Thanks for the additional responses.
The non-equality of the hash functions is enough to convince me that P(0)
== 0 is not worth the "convenience" of this type of coercion.
However, just to point out another inconsistency. It seems that coercion is
currently violating this hash equality in other circumstances.
{{{
sage: CC(3/2) == QQ(3/2)
True
sage: hash(CC(3/2)), hash(QQ(3/2))
(1610645504, 7461864723258187528)
}}}
--
For the other discussion: P(0) = (0:1). I don't have a strong preference
either way. I have never personally run into any inconsistency issues
making the assumption of which affine patch is 'default' in dimension 1. I
find the convenience convenient ;), but do see the potential difficulty in
tracking down issues this could cause. Actually, I don't find P1(0) = (0:1)
to be particularly concerning, but P2(0,0) = (0:0:1) (and so one in higher
dimensions) seems more concerning.
If we were find all the places in Sage where this is used and change them,
the only place I think a deprecation fits is where this is handled in point
initialization. My rough feeling of the prevalence of this shorthand seems
like we would be breaking enough existing code to be concerned about just
making the behavior change without some kind of user warning through
deprecation.
Any further thoughts?
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