#1956: implement multivariate power series arithmetic
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Reporter: was | Owner: malb
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: commutative algebra | Keywords: multivariate power
series
Author: Niles Johnson | Upstream: N/A
Reviewer: Martin Albrecht, Simon King | Merged:
Work_issues: |
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Changes (by niles):
* status: needs_work => needs_review
Comment:
Replying to [comment:31 mhansen]:
> I think there are still some problems with this. For example:
>
> 1. Pickling does not work for these objects -- one needs to define a
proper !__reduce!__ method.
done now; patch forthcoming.
>
> 2. I don't think we should continue the use of !__ attributes as they
just cause problems. For example, the code in here has to set attributes
like _PowerSeriesRing_generic!__power_series_class in subclasses.
The use of `__` attributes here is modeled after their use (for better or
worse) in `PowerSeriesRing_generic` (see 4. below); it is also in keeping
with the python philosophy, that `__` attributes or methods may be removed
or changed in future versions. It is entirely possible that someone will
eventually want to significantly rework multi/univariate power series.
Having said that, they can be removed without too much trouble if sage
development policy is strongly against them (in this case, perhaps the
developer guide should mention it clearly somewhere).
>
> 3. There are formating issues in some of the docstrings like '_latex_'
`_latex_` is fixed now, and I looked for other problems but didn't see
any; my best known method for checking docstring formatting is using `sage
-docbuild`, which only shows warnings/errors for non-underscore methods .
. . can you recommend a better way?
>
> 4. We shouldn't have a 'MPowerSeriesRing' -- that functionality should
just be in PowerSeriesRing. MPolynomialRing was deprecated for the same
reason a long time ago.
I agree, but I think that issue is beyond the scope of this ticket.
Implementing multivariate power series arithmetic is already long and
complex enough, without having to also worry about integrating them with
the univariate power series code (which is heavily specialized for the
single-variable case). I have spent time thinking about how to do this,
and I think it will be a subtle problem to solve; there is a sizable body
of code that depends on `PowerSeriesRing` as it stands, and one will have
to be careful about extending its functionality without breaking any of
the current uses. So I suggest that we merge this ticket and then open a
new ticket for ''Unify construction of uni- and multi-variate power series
rings, as has been done for polynomial rings''.
It would probably be good if the other people involved in this ticket
could comment on this last point.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:32>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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