#1956: implement multivariate power series arithmetic
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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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Comment(by SimonKing):
Replying to [comment:69 niles]:
> Hi Simon!
>
> Replying to [comment:68 SimonKing]:
> 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.
Sure univariate rings are usually preferable! I do think that most users
could care less about the different methods of univariate and singly
multivariate polynomials - they want speed!
> 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?
I did not suggest that ''by default'' the polynomial ring (or power series
ring) constructor should return a multivariate ring in one variable. I do
think that
{{{
sage: R.<x> = QQ[[]]
}}}
should turn `R` into a univariate ring.
What I was trying to explain was: The user must be able to override the
default implementation by passing appropriate arguments to the ring
constructor. Hence: `PowerSeriesRing(QQ,'x')` should return the default (a
univariate ring), but `PowerSeriesRing(QQ,1,'x')` should return a
multivariate ring.
In other words: I suggest that you just mimmick the current behaviour of
th polynomial ring constructor.
Cheers,
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:70>
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