#16618: Fix: the optimization Category_over_base._subcategory_hook_ really
belongs
to Category_over_base_ring
--------------------------+-------------------------------------
Reporter: nthiery | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: categories | Keywords:
Merged in: | Authors: Nicolas M. Thiéry
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
--------------------------+-------------------------------------
{{{
sage: from sage.categories.category_types import
Category_over_base
sage: D = Modules(Rings())
sage: class Cs(Category_over_base):
....: def super_categories(self):
....: return [D]
sage: C = Cs(SymmetricGroup(3))
sage: C.is_subcategory(D) # OOPS
False
}}}
This is due to:
{{{
sage: D._subcategory_hook_(C)
False
}}}
My analysis is that the optimization implemented in
`Category_over_base._subcategory_hook_` (if the base is not the same,
then they can't be comparable) is only actually valid for
`Category_over_base_ring`s. So I moved `_subcategory_hook_` down
there. This allows for improving the answer in one corner case that
was pinpointed in the doctests.
Does this sound reasonable? Are there `Category_over_base` for which
we care about such an optimization that are not
`Category_over_base_ring`?
For the record: this issue was detected while trying with Darij to use
categories over a base ring category in symmetric functions, while the
homset ticket #10668 was applied; this triggered a recursion loop in:
{{{
sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))
sage: P = Sym.macdonald().P()
sage: m = Sym.monomial()
sage: P.transition_matrix(m,2)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16618>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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