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cactus1.g
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cactus1.g
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LoadPackage("simpl");
Read("canon.g");
Read("old.g");
Read("VerticesInFacesHelp.g");
Read("BlockTypes.g");
Read("MultitetrahedralEmbedding.g");
Read("alg.g");
Read("Tetdecomp.g");
T:=SimplicialSurfaceByDownwardIncidence([[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]],
[[4,5,6],[2,3,6],[1,3,5],[1,2,4]]);
O:=Octahedron();
DT:=SimplicialSurfaceByDownwardIncidence([[1,2],[1,3],[1,4],
[5,2],[5,3],[5,4],
[2,3],[3,4],[2,4]],
[[1,2,7],[2,3,8],[1,3,9],,
[4,5,7],[5,6,8],[4,6,9]]);
CactusSymbolSoFar:=[];
#--------------------------------------------------------------------------
CRemove:=function(L,i)
local j,l,l2,l3,h,temp1,temp2,temp3,temp4,temp5;
temp2:=ShallowCopy(L);
j:=Minimum(List(temp2,g->Position(temp2,g)));
temp3:=ShallowCopy(temp2);
Remove(temp3,j);
temp1:=[];
while not(temp3=[]) do
l3:=Minimum(List(temp3,g->Position(temp3,g)));
l2:=Minimum(List(temp2,g->Position(temp2,g)));
l:=l3+1-l2;
Add(temp1,l);
Remove(temp2,l2);
Remove(temp3,l3);
od;
temp4:=[j];
for h in temp1 do
j:=j+h;
Add(temp4,j);
od;
temp5:=[];
for h in temp4 do
if not(h=i) then
temp5[h]:=L[h];
fi;
od;
return temp5;
end;
Iso:=function(SSiso,L)
local Simp;
for Simp in L do
if IsIsomorphic(Simp,SSiso) then
return true;
fi;
od;
return false;
end;
try:=function(SStry)
local V,copyV;
copyV:=Filtered(ShallowCopy(Vertices(SStry)),V->FaceDegreeOfVertex(SStry,V)=3);
if not(Iso(SStry,[T,DT])) then
#Print("not");
for V in copyV do
#Print(copyV,"\n");
SStry:=RemoveTetra(SStry,V);
od;
fi;
return SStry;
end;
#verticesoffaces
#kann man flaechen mit 3 wait auch ohne flaechen mit 2-waist erzzeugen
#EdgeTurn als Gruppenoperation
IsCactus:=function(SSiscactus)
local g;
while not(SSiscactus=try(SSiscactus)) and Length(Set(Faces(SSiscactus))) >6 do
SSiscactus:=try(SSiscactus);
od;
if not(IsIsomorphic(SSiscactus,T)) and not(IsIsomorphic(SSiscactus,DT)) then
return false;
else
return true;
fi;
end;
#-------------------------------------
ShallowList:=function(L)
local g;
return ShallowCopy(List(L,g->ShallowCopy(g)));
end;
#----------------------------------------
P:=function(S,VS)
if VS in VerticesOfEdges(S) then
#Print("if");
return Position(VerticesOfEdges(S),VS);
else
#Print("else");
return Position(VerticesOfEdges(S),[VS[2],VS[1]]);
fi;
end;
#---------------------------------------------------------------------
EdgeTurn:=function(SSedge,e)
local EOF,VOE,VOEe,Edg1,Edg2,FOE,VOF, g;
FOE:=FacesOfEdge(SSedge,e);
if Length( Union(VerticesOfFace(SSedge,FOE[1]),VerticesOfFace(SSedge,FOE[2])))=4 then
Edg1:=Filtered(EdgesOfFace(SSedge,FacesOfEdge(SSedge,e)[1]),g->not(g=e));
Edg2:=Filtered(EdgesOfFace(SSedge,FacesOfEdge(SSedge,e)[2]),g->not(g=e)) ;
VOF:=Union(VerticesOfFace(SSedge,FOE[1]),VerticesOfFace(SSedge,FOE[2]));
VOE:=ShallowCopy(VerticesOfEdges(SSedge));
VOEe:=Filtered(VOF,g-> not(g in VerticesOfEdge(SSedge,e)));
VOE[e]:=VOEe;
EOF:=ShallowCopy(EdgesOfFaces(SSedge));
if Length(Intersection(VerticesOfEdge(SSedge,Edg1[1]),VerticesOfEdge(SSedge,Edg2[1])))>0 and
IsSubsetSet(VerticesOfEdge(SSedge,e),Intersection(VerticesOfEdge(SSedge,Edg1[1]),VerticesOfEdge(SSedge,Edg2[1]))) then
EOF[FOE[1]]:=[e,Edg1[1],Edg2[1]];
EOF[FOE[2]]:=[e,Edg1[2],Edg2[2]];
else
EOF[FOE[1]]:=[e,Edg1[2],Edg2[1]];
EOF[FOE[2]]:=[e,Edg1[1],Edg2[2]];
