using pade approx

asked 2017-12-01 11:13:14 +0100

florin
69 ●2 ●5 ●14

updated 2023-05-19 14:31:57 +0100

FrédéricC

5311 ●4 ●44 ●118

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

edit retag flag offensive close merge delete

Comments

Please give us a, or the b from (1), so that potential helpers have a clear idea what kind of expressions are involved, and give the solution working in that particular case in any case.
- There is a function rational_reconstruction, indeed. But i do not see it as an alternative, it is designed only for the special use described in its doc string, offered e.g. by typing rational_reconstruction? in the sage interpreter.
- No, i would say, simplest for me is to use the pade method inside the class where it is genuinely defined. So just start with a b which is some function in s - say, convert is somehow to a power series, get the result, and possibly come back. But why do we need such a complication, why is the input b not directly in the PowerSeriesRing of QQ ?!

dan_fulea ( 2017-12-01 21:51:57 +0100 )edit

add a comment

sage: f=sin(x)+cos(x) sage: g=f.series(x,28) sage: h=QQ[['x']](g) sage: h.pade(4,4) (127441/6601*x^4 - 481140/6601*x^3 - 2632500/6601*x^2 + 709560/943*x + 749040/943)/(x^4 - 10940/6601*x^3 + 265500/6601*x^2 - 39480/943*x + 749040/943)

Comments

it works now! Thanks both of you and excuses for my silly novice questions. Both series and taylor which I had tried before work fine (I guess both must have advantages sometimes if they are kept ?)

adding the QQ magic changed the donna Here's the example var('s') L_F=(exp(-s)-1+s)/(s^2)
t=L_F.series(s,6) #t = taylor(L_F,s,0,6) h=QQ['s'] h.pade(2,2)

florin ( 2017-12-02 10:08:41 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

using pade approx

Comments

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

using pade approx edit

Comments

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

using pade approx