#10667: Morphisms and Objects of Categories
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Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: categories | Keywords: objects morphisms
containment
Work_issues: Cartesian products | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies: #9138, #11115, #11780
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Comment(by SimonKing):
It turns out that #11670 will not solve the problem. But it seems to me
that I come closer to a solution: In contrast to many other cases, hom
sets of number fields are ''not'' unique parents. With my patch, they are
even less unique. Here is a show case:
sage-4.6.2
{{{
sage: N = NumberField(x^12 - 4*x^11 + 6*x^10 - 5*x^9 + 5*x^8 - 9*x^7 +
21*x^6 - 9*x^5 + 5*x^4 - 5*x^3 + 6*x^2 - 4*x + 1, 'a')
sage: Hom(N,N) is Hom(N,N)
False
sage: Hom(N,N) == Hom(N,N)
True
}}}
With my patch, we still have
{{{
sage: N = NumberField(x^12 - 4*x^11 + 6*x^10 - 5*x^9 + 5*x^8 - 9*x^7 +
21*x^6 - 9*x^5 + 5*x^4 - 5*x^3 + 6*x^2 - 4*x + 1, 'a')
sage: Hom(N,N) is Hom(N,N)
False
}}}
but then
{{{
sage: Hom(N,N) == Hom(N,N)
False
}}}
I don't know yet why this is the case, because the `__cmp__` function of
number field homsets did not change.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:54>
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