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: 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 e46d9af..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, @@ -55,17 +55,17 @@ Status := "dev", AbstractHTML := "", PackageDoc := rec( - BookName := "WPR", + BookName := "WPrecog", ArchiveURLSubset := ["doc"], 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( - GAP := ">= 4.11", - NeededOtherPackages := [ ], + GAP := ">= 4.12", + NeededOtherPackages := [ ["recog", ">= 1.3.2"] ], SuggestedOtherPackages := [ ], ExternalConditions := [ ], ), 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/archive/Alt.gi b/archive/Alt.gi new file mode 100644 index 0000000..bb44d36 --- /dev/null +++ b/archive/Alt.gi @@ -0,0 +1,178 @@ +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 := RecogNode(S); + 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); + +# 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 + 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; + 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]; + 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; + Info(WPR_Info, 3, "\tSet b_i for i = ", i); + break; + fi; + fi; + wList := ListWreathProductElement(W, StripMemory(wMem)); + od; + if IsBound(b[1]) then + 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 + 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; + Info(WPR_Info, 2, "Couldn't find standard generators!"); + return TemporaryFailure; +end); \ No newline at end of file diff --git a/archive/Experiment.gi b/archive/Experiment.gi new file mode 100644 index 0000000..3e1dec2 --- /dev/null +++ b/archive/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/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/archive/MatImprimitive.mag b/archive/MatImprimitive.mag new file mode 100644 index 0000000..f12a13a --- /dev/null +++ b/archive/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/archive/WPrecog.gi b/archive/WPrecog.gi new file mode 100644 index 0000000..6eaafd8 --- /dev/null +++ b/archive/WPrecog.gi @@ -0,0 +1,452 @@ +# +# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component +# +# 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, + recogData, T, AutT, slpFuncForT, stdGensS, lambda, + domainData, t, domain, projFunc, + phiImageFunc, imagesG, H, riH, + W, stdGensData, stdGensBaseComponent, groupDataBaseComponent, stdGensBase, slpFuncForK, stdGensTop; + + #################################### + #### ------------------------ #### + #### Initialization of Bounds #### + #### ------------------------ #### + #################################### + + 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"; + 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; + Info(WPR_Info, 2, "eps = ", eps); + # TODO: maybe call subprocedures with smaller error bound? + + ################################## + #### ---------------------- #### + #### Single-Component Group #### + #### ---------------------- #### + ################################## + + # ------------------------------------------------------------- # + # 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 + origGensS := simpleCompData.origGensS; + hintsForT := simpleCompData.hintsForT; + if not IsList(origGensS) then + return TemporaryFailure; + fi; + + # ----------------------------------------------------------- # + # 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. + 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; + Info(WPR_Info, 2, "T = ", simpleGroupFamily); + + ####################################### + #### --------------------------- #### + #### Top Group Action and Domain #### + #### --------------------------- #### + ####################################### + + # ----------------------------------------------------------------- # + # 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; + + ################################## + #### ---------------------- #### + #### Isomorphism Definition #### + #### ---------------------- #### + ################################## + + # ------------------------------------------------------------------------------ # + # 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, "------------------------------------------------------------------"); + + ############################# + #### ----------------- #### + #### Image Computation #### + #### ----------------- #### + ############################# + + # ---------------------------------------------------------------------- # + # 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); + end; + imagesG := List(ri!.gensHmem, g -> phiImageFunc(g)); + + ################################ + #### -------------------- #### + #### PreImage Computation #### + #### -------------------- #### + ################################ + + # -------------------------------- # + # 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. + riH := RecogniseGroup(H); + + # -------------------------------------------------------- # + # 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; + stdGensBase := List([1 .. m], i -> OnTuples(stdGensBaseComponent, t[i])); + slpFuncForK := WPR_SLPforAlmostSimple(groupDataBaseComponent); + + # ------------------------------------------------------- # + # 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); + + ############################# + #### ----------------- #### + #### Correctness