Talk:Transseries

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Let me and other editors know (on this page) of suggestions for improving the article. I may or may not have time to implement them.Dmytro (talk) 04:42, 15 August 2018 (UTC)

I think this article is well written but there are things that should be added. First, the construction/definition is circular and somewhat imprecise as such (because of how monomials are defined). I think the construction using iterated well-based Hahn series should be given. There is an additional construction which is easy to give but relies on surreal numbers; it is given in the article Transseries as germs of surreal functions of Vincenzo Mantova and Alessandro Berarducci. Also, maybe the book Asymptotic Differential Algebra and Model Theory of Transseries is a better reference for the model theory of log-exp transseries.

I can add some of those things when I have some time in the following days. What do you think? Vincent Bagayoko (talk) 17:34, 21 August 2018 (UTC)

Sure; those things will be useful (including relation with surreal numbers). The article could also have more on accelero-summation and Hardy fields for transseries. I modified the article to clarify how the circularity in the definition of transseries is avoided. Dmytro (talk) 06:53, 23 August 2018 (UTC)

I am not sure I understand exactly the construction as it is now, but all the given rules seem to be a good explanation of the characteristics of transseries rather than a rigorous construction. Since the transseries do not possess a nice universal property (not that I know of), I fear this is not enough to give a clear account of them. Also, the mention of iterated Hahn series as an alternative method of construction suggests that the proposed construction is something else than iterated Hahn series, while I think it is just that (but I may be mistaken).

I have started to write a description of the construction starting with log-free transseries and that using surreal numbers that I will post in dedicated section, and you can tell me if you think it is too long or tedious. I'll also add some coments here and there that we can also discuss. The last thing that could be good would be to add examples of computations with transseries, since one of their main uses is to effectively solve equations. I can add some comments on Hardy fields later. As for accelerando-summation, I am not at all qualified to write about it. Other possible venues of extension of the article are: various generalized transseries and grid-based transseries. (by the way, the source of G.A. Edgar is focused on grid-based transseries; there is an older version of the paper focused on well-based transseries which I cannot seem to find).Vincent Bagayoko (talk) 16:29, 4 September 2018 (UTC) — Preceding unsigned comment added by Vincent Bagayoko (talk • contribs) 14:22, 4 September 2018 (UTC)

I made some minor changes, but overall your edits look very good. While having two similar constructions of transseries may seem duplicative, overall I think it enhances understanding. I define transseries while keeping complexity to a minimum (using essentially a repackaging of iterated Hahn field construction), while you go through formal auxiliary constructions and descriptions that enhance the readers knowledge. On a separate note, I do not think the exponential-logarithmic series are defined clearly. Also, I agree about things to add, including the importance of examples of computations with transseries (and examples of useful transseries). Dmytro (talk) 06:23, 5 September 2018 (UTC)

Maybe I could put the construction with iterated Hahn series in a box which one can close or open so as to make the article articifially smaller. I'll make the definition of EL series more clear right now and think of examples of computations later. Also, I have to fix my references.Vincent Bagayoko (talk) 07:18, 5 September 2018 (UTC)

Okay, I made some changes and will come back later. Thanks for your helpful edits!Vincent Bagayoko (talk) 08:47, 5 September 2018 (UTC)

Utterly exasperating article

This article is utterly exasperating, because it is virtually impossible to find any explanation of what its subject is.

Nothing could be more important than explaining to readers what an article is about.

But this article interposes a storm of highly technical verbiage that completely obscures any explanation of what the subject of the article might be.

I hope someone knowledgeable about transseries can improve this article.

(Very few Wikipedia articles need to be improved as much as this one.)