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 <john.crem...@gmail.com> wrote: > 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 series where the truncation occurs early > enough that division by the characteristic does not happen. Is it > possible to allow for that in a mathematically consistent way? > > John > > 2009/3/14 William Stein <wst...@gmail.com>: > > > > > On Fri, Mar 13, 2009 at 5:00 PM, David Kohel <drko...@gmail.com> wrote: > > >> Hi, > > >> I am finding problems, holes, or missing features in power series > >> rings > >> and Laurent series rings. > > >> sage: K.<u> = LaurentSeriesRing(QQ) > >> sage: R.<t> = PowerSeriesRing(QQ) > > >> 1. exp(t) is defined but exp(u) is not. > >> 2. log(1 - t) and log(1-u) -- I started filling in this gap (below) > >> for > >> Laurent series but ran into more problems. > >> 3. coercion to R does not work (R(u) fails trying to coerce to QQ). > > >> The style of implementations of source code look completely > >> independent. > >> I would like to have R == K.ring_of_integers() be defined and True > >> (maybe > >> if I call the variables the same). But the lack of coercion suggests > >> that > >> these where not designed together, as do the functions for creating > >> error > >> terms O(t^n). > > >> The names of the files hint at a design break: > > >> sage: type(t) > >> <type 'sage.rings.power_series_poly.PowerSeries_poly'> > >> sage: type(u) > >> <type 'sage.rings.laurent_series_ring_element.LaurentSeries'> > > >> Now there also exists a power_series_ring_element file, but it > >> implements > >> a class PowerSeries inheritted from PowerSeries_poly (in a separate > >> file). > >> There is also a power_series_mpoly, which must either be an attempt > >> at > >> multivariate power series or a sparse power series. > > >> Is there a reason for this split, and if so, why do Laurent series not > >> follow > >> the same dichotomy? > > > At least two different people probably implemented the code. You > > might start up sage and type > > > sage: hg_sage.browse() > > > or go to > > >http://hg.sagemath.org/sage-main/file/5c72dbb92d82/sage/rings > > > and start browsing around so you can see exactly who edited the files > > you're looking at and when. You can also do the following at the > > command line in the rings directory to see the history of any given > > file: > > > $ hg log laurent_series_ring.py |more > > > changeset: 11695:3e8e9cdd9715 > > user: Mike Hansen <mhan...@gmail.com> > > date: Tue Feb 24 09:13:31 2009 -0800 > > summary: Converting sage.rings.* docstrings to Sphinx > > > changeset: 8413:f4aeaf9e22c6 > > user: Martin Albrecht <m...@informatik.uni-bremen.de> > > date: Sun Jan 20 16:44:08 2008 +0000 > > summary: allow rational functions to be coerced into > > LaurentSeriesRings (fixes 1/3 of #1793) > > > changeset: 5481:1fb33b78a725 > > user: Robert Bradshaw <rober...@math.washington.edu> > > date: Wed Jul 18 01:35:31 2007 -0700 > > summary: Fix mathematical error I stupidly introduced > > > You can do > > > $ hg export 8413 > > > to see the actual 8413 patch (say). > > >> I think I need to understand what is intended before hacking around > >> all > >> of these classes. > > >> Cheers, > >> David > > >> P.S. A first start with log -- is there a more efficient algorithm > >> already > >> implemented somewhere or does someone want to put in place a more > >> efficient algorithm? > > >> {{{ > >> def log > >> (self): > > >> """ > >> The logarithm of the power series t, which must be in a > >> neighborhood of 1. > > >> TODO: verify that the base ring is a QQ-algebra. > > >> """ > >> u = > >> self-1 > >> if u.valuation() <= > >> 0: > >> raise AttributeError, "Argument t must satisfy val(t-1) > > >> 0." > >> N = self.prec > >> () > >> if isinstance(N, > >> sage.rings.infinity.PlusInfinity): > >> N = self.parent().default_prec > >> () > >> u.add_bigoh > >> (N) > >> err = LaurentSeries(self.parent(), 0, 0).add_bigoh > >> (N) > >> return sum([ u**k/k + err for k in range > >> (1,N) ]) > >> }}} > > > -- > > William Stein > > Associate Professor of Mathematics > > University of Washington > >http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