fi;
return SimplicialSurfaceByDownwardIncidence(VOE,EOF);
fi;
return SSedge;
end;
#---------------------------------------------------------------------
#CactusDistance:=function(SScactusdistance)
# local L,t,help1,help2;
# help1:=[];
# L:=CactusDistanceOfSimplicialSurfaceHelp(SScactusdistance,0,[SScactusdistance],[0]);
# for t in L[1] do
# if IsCactus(t) then
# Add(help1,[t,L[2][Position(L[1],t)]]);
# fi;
# od;
#return L;
# return help1;
#end;
#CactusDistanceOfSimplicialSurfaceHelp:=function(SScdhelp,i,L1,L2)
# local e,g,VOE,tempL;
# for e in Edges(SScdhelp) do
# VOE:=VerticesOfEdge(SScdhelp,e);
# if not(Iso(EdgeTurn(SScdhelp,e),L1)) then
# SScdhelp:=EdgeTurn(SScdhelp,e);
# Add(L1,SScdhelp);
# Add(L2,i+1);
# tempL:=CactusDistanceOfSimplicialSurfaceHelp(SScdhelp,i+1,L1,L2);
# for g in tempL[1] do
# if not(Iso(g,L1)) then
# Add(L1,g);
# Add(L2,tempL[Position(L1,g)]);
# fi;
# od;
# fi;
# od;
# return [L1,L2];
#end;
#------------------------------------------------------------------
Tetra:=function(M)
local ME,MF,V1,V2,V3,V4,copyM;
copyM:=ShallowCopy(M);
V1:=Minimum(copyM);
V4:=Maximum(copyM);
copyM:=CRemove(copyM,Position(copyM,V1));
copyM:=CRemove(copyM,Position(copyM,V4));
V2:=Minimum(copyM);
V3:=Maximum(copyM);
ME:=[[V1,V2],[V1,V3],[V1,V4],[V2,V3],[V2,V4],
[V3,V4]];
MF:=[[4,5,6],[2,3,6],[1,3,5],[1,2,4]];
return SimplicialSurfaceByDownwardIncidence(ME,MF);
end;
AddTetraF:=function(SSaddtetraf,F)
local T1,numbV;
#VerticesOfFace(S,F);
numbV:=Maximum(Vertices(SSaddtetraf));
T1:=Union([numbV+1],ShallowCopy(VerticesOfFace(SSaddtetraf,F)));
return AddTetra(SSaddtetraf,Tetra(T1));
end;
AddTetra:=function(SSaddtetra,T2)
local VerticesEdges,EdgesFaces,n,g,L,M;
VerticesEdges:=ShallowCopy(VerticesOfEdges(SSaddtetra));
EdgesFaces:=ShallowCopy(EdgesOfFaces(SSaddtetra));
n:=Length(VerticesEdges);
L:=[[],[]];
M:=[];
for g in VerticesOfEdges(T2) do
if not(g in VerticesEdges) then
Add(VerticesEdges,g);
Add(M,[Position(VerticesOfEdges(T2),g),g]);
else
Add(L[1],Position(VerticesOfEdges(SSaddtetra),g));
Add(L[2],g);
fi;
od;
# EdgesFaces:=CRemove(EdgesFaces,Position(EdgesFaces,Set(L[1])
# ));
if Intersection(L[2][1],M[1][2])=[] then
Add(EdgesFaces,[L[1][1],n+2,n+3]);
Add(EdgesFaces,[L[1][2],n+1,n+2]);
Add(EdgesFaces,[L[1][3],n+1,n+3]);
fi;
if Intersection(L[2][1],M[2][2])=[] then
Add(EdgesFaces,[L[1][1],n+1,n+3]);
Add(EdgesFaces,[L[1][2],n+1,n+2]);
Add(EdgesFaces,[L[1][3],n+2,n+3]);
fi;
if Intersection(L[2][1],M[3][2])=[] then
Add(EdgesFaces,[L[1][1],n+2,n+1]);
Add(EdgesFaces,[L[1][2],n+1,n+3]);
Add(EdgesFaces,[L[1][3],n+2,n+3]);
fi;
EdgesFaces:=CRemove(EdgesFaces,Position(EdgesFaces,Set(L[1])
));
return SimplicialSurfaceByDownwardIncidence(VerticesEdges,EdgesFaces);
end;
#------------------------------------
RemoveTetra:=function(SSremovetetra,V)
local Ver,NewEdgFac,E1,E2,E3,NewVerEdg,NewVerEdg2,NewVerEdg3,
NewEdgFac2,F,VF,i,NewEdgFac3,NewEdgFac4,NewEdg5,g,h,l;
if Length(Set(Faces(SSremovetetra)))<=6 and
not(IsIsomorphic(SSremovetetra,DT)) then
return SSremovetetra;
fi;
if IsIsomorphic(SSremovetetra,T) then
return SSremovetetra;
fi;
#Print(EdgesOfFaces(SSremovetetra),"\n",VerticesOfEdges(SSremovetetra),"\n");
NewEdgFac:=ShallowList(EdgesOfFaces(SSremovetetra));
NewVerEdg:=ShallowList(EdgesOfFaces(SSremovetetra));
if FaceDegreeOfVertex(SSremovetetra,V)=3 then
F:=FacesOfVertex(SSremovetetra,V);
NewEdgFac:=CRemove(NewEdgFac,Position(NewEdgFac,EdgesOfFace(SSremovetetra,F[1])));
