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#(C) Graham Ellis, 2005-2006
#####################################################################
#####################################################################
InstallGlobalFunction(PolytopalGenerators,
function(GG,v)
local
Points, Vertices,
Action,
G, D, CG, N,
proj,
StringToVector,
input,
EdgeGenerators,
Faces, FacesFinal, FacesFn,
Index, IndexFn, tmplst,
Count,
tmp, x, w, i, y, p,
AppendTo, PrintTo,
tmpInlog, tmp2Inlog,tmp3Inlog, tmp4Inlog, tmpDir;
AppendTo:=HAP_AppendTo;
PrintTo:=HAP_PrintTo;
tmpDir:=DirectoryTemporary();
tmpInlog:=Filename(tmpDir,"tmpIn.log");
tmp2Inlog:=Filename(tmpDir,"tmp2In.log");
tmp3Inlog:=Filename(tmpDir,"tmp3In.log");
tmp4Inlog:=Filename(tmpDir,"tmp4In.log");
if not (IsPermGroup(GG) or IsMatrixGroup(GG)) then
Print("The group G must be a permutation or matrix group.\n");
return fail;
fi;
if IsPermGroup(GG) then
GG:=Image(PermToMatrixGroup(GG));
fi;
#####################################################################
Action:=function(g,V) ;
return g*V;; #This actually works!
end;
#####################################################################
G:=[];
tmplst:=[];
for x in GG do
w:=Action(x,v);
if not w in tmplst and not w=v then
Add(G,x);
Add(tmplst,w);
fi;
od;
D:=Length(v);
CG:=List([1..D], i->0); #CG will eventually be the centre of gravity
Points:=[]; #of the polytope.
Vertices:=[];
EdgeGenerators:=[];
###################### CALCULATE CENTRE OF GRAVITY ##################
for x in G do
Add(Points, Action(x,v));
od;
Points:=SSortedList(Points);
G:=[];
for w in Points do
for x in GG do
if Action(x,v)=w then Add(G,x); break; fi;
##if Action(x,v) in Points then Add(G,x); fi;
od;
od;
for w in Points do
CG:=CG+w;
od;
CG:=CG/Size(Points);
##################### CENTRE OF GRAVITY DONE ########################
################# PROJECTION ################################
N:=CG-v; #This might be parallel to an edge!!!
proj:=function(w)
local k, m ;
m:=(w-v)*N;
k:= ((CG-v)*N)/m;
return v+(k*(w-v));
end;
#############################################################
################## CALCULATE HULL OF PROJECTED POINTS ###############
for i in [1..Length(Points)] do
Points[i]:=proj(Points[i]);
od;
AppendTo(tmpInlog,"POINTS","\n");
for p in Points do
AppendTo(tmpInlog,1);
for i in [1..Length(p)] do
AppendTo(tmpInlog," ",p[i]);
od;
AppendTo(tmpInlog,"\n");
od;
#Exec(Concatenation(POLYMAKE_PATH,tmpInlog," beneath_beyond VERTICES > ",tmp3Inlog)); #Added "beneath_beyond"
Exec(Concatenation(POLYMAKE_PATH,tmpInlog," VERTICES > ",tmp3Inlog));
################# HULL CALCULATED ###################################
#####################################################################
StringToVector:=function(s)
local V,x,y;
V:=[]; y:=[];
for x in s do
if not x=' ' then Append(y,[x]);
else
Append(V,[Rat(Chomp(y))]); y:=[];
fi;
od;
Append(V,[Rat(Chomp(y))]);
return V{[2..Length(V)]};
end;
#####################################################################
################# READ VERTICES #####################################
input:=InputTextFile(tmp3Inlog);
tmp:=ReadLine(input);
tmp:=ReadLine(input);
i:=1;
while tmp[1]='1' do
Vertices[i]:=tmp;
tmp:=ReadLine(input);
i:=i+1;
od;
Apply(Vertices, s->StringToVector(s));
RemoveFile(tmp3Inlog);
################ VERTICES READ ######################################
################ RECOVER THE EDGE GENERATORS ########################
for w in Points do
p:=w;
if p in Vertices then
x:=G[Position(Points,w)];
EdgeGenerators[Position(Vertices,p)]:=x;
fi;
od;
################ EDGE GENERATORS RECOVERED ##########################
################ READ HASSE DIAGRAM #################################
Exec(Concatenation(POLYMAKE_PATH,tmpInlog," \"HASSE_DIAGRAM -> FACES\" >",tmp2Inlog));
#Exec(Concatenation(POLYMAKE_PATH,tmpInlog," \"HASSE_DIAGRAM -> DIMS\" >",tmp4Inlog));
Exec(Concatenation(POLYMAKE_PATH,tmpInlog," \"F_VECTOR\" >",tmp4Inlog));
RemoveFile(tmpInlog);
Filename(tmpDir,tmp);
RemoveFile(tmp);
Faces:=[];
Index:=[];
#############################################################
IndexFn:=function(tmp)
local V,x,y;
V:=[];
y:=[];
for x in tmp do
if (not x=' ') and (not x='\n') then Append(y,[x]);
else
Append(V,[Rat(Chomp(y))]); y:=[]; fi;
od;
return V;
end;
############################################################
############################################################
FacesFn:=function(tmp)
local V,x,y;
V:=[]; y:=[];
for x in tmp do
if (not x='<') and (not x='(') and (not x='{') then
if (not x=' ') and (not x='}') then Append(y,[x]);
else
if Length(y)>0 then
Append(V,[Rat(Chomp(y))]); y:=[]; fi; fi;
fi;
if x='}' then break; fi;
od;
if Length(V)>0 then
return [V];
else
return []; fi;
end;
############################################################
input:=InputTextFile(tmp4Inlog);
tmp:=ReadLine(input);
tmp:=ReadLine(input);
#Index:=IndexFn(tmp);
tmp:= IndexFn(tmp); #Modified July 2019
Index:=[1]; #because Polymake has
for i in [1..Length(tmp)] do #discontinued the DIMS
Add(Index,Index[i]+tmp[i]); #property.
od; #
RemoveFile(tmp4Inlog);
input:=InputTextFile(tmp2Inlog);
tmp:=ReadLine(input);
tmp:=ReadLine(input);
while Length(tmp)>2 do
Append(Faces, FacesFn(tmp));
tmp:=ReadLine(input);
od;
RemoveFile(tmp2Inlog);
if Length(Faces[1])=1 then
FacesFinal:=[];
for i in [1..Length(Index)-1] do
Append(FacesFinal,[[Index[i]..Index[i+1]-1]]);
od;
Append(FacesFinal,[[Index[i+1]]]);
FacesFinal:=(List(FacesFinal,x->List(x,i->Faces[i])));
else
FacesFinal:=[[1..Index[1]]];
for i in [1..Length(Index)-1] do
Append(FacesFinal,[[Index[i]+1..Index[i+1]]]);
od;
FacesFinal:=Reversed(List(FacesFinal,x->List(x,i->Faces[i])));
fi;
RemoveFile(tmpInlog);
RemoveFile(tmp2Inlog);
RemoveFile(tmp4Inlog);
RemoveFile(tmp3Inlog);
RemoveFile(Filename(tmpDir," "));
############### HASSE DIAGRAM READ ##################################
return rec(
generators:=EdgeGenerators,
hasseDiagram:=FacesFinal,
vector:=v);
end);
#####################################################################
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