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2016-01-15 19:30:30 +0200 | commented question | Want to create a generic series with indexed coeffs, e.g. a[1], a[2],... Ahh you'r right, I was conflating two things. I'll fix it, Thanks |
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2016-01-15 04:12:02 +0200 | asked a question | Want to create a generic series with indexed coeffs, e.g. a[1], a[2],... Hello, I'm very new to Sage and would like to take a horrible equation, $H(e^v,z)=0$, and substitute into $v$ a power series, like $v(z)=\sum_{i=l}^{u} a[i] z^i, $ where maybe $l<0$. I'd then like to solve for the coefficients, at each power of $z$, or all at once like Mathematica does (or so I'm told). The Mathematica version is here in case it helps clear up my question. Everything is complex and I was thinking of something like this pseudo-script: But this is very scattered, rough, and not even meaningful. I'm not sure if using this 'experimental' AsymptoticRing is a good idea, nor if my growth group is correct. I also see things like .substitute, etc. from the /ref/Calculus. All I really want to do is take a generic expression $$H = \sum_i e^{a_iv + b_iz^2}=0,$$ where $a_i$ and $b_i$ are complex, and replace the $v$ with $\sum_{i=low}^{i=high} h_i z^i$ -- actually I am working on 'eq2', of several, in the first Mathematica block. Then take Taylor series and solve for the coefficients $a_i$ in ascending powers of $z$. This is much like Hinch's book, Perturbation Methods, in the very beginning, for "expansion methods". Thank you for your time and help! |