NewEdgFac:=CRemove(NewEdgFac,Position(NewEdgFac,EdgesOfFace(SSremovetetra,F[2])));
NewEdgFac:=CRemove(NewEdgFac,Position(NewEdgFac,EdgesOfFace(SSremovetetra,F[3])));
VF:=Union(VerticesOfFace(SSremovetetra,F[1]),VerticesOfFace(SSremovetetra,F[2]));
Remove(VF,Position(VF,V));
E1:=Filtered(EdgesOfFace(SSremovetetra,F[1]),g->Set(VerticesOfEdge(SSremovetetra,g)) in [Set([VF[1],VF[2]]),Set([VF[1],VF[3]]),Set([VF[2],VF[3]])])[1];
E2:=Filtered(EdgesOfFace(SSremovetetra,F[2]),g->Set(VerticesOfEdge(SSremovetetra,g)) in [Set([VF[1],VF[2]]),Set([VF[1],VF[3]]),Set([VF[2],VF[3]])])[1];
E3:=Filtered(EdgesOfFace(SSremovetetra,F[3]),g->Set(VerticesOfEdge(SSremovetetra,g)) in [Set([VF[1],VF[2]]),Set([VF[1],VF[3]]),Set([VF[2],VF[3]])])[1];
#E2:=Filtered(EdgesOfFace(S,F[2]),g->VerticesOfEdge(S,g)=P(S,[VF[2],VF[3]]))[1];
# E2:=P(S,[VF[2],VF[3]]);
# E3:=P(S,[VF[1],VF[3]]);
Add(NewEdgFac,[E1,E2,E3]);
NewVerEdg:=ShallowList(VerticesOfEdges(SSremovetetra));
for g in EdgesOfVertex(SSremovetetra,V) do
#NewVerEdg:=CRemove(NewVerEdg,Position(NewVerEdg,g));
NewVerEdg:=CRemove(NewVerEdg,g);
od;
fi;
return SimplicialSurfaceByDownwardIncidence(NewVerEdg,NewEdgFac);
#else
#return SSremovetetra;
#fi;
end;
#-----------------------------------------------------
AllSimplicialSurfacesWithTwoWaist:=function(n)
local L,SSallsimp;
if IsEvenInt(n) and n>1 then
SSallsimp:=AllSimplicialSurfaces(EulerCharacteristic,2,
NumberOfFaces,n,IsClosedSurface,true)[1];
#L:=CactusDistanceOfSimplicialSurfaceHelp(SSallsimp,0,[SSallsimp],[0]);
L:=EdgeTurnRek(SSallsimp);
return L[1];
else
return false;
fi;
end;
#--------------------------------------------------------
NameFacesAndVertices:=function(SSnamef,L)
local Vertname,t,Facename,ValueF,x,tempF,tempV,temp1,temp2,g,h,
newTetra,V,F,temp,temp3,temp4,i;
V:=Vertices(SSnamef);
F:=Faces(SSnamef);
Vertname:=[];
Facename:=[];
if IsIsomorphic(SSnamef,T) then
Vertname:=[[1,V[1]],[2,V[2]],[3,V[3]],[4,V[4]]];
for F in Faces(SSnamef) do
temp:=Filtered(Vertname,g->g[2] in VerticesOfFace(SSnamef,F));
temp:=List(temp,g->g[1]);
t:=Filtered([1,2,3,4],g->not(g in temp));
Facename[t[1]]:=[t[1],F];
od;
L[1]:=[Facename];
L[2]:=Vertname;
else
tempF:=[];
for g in L[1] do
for h in g do
#temp:=List(g,h->h[2]);
#tempF:=Union(tempF,temp);
Add(tempF,h[2]);
od;
od;
tempF:=Set(tempF);
tempF:=Filtered(Faces(SSnamef),g->not(g in tempF));
tempV:=List(L[2],g->g[2]);
tempV:=Filtered(Vertices(SSnamef),g->not(g in tempV));
temp:=[];
for h in FacesOfVertex(SSnamef,tempV[1]) do
temp:=Union(temp,ShallowCopy(VerticesOfFace(SSnamef,h)));
od;
CRemove(temp,Position(temp,tempV[1]));
temp1:=Filtered(L[2],g->g[2] in temp);
temp2:=List(temp1,g->g[1]);
t:=Filtered([[1,tempV[1]],[2,tempV[1]],
[3,tempV[1]],[4,tempV[1]]],g->not(g[1] in temp2));
Add(L[2],t[1]);
for g in tempF do
temp3:=Filtered(L[2],h->h[2] in VerticesOfFace(SSnamef,g));
temp4:=List(temp3,h->h[1]);
t:=Filtered([[1,g],[2,g],[3,g],[4,g]],
h->not(h[1] in temp4));
Add(Facename,t[1]);
od;
Add(L[1],Facename);
fi;
if not(IsIsomorphic(SSnamef,T)) then
for i in [1..Length(L[1])] do
L[1][i]:=Filtered(L[1][i],g->g[2] in Faces(SSnamef));
od;
fi;
#return [tempF,tempV,temp,temp1];
return L;
end;
########################################################
########################################################
#########################################################
AllSym2:=function(i,L)
