#12876: Fix element and parent classes of Hom categories to be abstract, and
simplify the Hom logic.
------------------------------------------+---------------------------------
Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.4
Component: categories | Resolution:
Keywords: categories, Hom | Work issues: fix doctests and
segfaults
Report Upstream: N/A | Reviewers: Simon King
Authors: Nicolas M. Thiéry | Merged in:
Dependencies: #11521, #12215, #12313 | Stopgaps:
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Comment (by SimonKing):
One question, Nicolas:
The first patch contains
{{{
sage: category = FiniteDimensionalModulesWithBasis(QQ)
sage: X = CombinatorialFreeModule(QQ, [1,2,3], category = category);
X.rename("X")
sage: Y = CombinatorialFreeModule(QQ, [1,2,3,4], category = category);
Y.rename("Y")
sage: H = Hom(X, Y)
sage: H.zero().category_for()
Category of finite dimensional modules with basis over Rational Field
}}}
Why are X and Y renamed? There is yet another location where things are
renamed, namely
{{{
Diagonal functions can be constructed using the ``diagonal`` option::
sage: X = CombinatorialFreeModule(QQ, [1,2,3,4]); X.rename("X")
sage: Y = CombinatorialFreeModule(QQ, [1,2,3,4], key="Y");
Y.rename("Y")
sage: H = Hom(X, Y)
}}}
Here, I also wonder about the "key" argument.
In sage.rings.ring.pyx, you state:
{{{
"""
This temporary alias is here for those instances of :class:`Ring`
that are not yet properly in the :class:`Rings`() category.
TESTS::
sage: A = Ring(ZZ)
sage: A._Hom_.__module__
'sage.categories.rings'
sage: Hom(A,A).__class__
<class 'sage.rings.homset.RingHomset_generic_with_category'>
"""
_Hom_ = Rings.ParentMethods.__dict__['_Hom_']
}}}
Are there any rings that do not initialise the category, after #9138?
Hence, what would happen without that alias? Perhaps I'll test it, after
finishing the tests for the original patches.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12876#comment:68>
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