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) 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)
sage: type(u)
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?
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) ])
}}}
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