local L1,g,h;
L1:=[];
#L:=List(AllSym(i-1),g->ConstructSurfaceBySymbol(g,[1,2,3,4]));
for g in L do
for h in Help(g) do
Add(L1,AddTetraF(g,h));
od;
od;
return IsomorphismRepresentatives(L1);
end;
############################################################
###########################################################
#----------------------------------------------------------------------
NeighbourVertices:=function(SSneighbour,V)
local F,temp,g;
F:=FacesOfVertex(SSneighbour,V);
temp:=[];
for g in F do
temp:=Union(temp,ShallowCopy(VerticesOfFace(SSneighbour,g)));
od;
return Filtered(temp,g->not(g=V));
end;
#-------------------------------------------------------
ConstructSurfaceBySymbol:=function(CacSym,M)
local g,h,Cac,Cac1,Cac2,help,L,Pos,LT2,LT3,gl,nvert,T,M1,M2,M3,M4,ME,MF;
#Cac:=Tetra(M);\
#Construct Tetra with Faces M1,M2,M3,M4
M1:=Minimum(M);
M4:=Maximum(M);
Remove(M,Position(M,M1));
Remove(M,Position(M,M4));
M2:=Minimum(M);
M3:=Maximum(M);
ME:=[[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]];
MF:=[];
MF[M4]:=[1,2,4];
MF[M3]:=[1,3,5];
MF[M1]:=[4,5,6];
MF[M2]:=[2,3,6];
Cac2:=SimplicialSurfaceByDownwardIncidence(ME,MF);
#Cac1:=SimplicialSurfaceByDownwardIncidence(ME,MF);
LT2:=[[[1,M1],[2,M2],[3,M3],[4,M4]]];
LT3:=[[[[1,M1],[2,M2],[3,M3],[4,M4]]],[[1,1],[2,2],[3,3],[4,4]]];
nvert:=5;
for gl in CacSym do
help:=Filtered(LT3[1][gl[1]], h->h[1]=gl[2]);
Pos:=Position(LT3[1][gl[1]],help[1]);
Cac2:=AddTetraF(Cac2,LT3[1][gl[1]][Pos][2]);
LT3:=NameFacesAndVertices(Cac2,LT3);
od;
#return [Cac,LT2,Cac1,LT3];
# return [LT3,Cac2];
return Cac2;
end;
#----------------------------------------------------------------------
khelp:=function(L,k)
local L1,i;
L1:=L;
for i in [1..Length(L)] do
Append(L1[i],k);
od;
return L1;
end;
khelp1:=function(L1,L)
local i,t,t1,j;
t:=L1;
t1:=[];
for i in [1..Length(t)] do
for j in L do
Append(t1,khelp(t,j));
od;
od;
return t1;
end;
kprod:=function(L,n)
local temp,t1,j,t,i,k;
temp:=List(L,g->[g]);
t:=List(L,g->[]);
t1:=t;
for j in [1..n] do
k:=Length(t1);
#for j in [1..k]
t1:=t;
od;
end;
GetSymbolHelp:=function(SSgetsymh)
local g,CS,SurfList,Numbv,F,V;
SurfList:=[];
CS:=[];
Numbv:=[];
if IsCactus(SSgetsymh) then
while(not(SSgetsymh=try(SSgetsymh))) do
Add(SurfList,SSgetsymh);
Add(Numbv,
Length(Filtered(Vertices(SSgetsymh),
V->FaceDegreeOfVertex(SSgetsymh,V)=3)));
SSgetsymh:=try(SSgetsymh);
od;
Add(SurfList,SSgetsymh);
Add(Numbv,0);
fi;
return [SurfList,CS,Numbv];
end;
#Anderes abspeichern fuer kakteen
#DrawSurfacetothreed
GetSymbol:=function(SSgetsym)
local L,helpL,hilf,hilf1,hilf2,hilf3,hilf4,hilf5,
CS,F,hL,tempSurf,newhelp,tr,it,Surf,t1,t2,t,V,
SSS,l,V3,VF1,VF2, trip, num,kp,kpfac,g,bool,new,Fac;
L:=GetSymbolHelp(SSgetsym);
Surf:=L[1][Length(L[1])];
#Print(L);
newhelp:=[];
CS:=[];
hL:=[];
helpL:=[];
new:=[];
if IsIsomorphic(Surf,T) then
F:=Faces(Surf);
helpL:=NameFacesAndVertices(Surf,[[],[]]);
new:=[];
fi;
if IsIsomorphic(Surf,DT) then
#Print("in");
V:=Vertices(Surf);
V3:=Filtered(Vertices(Surf),g->FaceDegreeOfVertex(Surf,g)=3);
VF1:=FacesOfVertex(Surf,V3[1]);
VF2:=FacesOfVertex(Surf,V3[2]);
V:=Filtered(Vertices(Surf),g->not(FaceDegreeOfVertex(Surf,g)=3));
hilf:=[[1,V3[1]],[2,V[1]],[3,V[2]],[4,V[3]],[1,V3[2]]];
helpL[2]:=hilf;
hilf4:=[];
hilf:=[];
for F in VF1 do
#hilf1:=VerticesOfFace(Surf,F);
hilf1:=List(VerticesOfFace(Surf,F),g->Filtered(helpL[2],
h->h[2]=g));
hilf2:=List(hilf1,g->g[1][1]);
