Hi,
While playing with prime numbers to understand facade sets in Sage, I
noticed the following surprising behavior:
sage: P = Primes() ; P
Set of all prime numbers: 2, 3, 5, 7, ...
sage: P.facade_for()
(Integer Ring,)
sage: P(4)
4
sage: P(4) in P
False
The culprit is _element_constructor_:
sage: P._element_constructor_(4)
4
Actually, for any integer n, P(n) returns n. On the contratry the behavior
of PrimeNumbers_Facade (used by Sets().example("facade") is more
satisfactory:
sage: PP = Sets().example("facade") ; PP
Set of prime numbers (facade implementation)
sage: PP.facade_for()
(Integer Ring,)
sage: PP(4)
Traceback (most recent call last):
...
ValueError: 4 is not a prime number
sage: 4 in PP
False
Is there any reason for the above behavior of Primes() ? (Maybe I am
missing something...)
Eric.
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