#1956: implement multivariate power series arithmetic
---------------------------------------------------------------------------------------------------+
Reporter: was
| Owner: pernici
Type: enhancement
| Status: needs_info
Priority: major
| Milestone: sage-4.6.1
Component: commutative algebra
| Keywords: multivariate power series
Author: Niles Johnson
| Upstream: N/A
Reviewer: Martin Albrecht, Simon King
| Merged:
Work_issues: multivariate series on 1 generator should remain different from a
univariate series |
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Changes (by niles):
* status: needs_work => needs_info
Old description:
> Multivariate power series arithmetic has been requested a *lot*.
>
> == Apply: ==
>
> 1. (unnecessary as of sage 4.6) patch from #9443
> 1. [attachment:trac_1956_multi_power_series_new_4.patch]
> 1. [attachment:trac_1956_uni_multi_ps_2.patch]
> 1. [attachment:trac_1956_multi_ps_cleanup.patch]
> 1. [attachment:trac_1956_one_variable_fix.patch]
New description:
Multivariate power series arithmetic has been requested a *lot*.
== Apply: ==
1. (unnecessary as of sage 4.6) patch from #9443
1. [attachment:trac_1956_multi_power_series_new_4.patch]
1. [attachment:trac_1956_uni_multi_ps_2.patch]
1. [attachment:trac_1956_multi_ps_cleanup.patch]
1. [attachment:trac_1956_one_variable_fix.patch] (perhaps not--see
comments 67 and following)
--
Comment:
Hi Simon!
Replying to [comment:68 SimonKing]:
> Replying to [comment:67 niles]:
> > It is difficult to imagine a situation where someone would want access
to the "multivariate in one variable" versions
>
> I find it very easy to imagine. I sometimes want it so, because multi-
and univariate polynomials have different methods, and thus I want to make
sure that my programs will always get a ''multi''variate polynomial.
>
> > (e.g. they want to use some algorithm implemented for the multivariate
case that is not available in the univariate case), and even more
difficult to imagine that this is the preferred option of most users.
>
> Agreed, and this is why the polynomial ring constructor returns a
univariate ring, unless requested otherwise (in contrast to your claim).
>
Thanks for this -- actually I find your arguments here quite compelling.
I was thinking before that arithmetic for univariate power series and
polynomials are probably optimized for that case, and so would be
preferable to the "multivariate in one variable" algorithms. But I
neglected, as you have pointed out, that one might want to write code
which, for simplicity, treats univariate and multivariate rings the same
and thus depends on the methods written for multivariate rings. This
would be especially likely if the code one were writing didn't depend on
the optimal univariate algorithms.
Of course this is precisely not the case for pernici and others who are
working on faster multiplication algorithms. Pernici, does this seem
reasonable to you? How difficult will it be for you to treat the
"multivariate in one variable" case?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:69>
Sage <http://www.sagemath.org>
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