Check #### + #### ----------------- #### + ############################# + + # 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 gens, gensB, P, logEps, l1, l2, delta, i, hints, hintsForT; + gens := ri!.gensHmem; + P := WPR_SimpleSingleComponentSuccessProb(simpleGroupFamily); + 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. + # TODO: better hints system + 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]))); + 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); +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentHintsFirstPhase, +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); + return rec(m := m, hintsForT := hintsForT); + else + ErrorNoReturn("TODO"); + fi; +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentBaseStep, +function(gens, L, delta) + local y, ord, z, n; + # TODO: how to generate random elements? + 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(gens, [z], n); + else + # TODO: return fail and count fails in main function + return gens; + fi; +end); + +InstallGlobalFunction( WPR_SimpleSingleComponentSuccessProb, +function(simpleGroupFamily) + if simpleGroupFamily = "Alt" then + return [1/2, 1/3]; + fi; + return fail; +end); + +InstallGlobalFunction( WPR_RecogniseAlmostSimple, +function(origGensS, simpleGroupFamily, hintsForT, eps) + if simpleGroupFamily = "Alt" then + return WPR_RecogniseAlt(origGensS, simpleGroupFamily, hintsForT, eps); + else + ErrorNoReturn("TODO"); + fi; +end); + +InstallGlobalFunction( WPR_TopGroupDomain, +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 := [stdGensS]; + 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(domain[i], 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, stdGensS, t, projFunc, lambda) + if simpleGroupFamily = "Alt" then + # TODO: check if filter works faster + return WPR_ImageAltGeneric(g, ri, stdGensS, t, projFunc, lambda); + fi; + return ErrorNoReturn("TODO"); +end); + +InstallGlobalFunction(WPR_StandardGensSingleComponent, +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_StandardGensTopGroup, +function(ri, stdGensBase, imagesG, slpFuncForK, riH) + local H, m, l, k, baseElm, g, gList, origGensH; + H := Grp(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); + +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/archive/difficultMat.mag b/archive/difficultMat.mag new file mode 100644 index 0000000..253880d --- /dev/null +++ b/archive/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, 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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, 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, 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, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 0, 1, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 2, 2, 2, 1, 2, 0, 0, 2, 0, 2, 1, 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, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, + 0, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 2, 1, 0, 1, 2, 2, 2, 0, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 0, 2, 1, + 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 0, 1, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, + 0, 0, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0, 1, 2, 2, 0, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 0, 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, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 1, 1, + 1, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 0, 1, 2, 0, + 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 1, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, + 2, 2, 1, 1, 2, 0, 0, 1, 0, 2, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 1, 0, + 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 0, 0, 2, 1, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, + 0, 2, 1, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2, 2, + 1, 2, 1, 2, 0, 1, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 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, 1, 0, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 1, 2, + 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, + 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, + 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, + 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 2, 1, 1, 2, 2, 2, 0, 0, 1, 1, 2, 1, 1, 1, 2, 2, 1, + 0, 0, 2, 1, 1, 0, 0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 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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 ]) >; diff --git a/archive/difficultMatG.mag b/archive/difficultMatG.mag new file mode 100644 index 0000000..4b273a7 --- /dev/null +++ b/archive/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, 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, 1, 0, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 1, 2, + 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, + 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, + 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, + 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 2, 1, 1, 2, 2, 2, 0, 0, 1, 1, 2, 1, 1, 1, 2, 2, 1, + 0, 0, 2, 1, 1, 0, 0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, + 2, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 1, 0, 0, 2, 0, 1, 2, 1, 2, 2, 0, 1, 2, + 0, 2, 2, 2, 