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#####################################################################
#####################################################################
InstallGlobalFunction(OrbitPolytope,
function(G,v,Props)
local
Points,p,x,i,w,Dim,tmp,input, tmpdir, tmpIn, tmp2dir, tmp2In,
a,b,c,d,U,V,W,AppendTo, PrintTo;
AppendTo:=HAP_AppendTo;
PrintTo:=HAP_PrintTo;
Dim:=Length(v);
Points:=[];
tmpdir := DirectoryTemporary();;
tmpIn:=Filename( tmpdir , "tmpIn.log" );
tmp2dir := DirectoryTemporary();;
tmp2In:=Filename( tmpdir , "tmp2In.log" );
############################CREATE POINTS###############
if IsPermGroup(G) then
for x in G do
w:=[];
for i in [1..Dim] do
Append(w,[v[i^x]]);
od;
Append(Points, [w]);
od;
else
for x in G do
w:=v*x;
Append(Points, [w]);
od;
fi;
######################POINTS CREATED###################
################## CALCULATE HULL POINTS ###############
AppendTo(tmpIn,"POINTS","\n");
for p in Points do
AppendTo(tmpIn,1);
for i in [1..Dim] do
AppendTo(tmpIn," ",p[i]);
od;
AppendTo(tmpIn,"\n");
od;
################# HULL CALCULATED ###################################
if "DIMENSION" in Props or "dimension" in Props then
Exec(Concatenation(POLYMAKE_PATH, tmpIn," DIM > ", tmp2In));
input:=InputTextFile(tmp2In);
tmp:=ReadLine(input);
tmp:=ReadLine(input);
Print("Dimension of orbit polytope is: ", tmp, "\n");
Exec(Concatenation("rm ", tmp2In));
fi;
if "VERTEX_DEGREES" in Props or "vertex_degrees" in Props then
Exec(Concatenation(POLYMAKE_PATH,tmpIn, " VERTEX_DEGREES > ",tmp2In));
input:=InputTextFile(tmp2In);
tmp:=ReadLine(input);
tmp:=ReadLine(input);
Print("Vertex degree in graph of polytope is: ", Rat(Concatenation([tmp{[1..Position(tmp,' ')-1]}])), "\n");
#Exec(Concatenation("rm ",tmp2In));
fi;
if "VISUAL_GRAPH" in Props or "visual_graph" in Props then
Exec(Concatenation(POLYMAKE_PATH,tmpIn ," VISUAL_GRAPH"));
fi;
if "SCHLEGEL" in Props or "schlegel" in Props then
Exec(Concatenation(POLYMAKE_PATH,tmpIn ," SCHLEGEL"));
fi;
if "VISUAL" in Props or "visual" in Props then
if IsPermGroup(G) and Length(v)=4 then
Exec(Concatenation("rm ",tmpIn));
AppendTo(tmpIn,"POINTS","\n");
for x in G do
a:=v[1^x]-v[1];
b:=v[2^x]-v[2];
c:=v[3^x]-v[3];
d:=v[4^x]-v[4];
U:=2*a-2*b;
V:=2*c-2*d;
W:=a+b-c-d;
AppendTo (tmpIn,1," ",U, " ",V," ",W, "\n");
od;
fi;
Exec(Concatenation(POLYMAKE_PATH,tmpIn ," VISUAL"));
fi;
#Exec(Concatenation("rm ",tmpIn));
end);
#####################################################################
#####################################################################
#####################################################################
#####################################################################
InstallOtherMethod(Display,
"method for displaying convex hulls of sets of points",
[IsPolymakeObject],
function(F)
local
Points,p,x,i,w,Dim,tmp,input, tmpdir, tmpIn, tmp2dir, tmp2In,
a,b,c,d,U,V,W,AppendTo, PrintTo;
AppendTo:=HAP_AppendTo;
PrintTo:=HAP_PrintTo;
Dim:=Length(Polymake(F,"F_VECTOR"));
Points:=Polymake(F,"VERTICES");
tmpdir := DirectoryTemporary();;
tmpIn:=Filename( tmpdir , "tmpIn.log" );
tmp2dir := DirectoryTemporary();;
tmp2In:=Filename( tmpdir , "tmp2In.log" );
################## CALCULATE HULL POINTS ###############
AppendTo(tmpIn,"POINTS","\n");
for p in Points do
AppendTo(tmpIn,1);
for i in [1..Dim] do
AppendTo(tmpIn," ",p[i]);
od;
AppendTo(tmpIn,"\n");
od;
################# HULL CALCULATED ###################################
Exec(Concatenation(POLYMAKE_PATH,tmpIn ," VISUAL"));
#Exec(Concatenation("rm ",tmpIn));
end);
#####################################################################
#####################################################################
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