ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 26 Nov 2020 00:46:27 +0100- power series method pade(m,n) off by 1?https://ask.sagemath.org/question/54385/power-series-method-pademn-off-by-1/If p = 1+ x + O(x^2) is a power series, then then the method p.pade(0,1) should give
p.pade(0,1) = 1/(1-x)
but instead it gives an error
> ValueError: the precision of the series is not large enough
The documentation says that p should be given up through O(x^(m+n+1)).
Isn't this wrong? Shouldn't it be up through O(x^(m+n)) ?
The PadÃ© approximant P_m(x)/Q_n(x) contains m+n+1 unknown coefficients, so m+n+1 terms should be included in the power series: x^0 ... x^(m+n).
I'm working with a power series that I generate numerically, term by term. I'm using the pade method to estimate the region of analyticity in order to make a conformal transformation that will accelerate the convergence. I want to use pade(n-1,n) when I have 2n terms in the power series. But the pade(m,n) throws the above error. It does not seem possible to get a PadÃ© approximation with the same number of coefficients as in the power series.
thanks for taking a look at this.
Daniel Friedan
Daniel Friedan
Daniel FriedanThu, 26 Nov 2020 00:46:27 +0100https://ask.sagemath.org/question/54385/
- using pade approxhttps://ask.sagemath.org/question/39870/using-pade-approx/ Hi 1) From the only example I found
s = PowerSeriesRing(QQ,'s').gen()
a=exp(s);a.pade(4, 0)
type(a)
it seems this works for type 'sage.rings.power_series_poly.PowerSeries_poly'
But I have a type 'sage.symbolic.expression.Expression' b,
and was unable to convert b to the type required to apply pade
2) There's an alternative rational.reconstruct , but that seems to be geared to computations modulo (n)
3) In conclusion, it seems at current stage the simplest is to write one's own Pade? Thanks, Florin
florinFri, 01 Dec 2017 11:13:14 +0100https://ask.sagemath.org/question/39870/