Talk:Cubic function

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The content of Cubic equation was merged into Cubic function. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. For the discussion at that location, see its talk page.

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As suggested before, this article is a mess. I have started to fix it. However, the number of issues makes the work harder than I thought previously. Here are the main issues:

• The order of presentation is not related to the importance of the the content nor to its technicality. For example, the section on depressed cubics was (before my edits) a subsection of an unrelated section, while reduction to a depressed cubic is fundamental for simplifying everything.
• Proof are presented with a lot of details (including very elementary computations, and proofs of side results that are better described in specific articles, generally not linked) that are confusing by making the exact results difficult to find, as well as the main ideas of the proofs.
• Some basic facts are lacking, such as that, up to translations and directional scalings along the axes, there is only three cubic functions, and thus three shapes for their graph.

So, restructuring the article will take some time, and the global reason of my edits needs to be explicited.

I would appreciate feedback on the section that I have already rewritten. D.Lazard (talk) 09:16, 22 September 2019 (UTC)Reply

In a preceding thread is has been suggested to split the article.

In december 2007, Cubic equation were merged into Cubic function, with almost no discussion. The main reason was that the "function" part was very short. This is no more true, specially after my recent additions, and my restructuration for grouping together the "function" sections. On the other hand, the "equation" part is very long. It can certainly be dramatically shortened by giving less details in the proofs, per MOS:MATH#Proofs. Nevertheless, even after this, the article would remain very long. This makes obsolete the argument for the past merge.

Another argument in favor of splitting is that the coefficients are always real in the "function" part, while most of the "equation" part does not depend on the nature of the coefficients.

My suggestion is to split the article into Cubic function and Cubic equation. Another suggestion would be to split out the various proofs of the cubic formula into a subpage. I am not convinced by this. In any case, such a split must be decided after having simplified the proofs, as suggsted above.

I could be bold, and proceed, but, as it is a strong restructuration, some further opinions would be helpful. D.Lazard (talk) 10:18, 24 September 2019 (UTC)Reply

• This proposal sounds sensible to me. --JBL (talk) 11:13, 24 September 2019 (UTC)Reply

• At first, I was confused as to which parts of the article would go to cubic function and which would go to cubic equation, since I would call "y = x^3 + px" a cubic equation (but not a cubic equation in one variable as defined in the lead). The suggestion seems reasonable otherwise though, and perhaps its implementation would be clearer than what I imagine right now. I'd say go for it. — MarkH21 (talk) 11:41, 24 September 2019 (UTC)Reply

 Done D.Lazard (talk) 17:25, 24 September 2019 (UTC)Reply

Your split looks good to me. --{{u|Mark viking}} {Talk} 18:08, 24 September 2019 (UTC)Reply

Thanks for taking care of this - Ramzuiv (talk) 00:41, 25 September 2019 (UTC)Reply

Why has the solution section been removed from this page? The formulas in that section were so helpful in solving cubic polynomials Aminabzz (talk) 18:40, 26 September 2019 (UTC)Reply

To editor Aminabzz: The solution section has not been removed. It has been rewritten and renamed Cardano's formula for the depressed case, and General cubic formula for the general case. If you find the old version better, please, explain why. I'll try to solve your concerns, if any. By the way, this article has been splitted, and everything that concern equations is in Cubic equation except for a link in the lead of Cubic function. D.Lazard (talk) 20:09, 26 September 2019 (UTC)Reply

Thank you for your answer. I've seen the other article and I found it very good too. Aminabzz (talk) 21:00, 26 September 2019 (UTC)Reply

https://en.wikipedia.org/w/index.php?title=Special:WhatLinksHere/Cubic_function&hidelinks=1&limit=500

Most of those now should point to the page on cubic equations. 73.89.25.252 (talk) 16:34, 6 August 2020 (UTC)Reply

I changed the redirects that clearly should go to the page cubic equation or its section on the Cardano formula. Some of the others could use attention but this solves most of the problem for now. 73.89.25.252 (talk) 21:26, 6 August 2020 (UTC)Reply

How do I solve cubic function given 4 points 41.13.200.129 (talk) 21:42, 24 February 2022 (UTC)Reply

It seems that you are talking of polynomial interpolation. D.Lazard (talk) 22:04, 24 February 2022 (UTC)Reply