Thanks Simon.
> The default behaviour of "x in P" for any parent P in Sage is:
> x in P
> <=>
> P(x)==x is True (and does not raise an error)
This default behavior is very badly suited. In parallel to my second
mail, I found the more striking example
{{{
sage: R = Zmod(5)
sage: i = ZZ(3)
sage: j = R(3)
sage: i in R and j in ZZ
True
sage: i == j
True
sage: 1/i in R
False
sage: 1/i == 1/j
False
}}}
I definitely think that "Zmod(5)(3) in ZZ" should return False.
Remarks that it is true as a subset as Zmod(5)(3) is the set of
integers equal to 3 mod 5. In other words "3 in Zmod(5)(3)" should
returns True but it returns an error.
> I think that's a mess. P should at least know that it is a subset of ZZ.
> Hence, its embedding into ZZ should be registered as a coercion. And it
> should be able to convert a positive python int.
It is easy to create an embedding into ZZ and modify the __contains__
method. Then many things work well.
Note that P is a facade and hence it is normal that its elements have
a parent different from P. But is there a canonical way to tell that a
Parent is a subset of another Parent?
Best,
Vincent
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