irizos's profile - activity

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.

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

It seems that sagemath is unable to calculate Fermic-Dirac type integrals, e. g.

integrate(x^2/(1+ e^x),x,0,oo) =>
limit(1/3*x^3 - x^2*log(e^x + 1) - 2*x*dilog(-e^x) + 2*polylog(3, -e^x), x, +Infinity, minus) + 3/2*zeta(3)

integrate(x^3/(1+ e^x),x,0,oo)==>
-7/120*pi^4 + limit(1/4*x^4 - x^3*log(e^x + 1) - 3*x^2*dilog(-e^x) + 6*x*polylog(3, -e^x) - 6*polylog(4, -e^x), x, 
+Infinity, minus)

Normally, the former evaluates to (3Zeta[3])/2 and the latter to (7Pi^4)/120, using Mathematica.

Thanks a lot for the reply. The bug is also present in cocalc.

Is there something wrong with the factorization of expressions containing exponentials ? I obtain the following strange results (Sagemath 8.6):
factor(exp(-x)+2*exp(x)) ---> 3*e^x,
factor(exp(-x)+x*exp(-x)) ---> (x + 1)*e^x

Any suggestions welcomed.