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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418423InstallGlobalFunction(ResolutionGTree, function(arg) local R,n,G,i,L, StabRes,StabGrps,Triple2Pair,Quad2One,GrpsRes,Pair2Quad,Quad2Pair, Dimension,Hmap,Gmult,Gmultrec,Mult,AlgRed,CorrectList,Boundary, Homotopy,FinalHomotopy, StRes,hmap,Action,PseudoBoundary,PseudoHomotopy, ZeroDimensionHmap, ZeroDimensionHtpy, HmapRec,p,q,r,s,HtpyRec,k,g, ZeroDimensionHmapRec, Pair2QuadRec, QuadToPairRec,DimensionRec; R:=arg[1]; n:=arg[2]; G:=R!.group; ############################################# Action:=function(p,r,g) if not IsBound(R!.action) then return 1; else return R!.action(p,r,g); fi; end; ############################################# AlgRed:=AlgebraicReduction; ############################################# Gmultrec:=[]; ############################################# Gmult:=function(i,j) local posit,g; if not IsBound(Gmultrec[i]) then Gmultrec[i]:=[]; fi; if not IsBound(Gmultrec[i][j]) then #Gmultrec[i][j]:=pos(R!.elts[i]*R!.elts[j]); g:=R!.elts[i]*R!.elts[j]; posit:=Position(R!.elts,g); if posit=fail then Add(R!.elts,g); posit:= Length(R!.elts); fi; Gmultrec[i][j]:=posit; fi; return Gmultrec[i][j]; end; ############################################# Mult:=function(g,w) # Multiply gth-element with a word local l,x; l:=StructuralCopy(w); if R!.elts[g]=[] then return [];fi; Apply(l,y->[y[1],Gmult(g,y[2])]); return l; end; ############################################## GrpsRes:=function(G,n) # Resolutions of Group local iso,Q,res,x; if IsBound(R!.resolutions) and HasName(G) then x:=Position(R!.resolutions[2], Name(G)); if not x=fail then return R!.resolutions[1][x]; fi; fi; iso:=RegularActionHomomorphism(G); Q:=Image(iso); res:=ResolutionFiniteGroup(Q,n); res!.group:=G; res!.elts:=List(res!.elts,x->PreImagesRepresentative(iso,x)); return res; end; ############################################# #Create list of stabilizer groups and resolutions StabGrps:= List([0..Length(R)],n-> List([1..R!.dimension(n)], k->R!.stabilizer(n,k))); StabRes:=[]; for L in StabGrps do Add(StabRes,List(L,g->ExtendScalars(GrpsRes(g,n),G,R!.elts)) ); od; ############################################# CorrectList:=function(list) local l,i; if list=[] then return [];fi; l:=StructuralCopy(list[1]); for i in [2..Length(list)] do Append(l,StructuralCopy(list[i])); od; return l; end; ############################################ # return nth-generator of F_(p,q) from (r,s)th-generator of # stabilizer Quad2One:=function(p,q,r,s) local n,d,i,j; n:=0; i:=SignInt(s); s:=AbsInt(s); d:=List([1..R!.dimension(p)],x->StabRes[p+1][x]!.dimension(q)); for j in [1..r-1] do n:=n+d[j]; od; n:=n+s; if q=0 and n>R!.dimension(p) then n:=R!.dimension(p);fi; return i*n; end; ############################################ Triple2Pair:=function(p,q,n) local r,s,d,i; r:=0; d:=List([1..R!.dimension(p)],x->StabRes[p+1][x]!.dimension(q)); i:=SignInt(n); n:=AbsInt(n); while n>0 do r:=r+1; s:=n; n:=n-d[r]; od; return [r,i*s]; end; ############################################ HmapRec:=[]; for p in [1..2] do HmapRec[p]:=[]; for q in [1..n+1] do HmapRec[p][q]:=[]; for r in [1..R!.dimension(p-1)] do