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A problem in powerseries

asked 2019-03-16 10:41:49 -0500

updated 2019-03-16 11:39:59 -0500

FrédéricC gravatar image

It seems there is a problem when expanding tan(t), sinh(t), cosh(t) using PowerSeries. The following works fine

R.<t> = PowerSeriesRing(QQ)
sin(t)/cos(t)
t + 1/3*t^3 + 2/15*t^5 + 17/315*t^7 + 62/2835*t^9 + 1382/155925*t^11 + 21844/6081075*t^13 + 929569/638512875*t^15 + 6404582/10854718875*t^17 + 443861162/1856156927625*t^19 + O(t^20)

However, tan(t) returns

TypeError: cannot coerce arguments: no canonical coercion from Power Series Ring in t over Rational Field to Symbolic Ring
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This is because the power series do have "sin" and "cos" methods, but no "tan" method. So Sage tries to fall back to the symbolic ring SR and fails.

FrédéricC gravatar imageFrédéricC ( 2019-03-16 11:38:51 -0500 )edit

For the situation you presented, you could use tan(t).taylor(t, 0, 10)

vdelecroix gravatar imagevdelecroix ( 2019-03-16 14:34:29 -0500 )edit

Thanks for the replies. Of course talylor can do the job, however I had in mind more compex calculations with several steps where the series expanded results from the first step can be used in the next one and so on. PowerSeries is very usefull to this end. I guess at some point in the future more methods will be included in PowerSeries. Some of them e.g. sinh(x), cosh(x) which can be explicitly written in terms of exponentials would be simple to implement , I guess.

irizos gravatar imageirizos ( 2019-03-16 19:04:30 -0500 )edit

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answered 2019-03-18 16:02:40 -0500

Emmanuel Charpentier gravatar image

If working in SR is good enough for your problem :

tan(x).maxima_methods().powerseries(x,0)
sum((2^(2*i1) - 1)*2^(2*i1)*(-1)^(i1 - 1)*x^(2*i1 - 1)*bern(2*i1)/factorial(2*i1), i1, 0, +Infinity)

HTH,

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Asked: 2019-03-16 10:41:49 -0500

Seen: 59 times

Last updated: Mar 18