduct(SymmetricGroup(n), SymmetricGroup(m));; -W := Group(Concatenation( - List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), - List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) -));; +P := SymmetricGroup(n*m); +W := WreathProduct(K, H);; # Random conjugation -c := PseudoRandom(PP);; +c := PseudoRandom(P);; G := W^(c^(-1));; -# # Nice isomorphism -# isoWreath := IsomorphismWreathProduct(W);; -# isoConj := GroupHomomorphismByFunction(G, W, g -> g^c); -# isoNice := isoConj * isoWreath;; - # Recognition output := RecogniseWreathProduct(RecogNode(G), rec( assumeSimpleBaseComponent := true, diff --git a/examples/PermPrimitive.gi b/examples/PermPrimitive.gi index e6b6c13..3656313 100644 --- a/examples/PermPrimitive.gi +++ b/examples/PermPrimitive.gi @@ -2,32 +2,32 @@ LoadPackage("WPE", false); LoadPackage("WPrecog", false); # Permutation Group : Product Action -m := 3; -d := 3; -q := 5; +m := 4; +d := 4; +q := 3; K := PSL(d,q); n := NrMovedPoints(K); n^m; H := Random(AllTransitiveGroups(NrMovedPoints, m)); # Construct wreath product -PP := SymmetricGroup(n^m); -P := WreathProductProductAction(K, H);; -W := P;; +P := SymmetricGroup(n^m); +W := WreathProductProductAction(K, H);; # Random conjugation -c := PermList(QuickRandomPermutedList(NrMovedPoints(PP)));; +c := PermList(QuickRandomPermutedList(NrMovedPoints(P)));; G := W^(c^(-1));; -# # Nice isomorphism -# isoWreath := IsomorphismWreathProduct(P);; -# isoConj := GroupHomomorphismByFunction(G, P, g -> g^c); -# isoNice := isoConj * isoWreath;; - # Recognition output := RecogniseWreathProduct(RecogNode(G), rec( action := "product action", + forSingleComponentGroup := rec( + lazy := false, + ), ));; res := output.res; -RecogniseGroup(G); \ No newline at end of file +timer := Runtime();; +riG := RecogniseGroup(G);; +timer := Runtime() - timer;; +Print("Total Time: ", FormatFloat(timer / 1000.0), " seconds"); \ No newline at end of file diff --git a/examples/PermPrimitiveLargeBase.gi b/examples/PermPrimitiveLargeBase.gi index 712f0fd..f0b0bf1 100644 --- a/examples/PermPrimitiveLargeBase.gi +++ b/examples/PermPrimitiveLargeBase.gi @@ -5,32 +5,27 @@ LoadPackage("WPrecog", false); m := 5; l := 15; k := 1; -n := k * l; l > 2*m*k^2; # Is Large Base? -K := Action(AlternatingGroup(n), Combinations([1..n],k), OnSets); +n := Binomial(l, k); +n^m; +K := Action(AlternatingGroup(l), Combinations([1..l],k), OnSets); H := Random(AllTransitiveGroups(NrMovedPoints, m)); # Construct wreath product -PP := SymmetricGroup(n^m); -P := WreathProductProductAction(SymmetricGroup(n), SymmetricGroup(m));; -W := Group(Concatenation( - List(GeneratorsOfGroup(K), x -> x^Embedding(P,1)), - List(GeneratorsOfGroup(H), x -> x^Embedding(P,m+1)) -));; +P := SymmetricGroup(n^m); +W := WreathProductProductAction(K, H);; # Random conjugation -c := PseudoRandom(PP);; +c := PseudoRandom(P);; G := W^(c^(-1));; -# # Nice isomorphism -isoWreath := IsomorphismWreathProduct(P);; -isoConj := GroupHomomorphismByFunction(G, P, g -> g^c); -isoNice := isoConj * isoWreath;; - # Recognition output := RecogniseWreathProduct(RecogNode(G), rec( action := "product action", ));; res := output.res; -RecogniseGroup(G); \ No newline at end of file +timer := Runtime();; +riG := RecogniseGroup(G);; +timer := Runtime() - timer;; +Print("Total Time: ", FormatFloat(timer / 1000.0), " seconds"); \ No newline at end of file diff --git a/gap/Recog.gi b/gap/Recog.gi index b647f95..e678a54 100644 --- a/gap/Recog.gi +++ b/gap/Recog.gi @@ -27,7 +27,7 @@ ############################################################################# BindGlobal( "RecogniseWreathProduct", function(args...) - local ri, userOptions, options, name, data, res, output; + local ri, userOptions, options, name, timer, data, res, output; # ======================================================================= # Input extraction @@ -81,6 +81,7 @@ BindGlobal( "RecogniseWreathProduct", function(args...) data := rec(currentStep := 0); output := rec(res := fail, data := data, options := options); + timer := Runtime(); # Init options res := WPR_InitOptions(ri, data, options); @@ -107,6 +108,18 @@ BindGlobal( "RecogniseWreathProduct", function(args...) return output; fi; + # TODO: handle this cleaner + if IsMatrixGroup(Grp(ri)) then + if options.action = "imprimitive action" then + if Dimension(data.domain[1]) * data.m = DimensionOfMatrixGroup(Grp(ri)) then + data.B := Concatenation(List(data.domain, Basis))^(-1); + output.res := true; + return output; + fi; + fi; + Error("TODO"); + fi; + # Recognise Base Component? if options.recogniseComponents and not options.recogniseBaseComponentBeforeDomain @@ -120,6 +133,10 @@ BindGlobal( "RecogniseWreathProduct", function(args...) return output; fi; + timer := Runtime() - timer; + Info(WPR_Info, 1, "==============================================================="); + Info(WPR_Info, 1, "Total Time: ", FormatFloat(timer / 1000.0), " seconds"); + output.res := true; return output; end); diff --git a/gap/Utils.gi b/gap/Utils.gi new file mode 100644 index 0000000..b454145 --- /dev/null +++ b/gap/Utils.gi @@ -0,0 +1,55 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## Utils.gi +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file's authors include Friedrich Rober. +## +## Please refer to the COPYRIGHT file for details. +## +## SPDX-License-Identifier: GPL-2.0-or-later +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## +## This file contains utility functions. +## +## ## +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +############################################################################# + + +FormatFloat := function(args...) + local x, nrDigits, s, parts, decimals; + if Length(args) = 0 or Length(args) > 2 then + Error("Usage: SingleComponentGroup(x[, nrDigits])"); + fi; + + x := args[1]; + nrDigits := 3; + if Length(args) = 2 then + nrDigits := args[2]; + fi; + + s := String(x); + parts := SplitString(s, "."); + if Length(parts) = 1 then + return Concatenation(s, ".000"); + fi; + decimals := parts[2]; + while Length(decimals) < nrDigits do + decimals := Concatenation(decimals, "0"); + od; + if Length(decimals) > nrDigits then + decimals := decimals{[1..nrDigits]}; + fi; + return Concatenation(parts[1], ".", decimals); +end; diff --git a/gap/subroutines/Image.gi b/gap/subroutines/Image.gi index 00e3e30..09f6a97 100644 --- a/gap/subroutines/Image.gi +++ b/gap/subroutines/Image.gi @@ -58,7 +58,7 @@ BindGlobal("WPR_Projection", function(g, ri, data, options) end); BindGlobal("WPR_Embedding", function(ri, data, options) - local W, embedding; + local res, W, embedding; Info(WPR_Info, 2, "\n"); Info(WPR_Info, 1, "Step ", data.currentStep, ": Compute embedding function"); Info(WPR_Info, 2, "--------------------------------------------------"); @@ -67,7 +67,10 @@ BindGlobal("WPR_Embedding", function(ri, data, options) return WPR_Projection(StripMemory(g), ri, data, options); end; - WPR_SetupImage(ri, data, options); + res := WPR_SetupImage(ri, data, options); + if res = fail then + return fail; + fi; data.imageFunc := function(g) return WPR_Image(StripMemory(g), ri, data, options); end; diff --git a/gap/subroutines/Init.gi b/gap/subroutines/Init.gi index 3e614e4..9d981e5 100644 --- a/gap/subroutines/Init.gi +++ b/gap/subroutines/Init.gi @@ -19,9 +19,11 @@ BindGlobal("WPR_InitOptions", function(ri, data, options) N := NrMovedPoints(G); F := Collected(PartialFactorization(N, 0)); M := F[1][2]; # upper bound for top degree - if ForAll(F, f -> f[2] = M) then + if options.action = fail and ForAll(F, f -> f[2] = M) and M < 10 then options.action := "product action"; isPrim := true; + fi; + if options.action = "product action" then Info(WPR_Info, 2, "Assume product action on n^m points with m <= ", M); fi; fi; diff --git a/gap/subroutines/RecogniseBaseComponent.gi b/gap/subroutines/RecogniseBaseComponent.gi index fe510e6..b86107c 100644 --- a/gap/subroutines/RecogniseBaseComponent.gi +++ b/gap/subroutines/RecogniseBaseComponent.gi @@ -25,11 +25,13 @@ BindGlobal("WPR_RecogniseBaseComponent", function(ri, data, options) timer := Runtime() - timer; if riS_reduced = fail then Info(WPR_Info, 1, "Failure: could not recognise base component"); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); return fail; fi; data.riS_reduced := riS_reduced; - data.niceGensForS := ResultOfStraightLineProgram(slptonice(data.riS_reduced), gensS); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + # SLPOfElms + # data.niceGensForS := ResultOfStraightLineProgram(slptonice(data.riS_reduced), gensS); + data.niceGensForS := CalcNiceGens(riS_reduced, riS_reduced!.gensHmem); + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); return true; end); \ No newline at end of file diff --git a/gap/subroutines/SingleComponentGroup.gi b/gap/subroutines/SingleComponentGroup.gi index 213368e..f126834 100644 --- a/gap/subroutines/SingleComponentGroup.gi +++ b/gap/subroutines/SingleComponentGroup.gi @@ -46,7 +46,7 @@ BindGlobal("WPR_SingleComponentGroup", function(ri, data, options) timer := Runtime(); S := SingleComponentGroup(ri, options.forSingleComponentGroup); # with memory timer := Runtime() - timer; - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); data.S := S; return true; end); @@ -87,6 +87,7 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) options := rec( # -- Error control ------------------------------------------------------------------------- heuristic := true, # whether to use heuristic values instead of explicit ones + lazy := true, # whether to try at most 2 log(m) tries eps := 1/100, # error probability M := 20, # upper bound for degree of top group @@ -156,13 +157,12 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) n := options.n1, primes := primes, ); - Info(WPR_Info, 2, "Bounds for Phase 1:"); - Info(WPR_Info, 2, "\tl_1 = ", l1); - Info(WPR_Info, 3, "Start Iteration for Phase 1..."); + Info(WPR_Info, 2, "Number of iterations for Phase 1: ", l1); + Info(WPR_Info, 3, "Start iteration for Phase 1..."); for i in [1 .. l1] do S := WPR_SCG_Descend(S, S, descendOptions); od; - Info(WPR_Info, 3, "...Finished Iteration for Phase 1"); + Info(WPR_Info, 3, "...Finished iteration for Phase 1"); # -- Update Parameters -------------------------------------------------- B := S; # supposedly inside base group @@ -172,17 +172,19 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) # -- Phase 2 ------------------------------------------------------------ l2 := WPR_SCG_NrIterations2(R[2], options.M, options.eps/2); + if options.lazy then + l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M))))); + fi; if options.heuristic then - l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M)))), options.l2); + l2 := Minimum(l2, options.l2); fi; descendOptions := rec( randomElementGenerator := options.randomElementGenerator, n := options.n2, primes := primes, ); - Info(WPR_Info, 2, "Bounds for Phase 2:"); - Info(WPR_Info, 2, "\tl_2 = ", l2); - Info(WPR_Info, 3, "Start Iteration for Phase 2..."); + Info(WPR_Info, 2, "Number of iterations for Phase 2: ", l2); + Info(WPR_Info, 3, "Start iteration for Phase 2..."); for i in [1 .. l2] do if options.useBaseGroupInPhase2 then S := WPR_SCG_Descend(S, B, descendOptions); @@ -190,7 +192,7 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) S := WPR_SCG_Descend(S, S, descendOptions); fi; od; - Info(WPR_Info, 3, "...Finished Iteration for Phase 2"); + Info(WPR_Info, 3, "...Finished iteration for Phase 2"); # -- Post --------------------------------------------------------------- # As a pre-caution, take normal closure in base group, if we descended too far diff --git a/gap/subroutines/TopGroupDomainAndAction.gi b/gap/subroutines/TopGroupDomainAndAction.gi index 5419fd9..c9d3fc3 100644 --- a/gap/subroutines/TopGroupDomainAndAction.gi +++ b/gap/subroutines/TopGroupDomainAndAction.gi @@ -43,7 +43,7 @@ BindGlobal("WPR_TopGroupDomain", function(ri, data, options) local timer, name, G, gensS, S_withoutMem, domainData, W; G := Grp(ri); if IsBound(data.niceGensForS) then - gensS := data.niceGensForS; + gensS := List(data.niceGensForS, StripMemory); else