HmapRec[p][q][r]:=[]; od; od; od; ZeroDimensionHmapRec:=[]; ############################################ ZeroDimensionHmap:=function(k) local i,j,pk; pk:=AbsInt(k); if not IsBound(ZeroDimensionHmapRec[pk]) then j:=0; for i in [1..pk-1] do j:=j+StabRes[1][i]!.dimension(0); od; j:=j+1; ZeroDimensionHmapRec[pk]:=j; fi; if k>0 then return ZeroDimensionHmapRec[pk]; else return -ZeroDimensionHmapRec[pk];fi; end; ############################################ Hmap:=function(p,q,r,s) #Horiziontal map Hmap:A(p,q)->A(p-1,q), acts on the (r,s) th-generator of A(p,q) local i,l,d0,m,bdr,ps,d1d0,w; ps:=AbsInt(s); if p<>1 then return []; else if not IsBound(HmapRec[p+1][q+1][r][ps]) then if q=0 then bdr:=StructuralCopy(R!.boundary(1,1)); #Print("bdr",bdr); Apply(bdr,w->[ZeroDimensionHmap(w[1]),w[2]]); #Print("bdr",bdr); HmapRec[p+1][q+1][r][ps]:=bdr; else l:=[];m:=[]; d0:=StructuralCopy(List(StabRes[p+1][r]!.boundary(q,ps),x->[Action(p,r,x[2])*x[1],x[2]])); for w in d0 do Append(m,Mult(w[2],Hmap(p,q-1,r,w[1]))); od; Apply(m,x->[Triple2Pair(p-1,q-1,x[1]),x[2]]); for w in m do Append(l,List(StabRes[p][w[1][1]]!.homotopy(q-1,[w[1][2],w[2]]),y->[Quad2One(p-1,q,w[1][1],y[1]),y[2]])); od; HmapRec[p+1][q+1][r][ps]:=AlgRed(l); fi; fi; fi; if SignInt(s)=1 then return HmapRec[p+1][q+1][r][ps]; else return NegateWord(HmapRec[p+1][q+1][r][ps]);fi; end; Pair2QuadRec:=[]; ############################################## Pair2Quad:=function(k,nn) local x,n,nnn, p,q,r,s,i,temp,j1,j2; i:=SignInt(nn); n:=AbsInt(nn); nnn:=n; if not IsBound(Pair2QuadRec[k+1]) then Pair2QuadRec[k+1]:=[]; fi; if not IsBound(Pair2QuadRec[k+1][n]) then temp:=0; for j1 in [0..k] do for j2 in [1..R!.dimension(j1)] do temp:=temp+StabRes[j1+1][j2]!.dimension(k-j1); od; od; #if n>temp then return "generator does not exist";fi; p:=-1; while n>0 do; p:=p+1; r:=0; while (n>0 and r<R!.dimension(p)) do r:=r+1; s:=n; n:=n-StabRes[p+1][r]!.dimension(k-p); od; od; q:=k-p; Pair2QuadRec[k+1][nnn]:=[p,q,r,s]; fi; x:=Pair2QuadRec[k+1][nnn]; return [x[1],x[2],x[3],i*x[4]]; end; QuadToPairRec:=[]; ############################################## Quad2Pair:=function(p,q,r,s) local k,n,i,j,p1,q1,r1,s1; p1:=p+1;q1:=q+1;r1:=r+1;s1:=AbsInt(s)+1; if not IsBound(QuadToPairRec[p1]) then QuadToPairRec[p1]:=[]; fi; if not IsBound(QuadToPairRec[p1][q1]) then QuadToPairRec[p1][q1]:=[]; fi; if not IsBound(QuadToPairRec[p1][q1][r1]) then QuadToPairRec[p1][q1][r1]:=[]; fi; if not IsBound(QuadToPairRec[p1][q1][r1][s1]) then k:=p+q; n:=0; for i in [0..p-1] do for j in [1..R!.dimension(i)] do n:=n+StabRes[i+1][j]!.dimension(k-i); od; od; for i in [1..r-1] do n:=n+StabRes[p+1][i]!.dimension(k-p); od; n:=n+AbsInt(s); QuadToPairRec[p+1][q+1][r+1][AbsInt(s)+1]:=[k,n]; fi; k:=QuadToPairRec[p1][q1][r1][s1]; return [k[1],SignInt(s)*k[2]]; end; ############################################# PseudoBoundary:=[]; for k in [1..n+1] do PseudoBoundary[k]:=[]; od; ############################################## Boundary:=function(k,n) local d,l,p,q,r,s,w,pn; pn:=AbsInt(n); if not IsBound(PseudoBoundary[k+1][pn]) then w:=Pair2Quad(k,pn); p:=w[1];q:=w[2];r:=w[3];s:=w[4]; d:=[]; if q<>0 then l:=StructuralCopy(List(StabRes[p+1][r]!.boundary(q,s),x->[Quad2Pair(p,q-1,r,Action(p,r,x[2])*x[1])[2],x[2]])); Append(d,StructuralCopy(l)); fi; if