Talk:Function of several complex variables: Difference between revisions

Revision as of 13:53, 26 December 2020

Revision as of 14:00, 26 December 2020

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{{maths rating|class=Start|importance=Mid|field=analysis}}

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== I would like to merge a Holomorphically convex hull into Several complex variables ==

{{archive top|result=Withdraw[[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 11:05, 3 December 2020 (UTC)}}

Holomorphically convex hulls are necessary to understand the properties that occur when increasing complex variables from one to several.So I wanted to add this topic to this page, but when I tried to add it, I noticed that the contents of the two pages were covered. I think the reason I came to think of the Holomorphically convex hull property was about the convergence region when the conditions described on the Holomorphically convex hull page were applied to the analytic function (holomorphic function).(Affects analytic continuation.) The power series is written on this page, so I would like to add a clause called Holomorphically convex hull on this page to integrate it. I would to leave the Holomorphically convex hull page as a redirect as a provisional. ( i.e. I do not object to increasing the content of the page and recreating a Holomorphically convex hull page.). thanks.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 07:55, 17 November 2020 (UTC)

:I completely changed my response here, sorry about that. This is fine with me, though I still believe it should all be merged into [[complex analysis]]. I have added templates that signify some of the problems I see with the article. In the eventuality that it is merged, many of them can be ignored. However, we do have to fix all the reference problems to make sure there is no original research. Thanks! [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 08:59, 17 November 2020 (UTC)

::Thank you for your feedback.I can't answer to the lead sentence because I didn't create it.The section on holomorphic functions supports your suggestion in the same part as in the case of one variable, and you may not need to distinguish it from one variable or several variables simply by saying complex analysis.On several variable pages, I added a note of order of integration because someone had already created a holomorphic function section, but personally, I think it's good to write on the complex analysis page.Unlike the case of one variable, there is no isolated zero of the holomorphic function, so the condition for establishing the identity theorem requires annotation. I think we need to consider a link to the identity theorem. [[Coherent sheaf]], [[Hartogs' phenomenon]], etc. are separate pages, so it seems that the reason why this page exists independently is weakening. I strongly agree that this page needs to be fix. I also understand that consolidating pages will increase the number of participants and improve the quality of the pages. Thanks!--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 09:55, 17 November 2020 (UTC)

:::[[User:SilverMatsu|SilverMatsu]], that makes sense to me. I apologize for my slurry of comments. When I reread the original, I realized it did not have the right tone. It sort of seemed like I was yelling about it and being a little too aggressive, when you were certainly not the right person to yell at (not that anyone is). So my apologies. I appreciate the work you are doing, keep it up! [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 10:34, 17 November 2020 (UTC)

::::[[User:Footlessmouse|Footlessmouse]] Don’t worry about it. Thank you for contributing to the article with a wealth of knowledge.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 11:18, 17 November 2020 (UTC)

:::::Added the contents of a Holomorphically convex hull under the analytic continuation section. I'll wait a little longer for discussion before deciding whether to redirect the original page. thanks!--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 13:14, 18 November 2020 (UTC)

:::::The merge is complete. Thank you for your advice.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 07:56, 25 November 2020 (UTC)

{{ping|Footlessmouse}} Are you saying this whole article ought to be merged into [[Complex analysis]]? If so I would certainly disagree. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 04:51, 2 December 2020 (UTC)

:{{ping|Michael Hardy}} Would you mind elaborating? Do you actually believe Several complex variables is a distinct topic from complex analysis Or is page size the problem? The lead is patently false, attempting to define the topic as if it were totally separate from complex analysis. Also, I proposed all that when the page was a fraction of its current size, and so at the time size wasn't an issue, so if that's the problem, we can brain storm on that later. I'm not in any rush to do anything. I brought up many issues because this page was misleading and it would be more helpful for it to not be misleading, so laypeople do not learn incorrect information. At the time of proposing, I thought that merging with was the easiest way to accomplish that. Note, I have not reviewed all the recent changes, but appreciate the effort. [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 05:07, 2 December 2020 (UTC)