gensS := List(GeneratorsOfGroup(data.S), StripMemory); fi; @@ -78,7 +78,7 @@ BindGlobal("WPR_TopGroupDomain", function(ri, data, options) timer := Runtime() - timer; if domainData = fail then Info(WPR_Info, 1, "Failure: invalid domain"); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); return fail; fi; for name in RecNames(domainData) do @@ -86,7 +86,7 @@ BindGlobal("WPR_TopGroupDomain", function(ri, data, options) data.m := Length(domainData.domain); od; Info(WPR_Info, 2, "m = ", data.m); - Info(WPR_Info, 1, "Time : ", timer / 1000.0, " seconds"); + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); return true; end); @@ -107,9 +107,9 @@ end); InstallGlobalFunction("BlackBoxOrbit", function(args...) local ri, s, userOptions, options, name, G, t, domain, i, a, b, g, p, isEq, foundNew, indistinguishablePoints, j; - # ================================================== + # ======================================================================= # Input extraction - # ================================================== + # ======================================================================= if Length(args) < 2 or Length(args) > 3 then Error("Usage: BlackBoxOrbit(ri, s[, options])"); fi; @@ -121,9 +121,9 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) userOptions := args[3]; fi; - # ================================================== + # ======================================================================= # Default options - # ================================================== + # ======================================================================= options := rec( # -- Strategy flags ------------------------------------------- recursionDepth := 1, @@ -141,9 +141,9 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) resolveConflict := {p, indistinguishablePoints} -> fail, # try to find different domain or return fail, ); - # ================================================== + # ======================================================================= # Input validation - # ================================================== + # ======================================================================= # Check recog node if not IsRecogNode(ri) then @@ -158,14 +158,14 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) options.(name) := userOptions.(name); od; - # ================================================== + # ======================================================================= # Algorithm - # ================================================== + # ======================================================================= if options.recursionDepth > options.recursionMaxDepth then return fail; fi; - Info(WPR_Info, 2, "Recursion Depth: ", options.recursionDepth); + Info(WPR_Info, 3, "Recursion Depth: ", options.recursionDepth); if options.useMemory then G := Group(ri!.gensHmem); else @@ -196,15 +196,14 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) foundNew := false; # If we can prove a conflict, we need to adjust the domain if options.isConflict(p, indistinguishablePoints) then - Info(WPR_Info, 2, "Found conflict"); + Info(WPR_Info, 3, "Found conflict"); # The domain is not invariant under the action, # thus we try compute a new point to resolve the conflict s := options.resolveConflict(p, indistinguishablePoints); if s = fail then - Info(WPR_Info, 2, "Could not resolve conflict"); + Info(WPR_Info, 3, "Could not resolve conflict"); return fail; fi; - Error("Examine Me!"); options.recursionDepth := options.recursionDepth + 1; return BlackBoxOrbit(ri, s, options); fi; @@ -212,7 +211,7 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) od; if foundNew then if Length(domain) >= options.maximalBoundOnTopDegree then - Info(WPR_Info, 2, "Domain too large, abort now"); + Info(WPR_Info, 3, "Domain too large, abort now"); return fail; fi; Add(t, t[i] * g); @@ -242,9 +241,10 @@ end); InstallGlobalFunction("BlackBoxAction", function(args...) local