#Print("hilf2 ",hilf2,"\n");
hilf3:=Filtered([1,2,3,4],g->not(g in hilf2));
Add(hilf4,[hilf3[1],F]);
od;
hilf[1]:=hilf4;
hilf5:=[];
for F in VF2 do
#hilf1:=VerticesOfFace(Surf,F);
hilf1:=List(VerticesOfFace(Surf,F),g->Filtered(helpL[2],
h->h[2]=g));
hilf2:=List(hilf1,g->g[1][1]);
#Print("hilf2 ",hilf2,"\n");
hilf3:=Filtered([1,2,3,4],g->not(g in hilf2));
Add(hilf5,[hilf3[1],F]);
od;
hilf[2]:=hilf5;
#Print("hilf ",hilf,"\n");
helpL[1]:=hilf;
#helpL:=[[[[4,VF1[1]],[2,VF1[2]],[3,VF1[3]]],
#[[4,VF2[1]],[2,VF2[2]],[3,VF2[3]]]],
#[[1,V[1]],[2,V[2]],[3,V[3]],[4,V[4]],[5,V[5]]]];
#Print(VerticesOfFaces(Surf));
new:=[[1,1]];
#Print(helpL);
#return [VF1,hilf2,helpL];
fi;
# Print(L[3]);
#Print(helpL);
for it in [1..Length( L[3])-1] do
bool:=false;
num:=L[3][Length(L[3])-it];
SSS:=L[1][Length(L[1])-it+1];
#old Fac:=ShallowCopy(Faces(Surf));
Fac:=ShallowCopy(Faces(Surf));
kpfac:=Combinations(Fac,num);
bool:=false;
#Print(IsIsomorphic(SSS,DT));
for trip in kpfac do
tempSurf:=Surf;
#Print(IsIsomorphic(tempSurf,DT));
#Print(trip);
if not(bool) then
#Print("aaaaaaaaaaaaaaaaaaaaa");
for l in [1..num] do
tempSurf:=AddTetraF(tempSurf,trip[l]);
#Print(trip ,IsIsomorphic(tempSurf,L[1][Length(L[1])-it]),"\n");
od;
fi;
#Print("beginning ",helpL,"\n");
#Print(IsIsomorphic(tempSurf,L[1][Length(L[1])-it]));
if IsIsomorphic(tempSurf,L[1][Length(L[1])-it]) and not(bool) then
#Print("Iso ", trip, "\n");
bool:=true;
for tr in trip do
t1:=Filtered(helpL[1],g->not(
Intersection([[1,tr],[2,tr],[3,tr],[4,tr]],g)=[]));
t2:=Filtered(t1[1],g->tr=g[2]);
Add(new,[Position(helpL[1],t1[1]),t2[1][1]]);
Surf:=AddTetraF(Surf,tr);
helpL:=NameFacesAndVertices(Surf,helpL);
#Print(tr," ",helpL,"\n","new ",new,"\n");
od;
fi;
od;
bool:=false;
od;
#return [new, tempSurf];
return new;
end;
Tetrahedralnumber:=function(SStetnum)
local tempS,Tetnum;
tempS:=SStetnum;
Tetnum:=[];
if IsCactus(SStetnum) then
while not(tempS=try(tempS)) and not(IsIsomorphic(tempS,T)) do
Add(Tetnum,
Length(Filtered(Vertices(tempS),g->FaceDegreeOfVertex(SStetnum,g)=3)));
tempS:=try(tempS);
od;
if IsIsomorphic(tempS,T) then
Add(Tetnum,1);
fi;
if IsIsomorphic(tempS,DT) then
Add(Tetnum,2);
fi;
fi;
return Tetnum;
end;
Butter:=function(SSbutter,E)
local temp,F,um,V;
V:=Intersection(VerticesOfEdge(SSbutter,E[1]),VerticesOfEdge(SSbutter,E[2]))[1];
um:=UmbrellaPathOfVertex(SSbutter,V);
um:=FacesAsList(um);
F:=FacesOfEdge(SSbutter,E[1])[1];
temp:=[F];
F:=Filtered(um, g->g in NeighbourFacesOfFace(SSbutter,F)
and not(E[1] in EdgesOfFace(SSbutter,g)))[1];
Add(temp,F);
#Print(um," ",F," ",temp,"\n");
while not(F in FacesOfEdge(SSbutter,E[2])) and not(F in temp) do
Add(temp,F);
F:=Filtered(um, g->g in NeighbourFacesOfFace(SSbutter,F)
and not(E[2] in EdgesOfFace(SSbutter,g)))[1];
od;
#F:=Filtered( um,g-> g in NeighbourFacesOfFace( S, F )
#and E[2] in EdgesOfFace( S, g ) and not(E[1] in EdgesOfFace(S,g)))[1];
#Add(temp,F);
return temp;
end;
ButterflyInsertion:=function(SSbutterfly,E)
local VE,EF,temp1,V,nv,ne,um,ef,g,h,f,bool,i,j,temp,ButtVE;
ne:=Length(Edges(SSbutterfly));
nv:=Length(Vertices(SSbutterfly));
VE:=ShallowList(VerticesOfEdges(SSbutterfly));
EF:=ShallowList(EdgesOfFaces(SSbutterfly));
V:=Intersection(VE[E[1]],VE[E[2]])[1];
um:=UmbrellaPathOfVertex(SSbutterfly,V);
um:=FacesAsList;
E:=Set(E);
bool:=false;
for ef in EF do
if IsSubset(ef,E) then
bool:=true;
f:=Position(EF,ef);
fi;
od;
if bool then
for i in [1,2] do
