#16402: Fix homsets from FGP_Module to objects of other categories
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.3
Component: categories | Keywords: module homset category
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Currently, a `Homset` whose domain is a `FGP_Module` (finitely generated
module over a principal ideal domain) is always of type
`FGP_Homset_class`, independently of whether the codomain is also a
`FGP_Module`. In particular, because `FGP_Module` does not have good
support for categories (see #10513), this causes the homsets to always end
up in the category of modules over the PID in question ("Category of
modules over Integer Ring"):
{{{
sage: V = ZZ^2
sage: W = V.quotient(V.span([[1, 0]]))
sage: H = W.Hom(QQ); H
Set of Morphisms from Finitely generated module V/W over Integer Ring with
invariants (0) to Rational Field in Category of modules over Integer Ring
sage: type(H)
<class 'sage.modules.fg_pid.fgp_morphism.FGP_Homset_class_with_category'>
}}}
The correct category in this case is "Category of commutative additive
groups". (This is mathematically the same as the category of
'''Z'''-modules, but the two categories are currently distinct in Sage.)
This ticket fixes the above behaviour by making `FGP_Module._Hom_()` use
`FGP_Homset_class` only in the case where the codomain is also a
`FGP_Module`, and using the superclass `_Hom_()` method (with `category`
parameter) otherwise.
This is a prerequisite for #15618.
--
Ticket URL: <http://trac.sagemath.org/ticket/16402>
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