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I have a poset $P$ already defined in SageMath. I would like to define a new poset $Q$ on the underlying set of $P$ such that every cover relation of $P$ is a cover relation in $Q$, i.e., I want to add more cover relations in $P$. I got to know that a poset in Sage is immutable (i.e. I can't modify one once it is built). Is it true?

The elements of $P$ are sets ${S_1,\ldots, S_n}$. Assume that the extra cover relation in $Q$ is $S_1$ is covered by $S_2$. I am doing the following to define $Q$:

Rel={ };
for i in P:
      if i==S_1:
          Rel.update({i : P.upper_covers(i) +[S_2]})
      else:
          Rel.update({i : P.upper_covers(i)})
Q = Poset(Rel)

I am getting the following error: TypeError: unhashable type: 'set'

Whereas the following code works:

Rel={ };
for i in P:
     Rel.update({i : P.upper_covers(i)})
Q = Poset(Rel)

Could anyone please help me with this?