1, 1, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 0, 1, + 0, 2, 0, 1, 2, 2, 1, 2, 1, 0, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 1, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 0, 2, 1, 0, 2, 1, 1, 2, + 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, + 1, 2, 2, 2, 2, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 2, 1, 0, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 0, 2, 1, 1, 1, + 2, 2, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 0, 2, 0, 0, 0, 0, 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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/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 new file mode 100644 index 0000000..4582ab3 --- /dev/null +++ b/examples/MatImprimitive.gi @@ -0,0 +1,28 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Matrix Group : Imprimitive +d := 9; +q := 5; +K := GL(d,q); +m := 12; +H := Random(AllTransitiveGroups(NrMovedPoints, m)); +D := d*m; + +# Construct wreath product +P := GL(D, q); +W := WreathProduct(K, H); + +# Random conjugation +c := PseudoRandom(P);; +G := W^(c^(-1));; + +# Recognition +output := RecogniseWreathProduct(RecogNode(G), rec( + assumeSimpleBaseComponent := false, + recogniseBaseComponentBeforeDomain := false, +));; +output.res; + +B := output.data.B; +Display(G.1^B); \ No newline at end of file diff --git a/examples/PermImprimitive.gi b/examples/PermImprimitive.gi new file mode 100644 index 0000000..c55e546 --- /dev/null +++ b/examples/PermImprimitive.gi @@ -0,0 +1,24 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); +ReadPackage("WPrecog", "examples/Utils.gi"); + +# Permutation Group : Imprimitive +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);; +G := W^(c^(-1));; + +# Recognition +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 new file mode 100644 index 0000000..3656313 --- /dev/null +++ b/examples/PermPrimitive.gi @@ -0,0 +1,33 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); + +# Permutation Group : Product Action +m := 4; +d := 4; +q := 3; +K := PSL(d,q); +n := NrMovedPoints(K); +n^m; +H := Random(AllTransitiveGroups(NrMovedPoints, m)); + +# Construct wreath product +P := SymmetricGroup(n^m); +W := WreathProductProductAction(K, H);; + +# Random conjugation +c := PermList(QuickRandomPermutedList(NrMovedPoints(P)));; +G := W^(c^(-1));; + +# Recognition +output := RecogniseWreathProduct(RecogNode(G), rec( + action := "product action", + forSingleComponentGroup := rec( + lazy := false, + ), +));; +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/PermPrimitiveLargeBase.gi b/examples/PermPrimitiveLargeBase.gi new file mode 100644 index 0000000..e53b384 --- /dev/null +++ b/examples/PermPrimitiveLargeBase.gi @@ -0,0 +1,36 @@ +LoadPackage("WPE", false); +LoadPackage("WPrecog", false); +ReadPackage("WPrecog", "examples/Utils.gi"); + +# Permutation Group : Product Action +m := 5; +l := 15; +k := 1; +l > 2*m*k^2; # Is Large Base? +n := Binomial(l, k); +n^m; +K := Action(AlternatingGroup(l), Combinations([1..l],k), OnSets); +H := Random(AllTransitiveGroups(NrMovedPoints, m)); + +# Construct wreath product +P := SymmetricGroup(n^m); +W := WreathProductProductAction(K, H);; +W := RandomGroup(W);; + +# Random conjugation +c := PseudoRandom(P);; +G := W^(c^(-1));; + +# Recognition +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);; +timer := Runtime() - timer;; +Print("Total Time: ", FormatFloat(timer / 1000.0), " seconds"); \ No newline at end of file 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/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/Recog.gi b/gap/Recog.gi new file mode 100644 index 0000000..8d1069e --- /dev/null +++ b/gap/Recog.gi @@ -0,0 +1,143 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## 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, timer, 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, + assumeSimpleBaseComponent := true, + recogniseComponents := true, + recogniseBaseComponentBeforeDomain := true, + recogniseBaseComponentViaIsomorphism := false, + M := 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 + # ======================================================================= + + data := rec(currentStep := 0); + output := rec(res := fail, data := data, options := options); + timer := Runtime(); + + # 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; + + # 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; + + # 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 + then + WPR_RecogniseBaseComponent(ri, data, options); + fi; + + # Embedding + res := WPR_Embedding(ri, data, options); + if res = fail then + 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/WPR.gd b/gap/WPR.gd deleted file mode 100644 index 8350c02..0000000 --- a/gap/WPR.gd +++ /dev/null @@ -1,19 +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 - -#! @Description -#! Insert documentation for your function here -DeclareGlobalFunction( "WPR_Example" ); diff --git a/gap/WPR.gi b/gap/WPR.gi deleted file mode 100644 index d0c5de2..0000000 --- a/gap/WPR.gi +++ /dev/null @@ -1,10 +0,0 @@ -# -# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component -# -# Implementations -# -InstallGlobalFunction( WPR_Example, -function() - Print( "This is a placeholder function, replace it with your own code.