g, domain, s, userOptions, options, name, m, images, i, j, a, b, p; - # ================================================== + # ======================================================================= # Input extraction - # ================================================== + # ======================================================================= + if Length(args) < 2 or Length(args) > 3 then Error("Usage: BlackBoxAction(g, domain[, options])"); fi; @@ -256,18 +256,19 @@ InstallGlobalFunction("BlackBoxAction", function(args...) userOptions := args[3]; fi; - # ================================================== + # ======================================================================= # Default options - # ================================================== + # ======================================================================= + options := rec( # -- Action oracles ------------------------------------------- act := OnPoints, isEqual := \=, # isEqual returns true if p and b are assumed to be equal ); - # ================================================== + # ======================================================================= # Input validation - # ================================================== + # ======================================================================= # Validate and apply user-provided options for name in RecNames(userOptions) do @@ -277,9 +278,10 @@ InstallGlobalFunction("BlackBoxAction", function(args...) options.(name) := userOptions.(name); od; - # ================================================== + # ======================================================================= # Algorithm - # ================================================== + # ======================================================================= + m := Length(domain); images := EmptyPlist(m); for i in [1 .. m] do @@ -299,5 +301,6 @@ InstallGlobalFunction("BlackBoxAction", function(args...) return fail; fi; od; + return PermList(images); end); diff --git a/read.g b/read.g index 62503e5..eb6c2af 100644 --- a/read.g +++ b/read.g @@ -10,6 +10,7 @@ BindGlobal("WPR_Info", NewInfoClass("WPR_Info")); SetInfoLevel(WPR_Info, 3); +ReadPackage( "WPrecog", "gap/Utils.gi"); ReadPackage( "WPrecog", "gap/Quick.gi"); ReadPackage( "WPrecog", "gap/subroutines/Init.gi"); From 137288f512263b2abc3ddfe67b3e71459adc443f Mon Sep 17 00:00:00 2001 From: Friedrich Rober Date: Mon, 14 Apr 2025 10:32:07 +0200 Subject: [PATCH 14/14] Fix bug in RecogniseBase --- {gap => archive}/Alt.gi | 0 {gap => archive}/Experiment.gi | 0 {gap => archive}/WPrecog.gi | 0 examples/PermImprimitive.gi | 6 ++- examples/PermPrimitiveLargeBase.gi | 5 +++ examples/Utils.gi | 38 +++++++++++++++++++ gap/Recog.gi | 1 + gap/subroutines/Init.gi | 8 ++-- gap/subroutines/RecogniseBaseComponent.gi | 2 +- gap/subroutines/SingleComponentGroup.gi | 17 ++++++--- gap/subroutines/TopGroupDomainAndAction.gi | 1 + .../ViaProductAction.gi | 1 + 12 files changed, 67 insertions(+), 12 deletions(-) rename {gap => archive}/Alt.gi (100%) rename {gap => archive}/Experiment.gi (100%) rename {gap => archive}/WPrecog.gi (100%) create mode 100644 examples/Utils.gi diff --git a/gap/Alt.gi b/archive/Alt.gi similarity index 100% rename from gap/Alt.gi rename to archive/Alt.gi diff --git a/gap/Experiment.gi b/archive/Experiment.gi similarity index 100% rename from gap/Experiment.gi rename to archive/Experiment.gi diff --git a/gap/WPrecog.gi b/archive/WPrecog.gi similarity index 100% rename from gap/WPrecog.gi rename to archive/WPrecog.gi diff --git a/examples/PermImprimitive.gi b/examples/PermImprimitive.gi index ae291de..c55e546 100644 --- a/examples/PermImprimitive.gi +++ b/examples/PermImprimitive.gi @@ -1,15 +1,17 @@ LoadPackage("WPE", false); LoadPackage("WPrecog", false); +ReadPackage("WPrecog", "examples/Utils.gi"); # Permutation Group : Imprimitive -n := 9; -m := 12; +n := 15; +m := 5; K := AlternatingGroup(n); H := SymmetricGroup(m); # Construct wreath product P := SymmetricGroup(n*m); W := WreathProduct(K, H);; +W := RandomGroup(W);; # Random conjugation c := PseudoRandom(P);; diff --git a/examples/PermPrimitiveLargeBase.gi