A strange behavior in passing from list to set

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Sets ensure uniqueness. Lists, strings and tuples preserve order.

Sometimes both uniqueness and order matter.

One can either carefully input a list, string or tupe, making sure oneself of uniqueness and order...

... or use a set to enforce uniqueness and sorted to ensure order.

Below we review a number of variations.

First define a special-purpose printing function, to save space when printing arrangements of characters (try list(A) for any of the examples below and compare with the output of xprint(A)):

sage: xprint = lambda A: print(f"{len(A)}: {' '.join(''.join(a) for a in A)}")

Use a string for cand, trusting ourselves to enter it in order and without repetition:

sage: cand = 'ABCD'
sage: A = Arrangements(cand, 2)
sage: print(cand); print(A); xprint(A)
ABCD
Arrangements of the set ['A', 'B', 'C', 'D'] of length 2
12: AB AC AD BA BC BD CA CB CD DA DB DC

The same A would be obtained starting from a list version of cand, obtained in any of those ways:

sage: cand = ['A', 'B', 'C', 'D']
sage: cand = [x for x in 'ABCD']
sage: cand = list('ABCD')

Use a list but forget to check uniqueness gives trouble:

sage: cand = 'ABCDA'
sage: A = Arrangements(cand, 2)
sage: print(cand); print(A); xprint(A)
ABCDA
Arrangements of the multi-set ['A', 'B', 'C', 'D', 'A'] of length 2
13: AA AB AC AD BA BC BD CA CB CD DA DB DC

sage: cand = 'ABDACADABCA'
sage: A = Arrangements(cand, 2)
sage: print(cand); print(A); xprint(A)
ABDACADABCA
Arrangements of the multi-set ['A', 'B', 'D', 'A', 'C', 'A', 'D', 'A', 'B', 'C', 'A'] of length 2
16: AA AB AD AC BA BB BD BC DA DB DD DC CA CB CD CC

Using a set for cand forces uniqueness but can cost order:

sage: cand = Set('ABDACADABDA')
sage: A = Arrangements(cand, 2)
sage: print(cand); print(A); xprint(A)
{'B', 'C', 'D', 'A'}
Arrangements of the set ['B', 'C', 'D', 'A'] of length 2
12: BC BD BA CB CD CA DB DC DA AB AC AD

Sorting the above out-of-order arrangements after the fact:

sage: B = sorted(A)
sage: print(B); xprint(B)
[['A', 'B'], ['A', 'C'], ['A', 'D'], ['B', 'A'], ['B', 'C'], ['B', 'D'],
 ['C', 'A'], ['C', 'B'], ['C', 'D'], ['D', 'A'], ['D', 'B'], ['D', 'C']]
12: AB AC AD BA BC BD CA CB CD DA DB DC

Here we lost some structure: while A was a set of arrangements, with dedicated methods:

sage: A.cardinality()
12
sage: A.an_element()
['B', 'C']
sage: A.random_element()  # random
['A', 'D']
sage: A.random_element()  # random
['C', 'B']

this is no longer the case for B which is only a list now, so that its string representation is less informative, and none of the above methods are available for it.

On of the final two versions below might combine all the qualities you seek.

Use both Set and sorted for cand, to get order and uniqueness:

sage: cand = sorted(Set('ABDACADABDA'))
sage: A = Arrangements(cand, 2)
sage: print(cand); print(A); xprint(A)
['A', 'B', 'C', 'D']
Arrangements of the set ['A', 'B', 'C', 'D'] of length 2
12: AB AC AD BA BC BD CA CB CD DA DB DC

Keep cand a set but use a sorted version of it to compute arrangements:

sage: cand = Set('ABDACADABDA')
sage: A = Arrangements(sorted(cand), 2)
sage: print(cand); print(A); xprint(A)
{'B', 'C', 'D', 'A'}
Arrangements of the set ['A', 'B', 'C', 'D'] of length 2
12: AB AC AD BA BC BD CA CB CD DA DB DC