:Note, I would also support it being a stand alone article if, after cleaning up and properly adding citations to everything that needs it and deleting the OR, there is still enough material for it to merit its own page, but several parts of the article need to be rewritten for verifiability. [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 05:25, 2 December 2020 (UTC)

::There are some things that make merging difficult, and the definition of "a holomorphic function f in ___domain D" is not well-defined for several complex variables. i.e. Whether a holomorphic function can be defined depends on the range of ___domain D. Also, in the case of one variable, I took a point at infinity on the complex plane and considered a Riemann sphere. This is because the complex plane <math>\Complex^n</math> is connected, and the compact and connected Riemann surface was only the Riemann sphere, but there are innumerable analytic varieties that are compact and connected with the connection of <math>\Complex^n \ (n\geq 2)</math>. However, the judgments differ depending on how you interpret the complex analysis page, so I think both opinions make sense. Adding a basic complex analysis (one-variable) textbook to this page may solve the citation problem. I haven't decided which textbook to use, but ... Thanks! --[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 07:59, 3 December 2020 (UTC)

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=== Continued discussion ===

{{archive top|result=The reference section was already used as a footnote, which made in-line citations difficult, but the Footlessmouse has improved the references so you can add citations. Thanks to Footlessmouse.[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 05:27, 21 December 2020 (UTC)}}

::Addendum: In relation to the topic of citation, I reorganized the references and footnotes to make them easier to cite, but since I divided them into annotations and footnotes, I would like to used the ref tag in two sections, but but I can't. Also, since analytic continuation is not fully explained in how to write a lead statement, I am thinking of not mentioning analytic continuation at the time of the lead statement. Thanks! --[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 08:52, 3 December 2020 (UTC)

:::I tried to change as little as possible in my edits, I just wanted to say it was part of complex analysis. As for the rest of it, I would have to read, I took a class on complex analysis, but it's been a while... I have fixed the footnotes, and regular references you add will automatically go in Footnotes while you can use ref name=note to add it to the annotations. I made a note in the edit summary. [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 10:39, 3 December 2020 (UTC)

:::My bad, I understand better now, use [[template:harvnb]] to make add in citations that link to one of the books, but just use the other citations inline where the fact they corroborate appears in the page. You can give each of them a name using "name=" in their opening ref tag. I moved the footnotes to further reading for now and you can add them inline wherever they are, only because there are too many footnote sections and it was a little confusing. [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 10:55, 3 December 2020 (UTC)

::::{{Ping|Footlessmouse}} Wow! The annotations and references section is now much easier to read. The talk page is also tidy and very convenient. Thank you very much! --[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 12:29, 3 December 2020 (UTC)

::::The part of the lead sentence that I said earlier is the part that '''I added''' to the lead sentence, and I apologize for making ambiguous expressions while there were multiple editors who created the lead sentence. I thought the additions other than me were great, so I'm sorry if they seemed to oppose making the lead statement clear that they were part of complex analysis. Therefore, I would also like to cooperate in explaining that Several complex variables are areas within complex analysis, and as soon as I come up with a good method, I will continue to discuss this on the complex analysis talk page. --[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 13:12, 3 December 2020 (UTC)

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== I'm would like to have a polydisc section ==

Writing the same ___domain over and over again makes the page hard to read, so I'd like to discuss it so that I can decide the symbol and write it concisely. Since wikipedia is edited by multiple people, the usage of symbols is different, and conversely, the symbols are not unified, so I think that it is difficult for anyone other than the first person to edit. For the time being, <math>\Delta</math> for the open disk, <math>\overline{\Delta}</math> for the closed disk, and the ___domain mapped to the convex ___domain by the logarithmic transformation <math>\ln| z-a |</math> is <math>D^{*}</math> or <math>\Delta^{*}</math>. After discussing it, I will decide on the symbol that you use most often, so please give me your opinion. thanks.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 14:02, 25 November 2020 (UTC)

== Proposed lead section ==