> sage: K. = LaurentSeriesRing(QQ)
> sage: R. = PowerSeriesRing(QQ)
> 3. coercion to R does not work (R(u) fails trying to coerce to QQ).
I guess this is the same sort of problem as what I reported in trac
#5468.
chris.
--~--~-~--~~~---~--~~
To post to this gro
I think so. But then you should be working in a ring of truncated
power series
(i.e. k[x]/(x^a)). This seems conceptually different from working
in a ring of power series where you only know the elements up to
a given precision
On Mar 14, 9:53 pm, John Cremona wrote:
> David says in the do
David says in the docstring for a possible log() function " TODO:
verify that the base ring is a QQ-algebra." Now I recall reading
(quite recent) papers of Morain et al on computing isogenies between
elliptic curves over finite fields where it is useful to be able to
take truncated logs of power
Dear David,
On Fri, Mar 13, 2009 at 05:00:55PM -0700, David Kohel wrote:
>
> Hi,
>
> I am finding problems, holes, or missing features in power series
> rings
> and Laurent series rings.
>
> sage: K. = LaurentSeriesRing(QQ)
> sage: R. = PowerSeriesRing(QQ)
...
+1 for making all of th
On Fri, Mar 13, 2009 at 5:00 PM, David Kohel wrote:
>
> Hi,
>
> I am finding problems, holes, or missing features in power series
> rings
> and Laurent series rings.
>
> sage: K. = LaurentSeriesRing(QQ)
> sage: R. = PowerSeriesRing(QQ)
>
> 1. exp(t) is defined but exp(u) is not.
> 2. log(1 - t) a
I didn't really mean "don't implement them" -- just don't do it
hastily and be sure you know what you are doing of you do! Of course,
everything should be implemented
John
On 16/11/2007, William Stein <[EMAIL PROTECTED]> wrote:
>
> On Nov 16, 2007 2:07 AM, John Cremona <[EMAIL PROTECTED]> w
On Nov 16, 2007 2:07 AM, John Cremona <[EMAIL PROTECTED]> wrote:
> Even before getting to Laurent series, multivariate power series are
> harder to define than you might think, so I would avoid implementing
> them at this point unless you have a specific need for them! You need
> to be really car
That looks like a good reference.
I was thinking of the remark in Ian Connell;s (free online) lecture
notes on elliptic curves, available from
http://www.math.mcgill.ca/connell/public/ECH1/, where he says (bottom
of first page of Chapter 2)
The pitfall to avoid here is that the isomorphic rings
Even before getting to Laurent series, multivariate power series are
harder to define than you might think, so I would avoid implementing
them at this point unless you have a specific need for them! You need
to be really careful since K[[x]][[y]], K[[y]][[x]] and K[[x,y]] are
not all the same.
T
I think you want the multivariate Laurent series to form a field. For
x + y to have an inverse, you should additionally make a choice of an
ordering x < y or y < x to decide what its series expansion looks
like. The best definition might therefore be the iterated Laurent
series, as described in Ch
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