IsEvenInt(q) then Append(d,StructuralCopy(Hmap(p,q,r,s))); else Append(d,StructuralCopy(NegateWord(Hmap(p,q,r,s)))); fi; PseudoBoundary[k+1][pn]:=AlgRed(d); fi; if SignInt(n)=1 then return PseudoBoundary[k+1][pn]; else return NegateWord(PseudoBoundary[k+1][pn]); fi; end; DimensionRec:=[]; ############################################## Dimension:=function(n) local dim,p,i; if not IsBound(DimensionRec[n+1]) then dim:=0; for p in [0..n] do for i in [1..R!.dimension(p)] do dim:=dim+StabRes[p+1][i]!.dimension(n-p); od; od; DimensionRec[n+1]:= dim; fi; return DimensionRec[n+1]; end; ############################################## HtpyRec:=[]; for k in [1..n] do HtpyRec[k]:=[]; for s in [1..Dimension(k-1)] do HtpyRec[k][s]:=[]; od; od; ############################################## ZeroDimensionHtpy:=function(k) local i,j,r; i:=0; while k>0 do i:=i+1; k:=k-StabRes[1][i]!.dimension(0); r:=i; od; return r; end; ############################################## Homotopy:=function(n,w) local t,g,h0,h11,e,h,dh, p,q,r,s,v,m,pt,ppt, h1,d1h1,x,k,y,ps; t:=w[1]; g:=w[2]; e:=[]; h:=[]; dh:=[]; pt:=AbsInt(t); v:=Pair2Quad(n,pt);#Print(v); p:=v[1];q:=v[2];r:=v[3];s:=v[4]; if not IsBound(HtpyRec[n+1][pt][g]) then if n=0 then ppt:=ZeroDimensionHtpy(pt); h1:=StructuralCopy(R!.homotopy(n,[ppt,g])); d1h1:=StructuralCopy(AlgRed(CorrectList(List(h1,x->Mult(x[2],Hmap(p+1,q,1,x[1])))))); for x in d1h1 do k:=Pair2Quad(n,x[1]); y:=StructuralCopy(StabRes[k[1]+1][k[3]]!.homotopy(q,[k[4],x[2]])); Apply(y,w->[Quad2Pair(k[1],k[2]+1,k[3],w[1])[2],w[2]]); Append(e,y); od; h0:=StructuralCopy(StabRes[p+1][r]!.homotopy(0,[s,g])); Apply(h0,w->[Quad2Pair(p,q+1,r,w[1])[2],w[2]]); h11:=List(h1,x->[Quad2Pair(p+1,q,Triple2Pair(p+1,q,x[1])[1],Triple2Pair(p+1,q,x[1])[2])[2],x[2]]); Append(h,NegateWord(e)); Append(h,h0); Append(h,h11); HtpyRec[n+1][pt][g]:=AlgRed(h); else if p=0 then h0:=StructuralCopy(StabRes[p+1][r]!.homotopy(q,[s,g])); Apply(h0,w->[Quad2Pair(p,q+1,r,w[1])[2],w[2]]); Append(h,h0); else ps:=Action(1,1,g)*s; m:=StructuralCopy(StabRes[p+1][r]!.homotopy(q,[ps,g])); Apply(m,x->[Action(1,1,x[2])*x[1],x[2]]); h0:=List(m,x->[Quad2Pair(p,q+1,r,x[1])[2],x[2]]); Append(h,h0); dh:=AlgRed(CorrectList(List(m,x->Mult(x[2],Hmap(p,q+1,1,x[1]))))); for x in dh do k:=Pair2Quad(n,x[1]); y:=StructuralCopy(StabRes[k[1]+1][k[3]]!.homotopy(k[2],[k[4],x[2]])); Apply(y,w->[Quad2Pair(k[1],k[2]+1,k[3],w[1])[2],w[2]]); Append(e,y); od; if IsEvenInt(q) then Append(h,e); else Append(h,NegateWord(e));fi; fi; HtpyRec[n+1][pt][g]:=AlgRed(h); fi; fi; if SignInt(t)=1 then return HtpyRec[n+1][pt][g]; else return NegateWord(HtpyRec[n+1][pt][g]); fi; end; ############################################## FinalHomotopy:=function(n,g) if R!.homotopy=fail then return fail; else return Homotopy(n,g); fi; end; ####ADDED MAY############################################## StRes:=function(n,k) return StabRes[n+1][k]; end; ############################################## return Objectify(HapResolution, rec( dimension:=Dimension, boundary:=Boundary, homotopy:=FinalHomotopy, elts:=R!.elts, group:=R!.group, stabres:=StRes, properties:= [["length",n], ["initial_inclusion",true], ["type","resolution"], ["characteristic",EvaluateProperty(R,"characteristic")] ] )); end);