#11935: Make parent/element classes independent of base rings
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Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7.3
Component: categories | Keywords: parent class, element class,
category
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies: #11900
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Comment(by SimonKing):
Replying to [comment:3 nthiery]:
> A good thing to do at this point would be to search through the sage
> pickle jar for how many parent_class's and element_class's are pickled
> there.
Old pickles will not break, I believe. Let `P3 =
Algebras(GF(3)).parent_class` and `PQ = Algebras(QQ).parent_class`. Here
are a few scenarios:
__1. P3 and PQ have been created and pickled with an old version of Sage__
In the old version of Sage, `P3!=PQ`. They are pickled by construction.
Hence, after applying my yet-to-be-submitted patches, they are unpickled
as `Algebras(GF(3)).parent_class` and `Algebras(QQ).parent_class` - which
is the same class after applying the patch.
'''Conclusion:''' An old pickle will not break, with either approach 2. or
3. The worst what could happen is `P3!=PQ` before pickling and `P3==PQ`
after unpickling. But the defining property
`P3==Algebras(GF(3)).parent_class` and `PQ==Algebras(QQ).parent_class` is
preserved.
__2. P3 and PQ are created and pickled according to approach 2. from
above__
Of course, `P3==PQ` at the time of pickling. The pickle will only depend
on the parent classes of the super categories of `Algebras(GF(3))` and
`Algebras(QQ)`. If there was a change in the super categories between
pickling and unpickling, we would have `P3!=Algebras(GF(3)).parent_class`
after unpickling.
'''Conclusion:''' A new pickle of P3 and PQ can be unpickled after a
change in the category graph, but a change in the category graph will
destroy the defining property `P3==Algebras(GF(3)).parent_class`.
__3. P3 and PQ are created and pickled according to approach 3. from
above__
Of course, `P3==PQ` at the time of pickling. `PQ` and `P3` will both be
pickled by construction. In particular, a change in the category graph
would not matter, as long as the super categories of `Algebras(QQ)` and
`Algebras(GF(3))` still coincide (up to the base ring) after the change in
the category graph.
A problem would arise if, in a distant future, the super categories of
`Algebras(QQ)` and `Algebras(GF(3))` would become essentially different.
Say, some algebra person finds that vector spaces over fraction fields
should have their own category, different from the usual category of
vector spaces. Then,
`Algebras(QQ).parent_class!=Algebras(GF(3)).parent_class`. In particular,
after such change, unpickling `P3` or `PQ` would result in either
`PQ!=Algebras(QQ).parent_class` or `P3!=Algebras(GF(3)).parent_class`.
'''Conclusion''': A new pickle of P3 and PQ can be unpickled after a
change in the category graph. Most changes in the category graph will
preserve the defining property `P3==Algebras(GF(3)).parent_class` and
`PQ==Algebras(QQ).parent_class` after unpickling. However, if the super
categories will depend on the base ring in a different way as it is now,
then either P3 or PQ will lose the defining property after unpickling,
while the other will keep the defining property - and we don't know which
of the two will break.
----------
It seems to me that approach 3. is less fragile than 2. But I believe that
in applications (hence, for pickling parents) both should be fine. So,
I'll prepare patches for both approaches.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11935#comment:5>
Sage <http://www.sagemath.org>
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