The weak_covers method gives incorrect answers:

sage: for w in Permutations(3):
....:     w, w.weak_covers()
....:
([1, 2, 3], [])
([1, 3, 2], [[1, 2, 3]])
([2, 1, 3], [[1, 2, 3]])
([2, 3, 1], [[3, 2, 1]])
([3, 1, 2], [[3, 2, 1]])
([3, 2, 1], [[3, 1, 2], [2, 3, 1]])

The fourth and fifth lines of the output are incorrect.  The correct values 
should be

([2, 3, 1], [[2, 1, 3]])
([3, 1, 2], [[1, 3, 2]])

Similarly:

sage: for w in Permutations(3):
....:     w, w.weak_covers(side='left')
....:
([1, 2, 3], [])
([1, 3, 2], [[1, 2, 3]])
([2, 1, 3], [[1, 2, 3]])
([2, 3, 1], [[3, 2, 1]])
([3, 1, 2], [[3, 2, 1]])
([3, 2, 1], [[2, 3, 1], [3, 1, 2]])

The fourth and fifth lines should be

([2, 3, 1], [[1, 3, 2]])
([3, 1, 2], [[2, 1, 3]])


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