#9054: create a class for basic function_field arithmetic for Sage
---------------------------------------------------------------------------------+
Reporter: was
| Owner: was
Type: enhancement
| Status: new
Priority: major
| Milestone: sage-wishlist
Component: algebra
| Resolution:
Keywords:
| Work_issues:
Upstream: N/A
| Reviewer:
Author: William Stein, Robert Bradshaw, Maarten Derickx, Moritz Minzlaff
| Merged:
Dependencies:
|
---------------------------------------------------------------------------------+
Comment(by SimonKing):
Replying to [comment:39 was]:
> Replying to [comment:37 SimonKing]:
> > Here are some comments on [attachment:trac_9054-all-parts.patch]:
> >
> > * Please remove the `__contains__` method from the category
`FunctionFields`. Containment in categories should rely on the default
implementation, unless there is a compelling reason to do otherwise.
> ...
>
> Technically this is true. But this category framework instead of
inheritance -- really two very different approaches to design -- leads
directly to slow code in some cases in practice, which is *really*
annoying, IMHO.
A while ago, I had worked on a ticket #10667 about category containment.
One purpose was to get a speedup. The trick was (again) to use Cython. For
some reason, the work on that ticket has stalled. Perhaps it would be
worth while to resume it.
Generally, I think it is better to improve the category framework, rather
than to work around it.
> For example, see #11657, where one of the root causes of slowness was
code in is_Ring that was added to support this category approach, and
which slowed everything down.
Then why is the existing `is_Ring` not rewritten along the lines of what
you do in #11657?
> is_Ring is only deprecated when used from the top level (i.e., the Sage
prompt).
Yes, this is what I meant. I did not mean "deprecated" in the sense of
"will soon be removed", but in the sense of "please don't try this at
home".
> And the is_Ring function does test for category stuff.
Actually I have not been aware that category stuff is tested in `is_Ring`.
I was thinking about various other `is_...` methods that really do nothing
more than isinstance.
> > * Is there a reason why you have a method `base_field` that simply
returns the function field itself? From the behaviour of the `base_ring`
method of polynomial rings, I would rather expect that
`FunctionField(QQ,['t']).base_field()` returns the rational field.
> >
>
> No. The base field of a function field is a rational function field in
1 variable.
Ouch, so I was mistaken.
> The base field of that rational function field is then a field such as
QQ. Most function fields aren't rational, e.g., they are finite
extensions K/QQ(t), or even relative extensions L/K. In the first case,
the base field is QQ(t) and in the second it is K.
> If Simon was confused by this, it should be documented better.
Not needed. What I stated was based on reading the patch "diagonally". I
only noticed one of the two base_field methods.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9054#comment:40>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
