#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):
Aha! I understand!
`Hom(N,N)` reduces to `N._Hom_(N)`, which ''directly'' constructs a number
field hom set.
By consequence, `Hom(N,N)` does not become a unique parent, even though it
inherits from `UniqueRepresentation` via inheritance from the category.
But that inheritance takes place ''after'' creation of the hom set, so
that it is too late for `Rings().HomCategory.ParentMethods.__classcall__`.
In other words: Via category inheritance, `Hom(N,N)` inherits `__eq__`
from `UniqueRepresentation`, which is used for comparison and precedes the
use of the custom `__cmp__` method of number field homsets. However,
`__eq__` expects unique parents.
We thus have:
{{{
age: 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: H = Hom(N,N)
sage: H == Hom(N,N)
False
sage: H > Hom(N,N)
False
sage: H < Hom(N,N)
False
}}}
I guess, until number fields are truly unique parents, I should add an
`__eq__` to number field hom sets, in order to not have it inherited from
`UniqueRepresentation`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:55>
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