Of course, the issue here is mathematics, not GiNaC. I totally agree with that. :) And thanks a lot for pointing out the method to find the leading power. Since there is also log(x)-terms in my expression, and leading power seems not be able to capture these log terms. Currently, I am trying to walk around by finding the all pattern: x^n, since n is rational number, and multiply n by lcm of all those denominators, and transform all rational powers to integer powers … BTW, when the input contains x^n (n as an integer) and log(x), it seems that series works fine around x=0. Thanks again! Best regards! Feng 原始邮件 发件人: Vladimir V. Kisil<kisilv@maths.leeds.ac.uk> 收件人: Feng Feng<F.Feng@outlook.com> 抄送: GiNaC discussion list<ginac-list@ginac.de>; Vladimir V. Kisil<V.Kisil@leeds.ac.uk> 发送时间: 2019年12月22日(周日) 06:17 主题: Re: [GiNaC-list] series of x^n around x=0

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On Sat, 21 Dec 2019 11:14:58 +0000, Feng Feng <F.Feng@outlook.com<mailto:F.Feng@outlook.com>> said:

FF> Thanks very much for the reply.! And yes, it is not FF> well-defined in mathematical sense to taylor expand x^(3/2) FF> around x=0. What I exactly want is to get the asyptotic FF> behaviour of a function f(x) around x=0. For example, f(x) = FF> x^(3/2) (1 + x + x^2 + …), the asyptotic behaviour at leading FF> order (LO) and next-to-leading order (NLO) are x^(3/2) and FF> x^(5/3), respectively. FF> So I wonder there is a way to get the asyptotic behaviour of a FF> function f(x), for example, Input: x^(3/2) * (1+x+x^2+x^3), and FF> request the terms at LO and NLO Output: x^(3/2) + x^(5/3) I am not sure that is NLO, but the leading term can be obtained as follows: ex e=pow(x, numeric(3,2))*(1+x+x^2+x^3); cout << (log(e).diff(x)*x).expand().subs(x==0); // -> 3/2 So now e can be multiplied by x^(2/3) to remove the singularity. See for explanations: https://en.wikipedia.org/wiki/Logarithmic_derivative So, the issue here is mathematics, not GiNaC. Once you know the right method, it shall be easier to implement in the code. -- Vladimir V. Kisil http://www.maths.leeds.ac.uk/~kisilv/ Book: Geometry of Mobius Transformations http://goo.gl/EaG2Vu Software: Geometry of cycles http://moebinv.sourceforge.net/ Jupyter (Colab): https://github.com/vvkisil/MoebInv-notebooks Jupyter (CodeOcean): https://codeocean.com/capsule/7952650/tree