On 7 September 2017 at 23:34, Nils Bruin <nbr...@sfu.ca> wrote:
>
> What is the argument that makes PP(0) == 0 bad? If PP(0) is allowed, I don't
> see how PP(0) == 0 is particularly worse.
>
> Because PP(AA(0)) and PP(BB(0)) should be different points, so it's not so
> clear which one should have precedence. PP(0) happens to choose PP(BB(0)). I
> don't think that's canonical enough to promote to PP(0) == 0 working as
> well.
For what it's worth I agree that having 0 automatically coerce to
[0:1] in P^1 seems like a bad idea, even if we think of the first
affine patch (A in the example) as the "standard" one, and
consequently may think of P^1(QQ) = A^1(QQ) union {oo}.
This little coercion saves essentially no time for the user /
programmer and clearly risks resulting in bugs which would be very
hard to track down.
John
>
> sage: hash(0)
> 0
> sage: hash(ProjectiveSpace(QQ,1)(0))
> 3713080549409410656
>
> also suggests that equality is not warranted.
>
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