\n" ); -end ); - diff --git a/gap/WPrecog.gd b/gap/WPrecog.gd new file mode 100644 index 0000000..305a45e --- /dev/null +++ b/gap/WPrecog.gd @@ -0,0 +1,22 @@ +# +# 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("SingleComponentGroup"); +DeclareGlobalFunction("BlackBoxOrbit"); +DeclareGlobalFunction("BlackBoxAction"); + + + diff --git a/gap/subroutines/Image.gi b/gap/subroutines/Image.gi new file mode 100644 index 0000000..09f6a97 --- /dev/null +++ b/gap/subroutines/Image.gi @@ -0,0 +1,87 @@ + +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 res, 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; + + 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; + + 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..6742f5e --- /dev/null +++ b/gap/subroutines/Init.gi @@ -0,0 +1,58 @@ +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 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; + 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 options.M <> fail then + Info(WPR_Info, 2, "User specified an upper bound for m"); + options.M := Minimum(M, options.M); + Info(WPR_Info, 2, "Assume m <= ", M); + else + 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 new file mode 100644 index 0000000..c66a79a --- /dev/null +++ b/gap/subroutines/RecogniseBaseComponent.gi @@ -0,0 +1,37 @@ +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: ", FormatFloat(timer / 1000.0), " seconds"); + return fail; + fi; + data.riS_reduced := riS_reduced; + # SLPOfElms + # data.niceGensForS := ResultOfStraightLineProgram(slptonice(data.riS_reduced), gensS); + 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/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..e45566a --- /dev/null +++ b/gap/subroutines/SingleComponentGroup.gi @@ -0,0 +1,211 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## 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, 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(); + singleCompData := SingleComponentGroup(ri, options.forSingleComponentGroup); # with memory + timer := Runtime() - timer; + Info(WPR_Info, 1, "Time: ", FormatFloat(timer / 1000.0), " seconds"); + for name in RecNames(singleCompData) do + data.(name) := singleCompData.(name); + od; + 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 + 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 + + # -- Strategy flags ------------------------------------------------------------------------ + primes := [2, 3, 5, 7], # prime numbers to use in a step + randomElementGenerator # function to generate random elements + := 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) + 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 + 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 + 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); + l1 := Maximum(l1, options.l1Min); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n1, + primes := primes, + ); + 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"); + + # -- 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.lazy then + l2 := Minimum(l2, Int(Ceil(2*Log(Float(options.M))))); + fi; + if options.heuristic then + l2 := Minimum(l2, options.l2); + l2 := Maximum(l2, options.l2Min); + fi; + descendOptions := rec( + randomElementGenerator := options.randomElementGenerator, + n := options.n2, + primes := primes, + ); + 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); + 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 rec(B := B, S := 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..3dfcb1c --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction.gi @@ -0,0 +1,307 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## 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 := List(data.niceGensForS, StripMemory); + 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: ", FormatFloat(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: ", FormatFloat(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, 3, "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 + Error("Inspect Me"); + 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, 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, 3, "Could not resolve conflict"); + return fail; + fi; + 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, 3, "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..c7aa45d --- /dev/null +++ b/gap/subroutines/TopGroupDomainAndAction/ViaProductAction.gi @@ -0,0 +1,67 @@ +############################################################################# +##-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-## +## ## +## 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))); + # userOptions.resolveConflict := {p, P} -> QuickNormalClosure(Group(Concatenation(List(Concatenation(P, [p]), GeneratorsOfGroup))), userOptions.B, 5); + + 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/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 072b5a8..eb6c2af 100644 --- a/read.g +++ b/read.g @@ -1,6 +1,35 @@ # -# 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"); + +# 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/Utils.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"); 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 835acb2..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" ), +TestDirectory(DirectoriesPackageLibrary( "WPrecog", "tst/files" ), rec(exitGAP := true)); FORCE_QUIT_GAP(1); # if we ever get here, there was an error