temp:=[];
for j in [1,2] do
if VE[E[i]][j]=V then
temp[j]:=nv+1;
else
temp[j]:=VE[E[i]][j];
fi;
od;
Add(VE,temp);
od;
VE[ne+3]:=[V,nv+1];
for i in [1,2,3] do
if EF[f][i]=E[1] then
EF[f][i]:=ne+1;
fi;
if EF[f][i]=E[2] then
EF[f][i]:=ne+2;
fi;
od;
Add(EF,[E[1],ne+1,ne+3]);
Add(EF,[E[2],ne+2,ne+3]);
#return [VE];
return SimplicialSurfaceByDownwardIncidence(VE,EF);
else
#Print("elseeeeeeeeeeeee");
temp:=[];
for i in Butter(SSbutterfly,E) do
temp:=Union(temp,EF[i]);
od;
temp1:=Set(temp);
ButtVE:=Filtered([1..Length(VE)],i->i in temp1 and V in VE[i]);
for i in E do
temp:=[];
for j in [1,2] do
if VE[i][j]=V then
temp[j]:=nv+1;
else
temp[j]:=VE[i][j];
fi;
od;
Add(VE,temp);
od;
for i in Filtered(ButtVE,g->not(g in E)) do
for j in [1,2] do
if VE[i][j]=V then
VE[i][j]:=nv+1;
else
VE[i][j]:=VE[i][j];
fi;
od;
od;
for i in Butter(SSbutterfly,E) do
for j in [1,2,3] do
if EF[i][j] in E then
#Print("i ",i," j ",j," Eij ",EF[i][j],"\n");
EF[i][j]:=ne+Position(E,EF[i][j]);
fi;
od;
od;
Add(VE,[V,nv+1]);
Add(EF,[E[1],ne+1,ne+3]);
Add(EF,[E[2],ne+2,ne+3]);
return SimplicialSurfaceByDownwardIncidence(VE,EF);
fi;
end;
ButterflyEdges:=function(SSbedges)
local L,g,h;
L:=[];
for g in Edges(SSbedges) do
for h in Edges(SSbedges) do
if Length(Intersection(VerticesOfEdge(SSbedges,g),
VerticesOfEdge(SSbedges,h)))=1 then
Add(L,Set([g,h]));
fi;
od;
od;
return Set(L);
end;
EdgeTurnRek:=function(SSedgerek)
local Simprek,K,L,g;
SSedgerek:=CanonicalRepresentativeOfPolygonalSurface2(SSedgerek)[1];
K:=[[SSedgerek],[0]];
#L:=[];
K:=EdgeTurnRekHelp(SSedgerek,[[SSedgerek],[0]],0);
return K;
end;
###############################
#################################
EdgeTurnRek1:=function(SSedgerek)
local Simprek,K,L,g;
SSedgerek:=CanonicalRepresentativeOfPolygonalSurface2(SSedgerek)[1];
#K:=[SSedgerek];
#L:=[];
K:=EdgeTurnRekHelp1(SSedgerek,[SSedgerek]);
return K;
end;
helpedge:=function(S)
local L,o,G,g,h;
G:=AutomorphismGroupOnEdges(S);
o:=Orbits(G,Edges(S));
L:=Filtered(List(o,g->g[1]),h->checkbufl(S,h));
return Filtered(L, g-> not(3 in
[FaceDegreesOfVertices(S)[VerticesOfEdge(S,g)[1]],FaceDegreesOfVertices(S)[VerticesOfEdge(S,g)[2]]]));
end;
bufl:=function()
return SimplicialSurfaceByVerticesInFaces([[1,2,3],[2,3,4]]);
end;
checkbufl:=function(S,e)
local sS;
if not (e in InnerEdges(S)) then Error("not inner");fi;
sS:=FacesOfEdge(S,e);
sS:=SubcomplexByFaces(S,sS);
return IsIsomorphic(bufl(),sS);
end;
no2waist:=function(S)
local L,g;
L:=List(VerticesOfEdges(S),g->Set(g));
if Length(L)=Length(Set(L)) then
return true;
else
return false;
fi;
end;
EdgeTurnRekHelp1:=function(SSedgerekh,K)
local T,g,L;
for g in helpedge(SSedgerekh) do
#Print("a","\n");
T:=turnedge(SSedgerekh,g)[1];
#T:=turnedge(SSedgerekh,g)[1];
T:=CanonicalRepresentativeOfPolygonalSurface2(T)[1];
if not(T in K) and no2waist(T) then
Add(K,T);
# Add(K[2],i+1);
K:=EdgeTurnRekHelp1(T,K);
fi;
# if T in K[1] and K[2][Position(K[1],T)]>i+1 then
# K[2][Position(K[1],T)]:=i+1;
# fi;
od;
return K;
end;
#######################################
######################################
EdgeTurnRekHelp:=function(SSedgerekh,K,i)
local S,g,L;
for g in Edges(SSedgerekh) do
S:=EdgeTurn(SSedgerekh,g);
#T:=turnedge(SSedgerekh,g)[1];
S:=CanonicalRepresentativeOfPolygonalSurface2(S)[1];
if not(S in K[1]) and no2waist(S) then
Add(K[1],S);
Add(K[2],i+1);
K:=EdgeTurnRekHelp(S,K,i+1);
fi;
if S in K[1] and K[2][Position(K[1],S)]>i+1 then
