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InstallMethod(HasseDiagramAsList,[IsRecord],
function(hasse)
local faceblocks, facenumber, nodes, permlist, pi, node,
maxnode, i, upface, blockindex, downshift, upshift,
face;
#
#make a mutable copies:
##
faceblocks:=List(hasse.faceindices,i->List(i));
nodes:=List(hasse.hasse,face->[List(face[1]),List(face[2])]);
facenumber:=Size(hasse.hasse);
if nodes[1][2]=[]
then
Info(InfoPolymaking,1,"polymake returned dual Hasse diagram. Recovering original");
####
# if the Hasse diagram ends in a list of points,
# we do some strange permutation and renumbering to get a Hasse
# diagram starting with points (and the dimension of the faces
# increases as we proceed down)
####
Apply(faceblocks,i->Reversed(facenumber-i+1));
# permlist:=[facenumber];
permlist:=Concatenation(faceblocks);
# Append(permlist,Concatenation(faceblocks));
# Add(permlist,1);
pi:=PermList(permlist);
nodes:=Permuted(nodes,pi);
# now we have the faces in ascending order. But the second
# column is still wrong. So we do some renumbering:
#permlist[1]:=Size(nodes);
#pi2:=PermList(permlist);
for node in nodes
do
node[2]:=OnSets(node[2],pi);
od;
fi;
####
# now the Hasse <nodes>diagram starts with a list of points (i.e.
# the faces are ordered ascendingly wrt dimension), this will work:
####
Remove(nodes,1);
Apply(nodes,i->Concatenation(i,[[]]));
maxnode:=Size(nodes);
# Remove(nodes,maxnode);
for i in [1..maxnode]#-1]
do
# Apply(nodes[i][1],i->i+1);
# if nodes[i][2]=[maxnode]
# then
# nodes[i][2]:=[];
# else
for upface in nodes[i][2]
do
Add(nodes[upface-1][3],i);
od;
# fi;
od;
for node in nodes
do
Apply(node,Set);
od;
Apply(faceblocks,i->i-1);
# Add(faceblocks,[maxnode]);
#
# And now we split the nodes of the Hasse diagram according to dimension.
# This was added when the function was already complete. So this is
# probably not the right order of doing things. But I didn't want to
# rewrite the renumbering part above...
#
faceblocks:=Set(faceblocks);
RemoveSet(faceblocks,[0]);
for blockindex in [1..Size(faceblocks)]
do
nodes[blockindex]:=nodes{faceblocks[blockindex]};
od;
while Size(nodes)>Size(faceblocks)
do
Remove(nodes);
od;
for blockindex in [1..Size(nodes)]
do
if blockindex>1
then
downshift:=-faceblocks[blockindex-1][1]+1;
else
downshift:=0;
fi;
if blockindex<Size(nodes)
then
upshift:=-faceblocks[blockindex+1][1];
else
upshift:=0;
fi;
for face in nodes[blockindex]
do
face[2]:=face[2]+upshift;
face[3]:=face[3]+downshift;
od;
od;
#ForAll(faceblocks,IsRange);
# returnrec:=rec(hasse:=nodes,
# modgens:=List(nodes,n->List(n,i->i[1])),
# elts:=[]); #faceindices:=Set(faceblocks));
# return returnrec;
MakeImmutable(nodes);
return nodes;
end);
[ Dauer der Verarbeitung: 0.32 Sekunden
(vorverarbeitet)
]
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