Let G be a set of subsets of a set with $n$ elements. Here a (stupid) example:
p=5
S = Subsets([1,..,p])
G=[t for t in S if sum(t)==p]
display(S)
display(G)
My question is how do I obtain the set G as a poset in Sage? Thanks for any help.
I assume you want to construct boolean lattice. If so, it's defined in Sage's Catalog of posets and lattices:
posets.BooleanLattice(p, use_subsets=True)
ADDED. A subposet can be constructed as
p=5
B = posets.BooleanLattice(p, use_subsets=True)
B.subposet(t for t in B if sum(t)==p)
Then you can use .subposet() method to obtain that of boolean lattice.
Like this
sage: S = Subsets([1,..,5])
sage: G = [t for t in S if sum(t)<=3]
sage: Poset((G, lambda x,y: x.issubset(y)))
Finite poset containing 5 elements
And I am slightly tempted to say RTFM.
Asked: 2023-05-08 12:57:47 +0100
Seen: 231 times
Last updated: May 09 '23
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