K[2][Position(K[1],S)]:=i+1;
fi;
od;
return K;
end;
turnedge:=function(S,e)
local sS,sB,v,ee;
sB:=SubcomplexByFaces(S,FacesOfEdge(S,e));
ee:=Difference(Edges(sB),[e]);
v:=Intersection(VerticesOfEdge(sB,ee[1]),VerticesOfEdge(S,e))[1];
sS:=Difference(Faces(S),FacesOfEdge(S,e));
sS:=SubcomplexByFaces(S,sS);
return JoinBoundaries(sS,[v,ee[1]],sB,[Difference(VerticesOfEdge(sB,ee[1]),[v])[1],ee[1]]);
end;
CactusDistance:=function(SScactus)
if IsCactus(SScactus) then
return 0;
else
Minimum(EdgeTurnRek(SScactus)[2]);
fi;
return EdgeTurnRek(SScactus);
end;
CrossProduct:=function(A,B)
local CP;
CP:=[A[2]*B[3]-A[3]*B[2],
A[3]*B[1]-A[1]*B[3],
A[1]*B[2]-A[2]*B[1]];
return 1/Sqrt(CP[1]*CP[1]+CP[2]*CP[2]+CP[3]*CP[3])*CP;
end;
N:=function(V)
return Sqrt(V[1]*V[1]+V[2]*V[2]+V[3]*V[3]);
end;
#GetVert:=function(SSgetvert,Lgetvert,A,B,C)
# local M,MAB,MBC,hl,RA,RC,VV1,VV2,VV3,t,RV,H,i;
#for i in [1,2,3] do
# A[i]:=Float(A[i]);
# B[i]:=Float(B[i]);
# C[i]:=Float(C[i]);
# od;
# MAB:=A+1/2*(B-A);
# MBC:=B+1/2*(C-B);
# RA:=A-MBC;
# RC:=C-MAB;
# t:=SolutionMat([RA,(-1)*RC],MAB-MBC);
# M:=MBC+t[1]*RA;
# H:=CrossProduct(B-A,C-A);
# hl:=Sqrt((B-A)*(B-A)-N(M-A)*N(M-A));
# if M+hl*H in Lgetvert then
# return M-hl*H;
# else
## return M+hl*H;
# fi;
#end;
#DrawCactusToJavaFile:=function(SSdraw,html)
#
# local VC,V,i,help,SSdra,Nd,len,Fd,Vd,height,printRecord,vertvisited,PH;
# height:=0.;
# VC:=[];
## #SSdra:=SimplicialSurfaceByDownwardIncidence(VerticesOfEdges(SSdraw),Set(EdgesOfFaces(SSdraw)));
# PH:=GetSymbolHelp(SSdra)[1];
# if IsIsomorphic(PH[Length(PH)],T) then
# Vd:=Vertices(PH[Length(PH)]);
# VC[Vd[1]]:=[0.,0.,0.];
# VC[Vd[2]]:=[1.,0.,0.];
# VC[Vd[3]]:=[1/2.,0.,Sqrt(3/4.)];
# VC[Vd[4]]:=GetVert(PH[Length(PH)],VC,[0.,0.,0.],[1.,0.,0.],[1/2.,0.,Sqrt(3/4.)]);
# else
# Vd:=Filtered(Vertices(PH[Length(PH)]),g->not(FaceDegreeOfVertex(PH[Length(PH)],g)=3));
# VC[Vd[1]]:=[0.,0.,0.];
# VC[Vd[2]]:=[1.,0.,0.];
# VC[Vd[3]]:=[1/2.,0.,Sqrt(3/4.)];
# Vd:=Filtered(Vertices(PH[Length(PH)]),g->FaceDegreeOfVertex(PH[Length(PH)],g)=3);
# VC[Vd[1]]:=GetVert(PH[Length(PH)],VC,[0.,0.,0.],[1.,0.,0.],[1/2.,0.,Sqrt(3/4.)]);
# VC[Vd[2]]:=GetVert(PH[Length(PH)],VC,[0.,0.,0.],[1.,0.,0.],[1/2.,0.,Sqrt(3/4.)]);
# fi;
# for i in [1..Length(PH)-1] do
# len:=Length(PH)-i+1;
# Vd:=Filtered(Vertices(PH[len-1]),g->not(g in Vertices(PH[len])) );
# for V in Vd do
# Nd:=NeighbourVertices(PH[len-1],V);
# VC[V]:=GetVert(PH[len],VC,Nd[1],Nd[2],Nd[3]);
# od;
# od;
# printRecord:=SetVertexCoordiantes3D(SSdra,VC,rec());
# DrawSurfaceToJavaScript(SSdra,html,printRecord);
# return [VC,printRecord];
#end;
#
#DrawCactusToJavaFileByCactusSymbol:=function(CCdraw,html)
# local SSdra,VC,g,i,t,tem;
# SSdra:=T;
# VC:=[];
# VC[1]:=[0.,0.,0.];
# VC[2]:=[1.,0.,0.];
# VC[3]:=[1/2.,0.,Sqrt(3/4.)];
# VC[4]:=GetVert(SSdra,VC,[0.,0.,0.],[1.,0.,0.],[1/2.,0.,Sqrt(3/4.)]);
# for i in [1..Length(CCdraw)] do
# t:=List([1..i],g->CCdraw[g]);
# SSdra:=ConstructSurfaceBySymbol(t,[1,2,3,4]);
# tem:=Filtered(Vertices(SSdra),
# V-#>not(Intersection([Set([i+4,V]),Set([V,i+4])],VerticesOfEdges(SSdra))=[]));
# VC[i+4]:=GetVert(SSdra,VC,VC[tem[1]],VC[tem[2]],VC[tem[3]]);
# Print(tem);
# od;
# #DrawCactusToJavaFile(SSdraw1,html);
# Print(VC);
# return VC;
#end;
Is3WaistFree:=function(Sdj)
local n,e1,e2,e3,Ed,V1,V2,V3,F1,F2,F3;
Ed:=Edges(Sdj);
n:=Length(Ed);
for e1 in [1..n] do
for e2 in [e1+1..n] do
for e3 in [e2+1..n] do