b/examples/PermPrimitiveLargeBase.gi index f0b0bf1..e53b384 100644 --- a/examples/PermPrimitiveLargeBase.gi +++ b/examples/PermPrimitiveLargeBase.gi @@ -1,5 +1,6 @@ LoadPackage("WPE", false); LoadPackage("WPrecog", false); +ReadPackage("WPrecog", "examples/Utils.gi"); # Permutation Group : Product Action m := 5; @@ -14,6 +15,7 @@ H := Random(AllTransitiveGroups(NrMovedPoints, m)); # Construct wreath product P := SymmetricGroup(n^m); W := WreathProductProductAction(K, H);; +W := RandomGroup(W);; # Random conjugation c := PseudoRandom(P);; @@ -24,6 +26,9 @@ output := RecogniseWreathProduct(RecogNode(G), rec( action := "product action", ));; res := output.res; +emb := output.data.embedding;; +R := Range(emb);; +ListWreathProductElement(R, ImageElm(emb, G.1)); timer := Runtime();; riG := RecogniseGroup(G);; diff --git a/examples/Utils.gi b/examples/Utils.gi new file mode 100644 index 0000000..0f8b8e0 --- /dev/null +++ b/examples/Utils.gi @@ -0,0 +1,38 @@ + +BindGlobal("RandomGenerator_ExtendGens", function(gens) + local n, A, B; + n := Length(gens); + A := List([1 .. n], i -> Random([-1,1])); + B := QuickRandomPermutedList(n); + Add(gens, Product([1 .. n], i -> gens[B[i]]^A[i])); +end); + +BindGlobal("RandomGenerator_SingleReplacement", function(gens) + local n, A, B, F, p, g; + n := Length(gens); + A := List([1 .. n], i -> Random([-1,0,1])); + F := Filtered([1 .. n], i -> A[i] <> 0); + if Length(F) = 0 then + return; + fi; + p := Random(F); + B := QuickRandomPermutedList(n); + gens[B[p]] := Product([1 .. n], i -> gens[B[i]]^A[i]); +end); + +BindGlobal("RandomGenerators", function(gens) + local i; + for i in [1 .. 5] do + RandomGenerator_ExtendGens(gens); + od; + for i in [1 .. 10] do + RandomGenerator_SingleReplacement(gens); + od; +end); + +BindGlobal("RandomGroup", function(G) + local gens; + gens := List(GeneratorsOfGroup(G)); + RandomGenerators(gens); + return Group(gens); +end); diff --git a/gap/Recog.gi b/gap/Recog.gi index e678a54..8d1069e 100644 --- a/gap/Recog.gi +++ b/gap/Recog.gi @@ -56,6 +56,7 @@ BindGlobal( "RecogniseWreathProduct", function(args...) recogniseComponents := true, recogniseBaseComponentBeforeDomain := true, recogniseBaseComponentViaIsomorphism := false, + M := fail, ); # ======================================================================= diff --git a/gap/subroutines/Init.gi b/gap/subroutines/Init.gi index 9d981e5..6742f5e 100644 --- a/gap/subroutines/Init.gi +++ b/gap/subroutines/Init.gi @@ -45,12 +45,14 @@ BindGlobal("WPR_InitOptions", function(ri, data, options) Error("todo"); fi; - if IsBound(options.forSingleComponentGroup.M) then + if options.M <> fail then Info(WPR_Info, 2, "User specified an upper bound for m"); - options.forSingleComponentGroup.M := Minimum(options.forSingleComponentGroup.M, M); + options.M := Minimum(M, options.M); Info(WPR_Info, 2, "Assume m <= ", M); else - options.forSingleComponentGroup.M := M; + options.M := M; fi; + options.forSingleComponentGroup.M := options.M; + options.forTopGroupDomain.maximalBoundOnTopDegree := options.M; return true; end); diff --git a/gap/subroutines/RecogniseBaseComponent.gi b/gap/subroutines/RecogniseBaseComponent.gi index b86107c..c66a79a 100644 --- a/gap/subroutines/RecogniseBaseComponent.gi +++ b/gap/subroutines/RecogniseBaseComponent.gi @@ -31,7 +31,7 @@ BindGlobal("WPR_RecogniseBaseComponent", function(ri, data, options) data.riS_reduced := riS_reduced; # SLPOfElms # data.niceGensForS := ResultOfStraightLineProgram(slptonice(data.riS_reduced), gensS); - data.niceGensForS := CalcNiceGens(riS_reduced, riS_reduced!.gensHmem); + data.niceGensForS := CalcNiceGens(riS_reduced, GeneratorsOfGroup(data.S)); Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); return true; end); \ No newline at end of file diff --git a/gap/subroutines/SingleComponentGroup.gi b/gap/subroutines/SingleComponentGroup.gi index f126834..e45566a 100644 --- a/gap/subroutines/SingleComponentGroup.gi +++ b/gap/subroutines/SingleComponentGroup.gi @@ -38,16 +38,18 @@ ############################################################################# BindGlobal("WPR_SingleComponentGroup", function(ri, data, options) - local timer, name, S; + local timer, name, singleCompData; Info(WPR_Info, 2, "\n"); Info(WPR_Info, 1, "Step ", data.currentStep, ": Compute a single-component group S"); Info(WPR_Info, 2, "---------------------------------------------------------------"); data.currentStep := data.currentStep + 1; timer := Runtime(); - S := SingleComponentGroup(ri, options.forSingleComponentGroup); # with memory + singleCompData := SingleComponentGroup(ri, options.forSingleComponentGroup); # with memory timer := Runtime() - timer; Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); - data.S := S; + for name in RecNames(singleCompData) do + data.(name) := singleCompData.(name); + od; return true; end); @@ -94,7 +96,7 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) # -- Strategy flags ------------------------------------------------------------------------ primes := [2, 3, 5, 7], # prime numbers to use in a step randomElementGenerator # function to generate random elements - := QuickRandomSubproduct, + := PseudoRandom, useMemory := true, # whether to use memory for group elements useBaseGroupInPhase2 := false, # use base group instead of previous group in phase 2 useBaseGroupAtEnd := true, # use base group at end (ignored if useBaseGroupInPhase2) @@ -104,6 +106,8 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) # -- Phase iteration counts ---------------------------------------------------------------- l1 := 5, # number of iterations in phase 1 l2 := 35, # number of iterations in phase 2 + l1Min := 5, # minimal number of iterations in phase 1 + l2Min := 5, # minimal number of iterations in phase 2 # -- Normal closure effort parameters ------------------------------------------------------ n1 := 5, # effort per step in phase 1 @@ -151,6 +155,7 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) l1 := WPR_SCG_NrIterations1(R[1], options.eps/2); if options.heuristic then l1 := Minimum(l1, options.l1); + l1 := Maximum(l1, options.l1Min); fi; descendOptions := rec( randomElementGenerator := options.randomElementGenerator, @@ -177,6 +182,7 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) fi; if options.heuristic then l2 := Minimum(l2, options.l2); + l2 := Maximum(l2, options.l2Min); fi; descendOptions := rec( randomElementGenerator := options.randomElementGenerator, @@ -201,6 +207,5 @@ InstallGlobalFunction("SingleComponentGroup", function(args...) S := QuickNormalClosure(S, B, options.n0); Info(WPR_Info, 3, "... Finished computing normal closure in base group"); fi; - return S; - + return rec(B := B, S := S); end); diff --git a/gap/subroutines/TopGroupDomainAndAction.gi b/gap/subroutines/TopGroupDomainAndAction.gi index c9d3fc3..3dfcb1c 100644 --- a/gap/subroutines/TopGroupDomainAndAction.gi +++ b/gap/subroutines/TopGroupDomainAndAction.gi @@ -190,6 +190,7 @@ InstallGlobalFunction("BlackBoxOrbit", function(args...) break; # can we distinguish between p and b via our action? elif not options.isDistinguishable(p, b) then + Error("Inspect Me"); Add(indistinguishablePoints, b); # We cannot distinguish between these points, # so we need to assume for now that they are equal. diff --git a/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi b/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi index de7b8f1..c7aa45d 100644 --- a/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi +++ b/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi @@ -44,6 +44,7 @@ BindGlobal("WPR_TopGroupDomainViaProductAction", function(args...) userOptions.isDistinguishable := {a, b} -> Size(Intersection(Orbit(a, 1), Orbit(b, 1))) = 1; userOptions.isConflict := {p, P} -> Length(P) >= 1; userOptions.resolveConflict := {p, P} -> Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))); + # userOptions.resolveConflict := {p, P} -> QuickNormalClosure(Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))), userOptions.B, 5); return BlackBoxOrbit(ri, s, userOptions); end);