Talk:Quintic function

message: Auxiliary equation is mentioned three times, it needs explaining! 86.166.163.239 (talk) 08:26, 19 May 2015 (UTC)
replies: text: I have edited the article for clarifying this. D.Lazard (talk) 09:56, 19 May 2015 (UTC)
thread_title:  Auxiliary equation 

message: Article reads: "the Tschirnhaus transformation ...which depresses the quintic". I bet most readers have no idea what it means to "depress" a quintic. Some more explanation would be helpful (or maybe even an article on depressing polynomials?). --104.132.34.86 (talk) 23:36, 15 February 2016 (UTC)
replies: text: . D.Lazard (talk) 09:32, 16 February 2016 (UTC)
thread_title: Depressing the quintic

message: The section Quintic function#Roots of a solvable quintic (paragraph 2) says
:If the quintic is solvable, one of the solutions may be represented by an algebraic expression involving a fifth root and at most two square roots, generally nested. 
Should this start out as "If an irreducible quintic is solvable..."? I ask because a quintic that can be factored into a cubic and a quadratic can be solved without fifth roots—can it also be solved using a fifth root? Loraof (talk) 21:13, 13 June 2016 (UTC)
replies: text: Every equation may be solved using a fifth root. It suffice to replace any number appearing in the solution by the fifth power of its fifth root. This may seem a joke, but Galois theory allows showing that fifth roots (if any) may always be eliminated from any solution of an equation of lower degree. The beginning of the section already said that "solvable quintics" refer to irreducible quintics solving by radicals. I have clarified this by adding that only irreducible quintics are considered in the section. D.Lazard (talk) 22:29, 13 June 2016 (UTC)
thread_title:  Quintic or irreducible quintic? 

message: Hello fellow Wikipedians,
I have just modified  on Quintic function. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20140701060849/http://library.wolfram.com/examples/quintic/ to http://library.wolfram.com/examples/quintic/
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).
Cheers.—InternetArchiveBot (Report bug) 15:35, 21 July 2016 (UTC)
thread_title:  External links modified 

message: This page in english is now an orphan on wikidata, no more linked to the corresponding pages in other languages. Anne Bauval (talk) 22:21, 9 August 2017 (UTC)
replies: text: .  The problem is that somebody has decided that "Quintic function" should be different from "Quintic equation". Some time ago, I have encountered this problem with Fibonacci number and Fibonacci sequence. I have copied from there the mysterious way for fixing the problem. D.Lazard (talk) 08:31, 10 August 2017 (UTC)
replies: text: You fixed the problem here (made the corresponding pages in other languages visible from here), and so did I on the page in french (made your page in english visible from there), but this page in english is still no longer visible from, for instance, the page in german. Anne Bauval (talk) 08:04, 20 August 2017 (UTC)
thread_title:  Interwiki links recently disappeared 

message: Unfortunately I am unable to find the relation between the root z in the Cayley's resolvent and the actual root y of the depressed quintic equation - the one lacking the biquadratic term in y! I scanned several times the related paragraphs in the main wiki-article but couldn't see a given relation. Can you help me see if there is any of such relation given in the article? If not, please add it immediately. I wait for your reply in my e-mail account. Yours truly, 
Quinctic reader (talk) 19:44, 22 December 2017 (UTC)
replies: text: The article says:  This means that it is difficult to find the relationship between the rational root of Cayley's resolvent and the roots of the quintic. In fact, I have given a solution to this problem (cited in the article), and the description of the formula is three pages length. D.Lazard (talk) 20:46, 22 December 2017 (UTC)
thread_title:  The root z in the Cayley's resolvent 

message: The first external link to the Quintic Equation Solver appears to be broken, or the solver isn't working. Page comes up blank.
173.243.178.8 (talk) 22:58, 14 June 2018 (UTC)
replies: text: I have removed it.  Thank you for pointing this out.—Anita5192 (talk) 23:35, 14 June 2018 (UTC)
thread_title:  Broken link or bad external reference 

message: Insists to add a section specifically on Hermite's work on the subject. This section is not convenient for this Wikipedia article. Firstly, it seems to be an wp:original synthesis of several Hermite's articles. In any case, no WP:secondary sources are provided. Moreover, this editor describes (in an edit summary) his edit as "I made everything very carefully. Read the Hermite essay in the Italian version on page 258! These is this special formula. And I only did regular calculation algorithms we all know. And the last step I wrote down in this article just needs the theorems of the lemniscate elliptic functions that are also known already". This is exactly what is called "original research" in Wikipedia. So, the Wikipedia policy WP:NOR implies to remove this new section.
There are other reasons to remove this section: firstly, notations are not defined, nothing is said on the relation of the first formula with the general quintic, and the final result is not explained. This is not acceptable for an encyclopedia.
Also, Hermite's work is mentioned in the preceding section, which refers to Bring radical for details. In the linked article, the relation of the subject with elliptic integrals is detailed and the other authors who have contributed are mentioned. 
In other words, this new section is a poor duplication of an existing content. This is a further reason for removing it. D.Lazard (talk) 15:22, 13 August 2023 (UTC)
thread_title:  Section on Hermite's work