V1:=VerticesOfEdge(Sdj,e1);
V2:=VerticesOfEdge(Sdj,e2);
V3:=VerticesOfEdge(Sdj,e3);
F1:=FacesOfEdge(Sdj,e1);
F2:=FacesOfEdge(Sdj,e2);
F3:=FacesOfEdge(Sdj,e3);
if Length(Union(V1,V2,V3))=3 and Length(Union(F1,F2,F3))=Length(F1)+Length(F2)+Length(F3) then
if not(Set(V1)=Set(V2)) and not(Set(V1)=Set(V3)) and not(Set(V2)=Set(V3)) then
return false;
fi;
fi;
od;
od;
od;
return true;
end;
#Create3Waist:=function(ssw1,ssw2,face,edge)
# local Vertfix,Edgefix,copy1,copy2,g,temp,Map,h,ES1,ES2,VS1,VS2,Vlen,
# i,j,Elen,NewE,NewV,tempVE,tempEF,temp1,temp2,F1,F2,SSw1,SSw2;
# temp1:=EdgesOfFace(ssw1,face[1]);
# temp2:=EdgesOfFace(ssw2,face[2]);
# SSw1:=SimplicialSurfaceByDownwardIncidence(VerticesOfEdges(ssw1),Set(EdgesOfFaces(ssw1)));
#SSw2:=SimplicialSurfaceByDownwardIncidence(VerticesOfEdges(ssw2),Set(EdgesOfFaces(ssw2)));
# F1:=Position(EdgesOfFaces(SSw1),temp1);
# F2:=Position(EdgesOfFaces(SSw2),temp2);
## face:=[F1,F2];
# Elen:=Maximum(Edges(SSw1));
# Vlen:=Maximum(Vertices(SSw1));
# ES1:=CRemove(ShallowList(EdgesOfFaces(SSw1)),face[1]);
# ES2:=ShallowList(EdgesOfFaces(SSw2));
# VS1:=ShallowList(VerticesOfEdges(SSw1));
# VS2:=ShallowList(VerticesOfEdges(SSw2));
# Vertfix:=VerticesOfFace(SSw2,face[2]);
# Edgefix:=EdgesOfFace(SSw2,face[2]);
# temp:=[Filtered(VerticesOfFace(SSw1,face[1]),g->not(g in VerticesOfEdge(SSw1,edge[1])))[1],Filtered(VerticesOfFace(SSw2,face[2]),g->not(g in VerticesOfEdge(SSw2,edge[2])))[1]];
# Map:=[[edge],[[VerticesOfEdge(SSw1,edge[1])[1],VerticesOfEdge(SSw2,edge[2])[1]],[VerticesOfEdge(SSw1,edge[1])[2],VerticesOfEdge(SSw2,edge[2])[2]],temp]];
# temp:=[Filtered(EdgesOfFace(SSw1,face[1]),g->not(g=edge[1]) and Map[2][1][1] in VerticesOfEdge(SSw1,g))[1],
# Filtered(EdgesOfFace(SSw2,face[2]),g->not(g=edge[2]) and Map[2][1][2] in VerticesOfEdge(SSw2,g))[1]];
# Map[1][2]:=temp;
# temp:=[Filtered(EdgesOfFace(SSw1,face[1]),g->not(g=edge[1]) and Map[2][2][1] in VerticesOfEdge(SSw1,g))[1],
# Filtered(EdgesOfFace(SSw2,face[2]),g->not(g=edge[2]) and Map[2][2][2] in VerticesOfEdge(SSw2,g))[1]];
# Map[1][3]:=temp;
# tempEF:=ES1;
# for i in Faces(SSw2) do
# temp:=[];
# for j in [1,2,3] do
# if not(ES2[i][j] in Edgefix) and not(i=face[2]) then
# ES2[i][j]:=ES2[i][j]+Elen;
# temp[j]:=ES2[i][j];
# else
# if ES2[i][j]=Map[1][1][2] then
# ES2[i][j]:=Map[1][1][1];
# temp[j]:=Map[1][1][1];
# elif ES2[i][j]=Map[1][2][2] then
# ES2[i][j]:=Map[1][2][1];
# temp[j]:=Map[1][2][1];
# elif ES2[i][j]=Map[1][3][2] then
# ES2[i][j]:=Map[1][3][1];
# temp[j]:=Map[1][3][1];
## fi;
# fi;
# od;
# tempEF[i+Maximum(Faces(SSw1))]:=ES2[i];
# od;
# tempVE:=VS1;
# for i in Edges(SSw2) do
# for j in [1,2] do
# if not(VS2[i][j] in Vertfix) and not(i in Edgefix) then
# VS2[i][j]:=VS2[i][j]+Vlen;
# else
# if VS2[i][j]=Map[2][1][2] then
# VS2[i][j]:=Map[2][1][1];
# elif VS2[i][j]=Map[2][2][2] then
# VS2[i][j]:=Map[2][2][1];
# elif VS2[i][j]=Map[2][3][2] then
# VS2[i][j]:=Map[2][3][1];
# fi;
# fi;
# od;
# tempVE[i+Maximum(Edges(SSw1))]:=VS2[i];
# od;
#
# tempVE:=CRemove(tempVE,Maximum(Edges(SSw1))+Edgefix[1]);
# tempVE:=CRemove(tempVE,Maximum(Edges(SSw1))+Edgefix[2]);
# tempVE:=CRemove(tempVE,Maximum(Edges(SSw1))+Edgefix[3]);
# tempEF:=CRemove(tempEF,Maximum(Faces(SSw1))+face[2]);
# return SimplicialSurfaceByDownwardIncidence(tempVE,tempEF);
#end;
AllSimplicialSurfacesWith3Waist:=function(i)
local LS,L3W,g;
LS:=AllSimplicialSurfaces(i,IsClosedSurface,EulerCharacteristic,2);