#Hey Dr. Z,
# My program now works!
#
#---Phil
###########################
# class10_SCD.mpl
#
# simple chain decomposition....

SCD:=proc(n) local C1l,C2l,c,cn,sn,i,j,S,le:

if n <= 0 then
	return FAIL:
fi:

# base case n=1
if n =1 then
	return {[{},{1}]}:
fi:

C1l:=convert(SCD(n-1),list):

C2l:=[]:
# append the n to each element in the lattice for C2
for i from 1 to nops(C1l) do
	c:=C1l[i]:
	cn:=[]:
	for j from 1 to nops(c) do
		sn:= c[j] union {n}:
		cn:= [op(cn),sn]:
	od:
	C2l:= [op(C2l),cn]:
od:

#print(C1l,C2l):
S:={}:
for i from 1 to nops(C1l) do
	le:= nops(C1l[i]):
	S:= S union {[op(C1l[i]),C2l[i][le]],[op(1..le-1,C2l[i])]}:
od:

S minus {[]}:

end:

## HOMEWORK:  do this, but do it lexicographically (greedy) as per last class.
## then check that the two of them give the same thing.