Talk:Cubic function/Archive 8

Splitting Cubic Formula into new page

Hi, I recently took steps to split information about the solutions to a cubic function to its own page, but my edit was undone to allow this to be discussed here. I would therefore like to formally propose that we split these two topics into distinct pages. This current page is around 80,000 characters, which WP:WHENSPLIT says "Probably should be divided (although the scope of a topic can sometimes justify the added reading time)". Beyond pure length, these two subjects deserve independent treatment - the cubic formula is interesting in and of itself, for reasons that are distinct from why cubic functions are interesting. We have separate articles for Quadratic formula and Quadratic function, and various other language Wikipedias treat Cubic Functions and the Cubic Formula independently, including German, Spanish, French, Chinese, and Russian, among others. As such, this split follows an established precedent, and I strongly recommend splitting these two subjects.

I would also like to ask for potential names for the new page. My original edit called the page "Cubic Formula", but I am open to alternative names. For the record, several other language wikis use some variation on "Cardano's Formula", but I do not feel this is appropriate, since the page treats other methods of finding cubic roots other than just Cardano's original formula.

Thoughts? -Ramzuiv (talk) 06:45, 6 September 2019 (UTC)

I agree to split the article, but, as I said in my edit summary, this is a major edit that require a consensus and a discussion on some details. Here are some of them

• What should be moved away? There are two possible choices: 1/ Moving all the content relative to the cubic equation. The drawback is that the remainder article would be very short (this was the motivation of a merge in 2007). 2/ Moving away only the cubic formula and its derivation. If this is chosen, many things that are in you article Cubic formula must be kept in Cubic function, such as the reduction to a depressed cubic (misplaced in the present version), the nature of the roots as a function of the discriminant, the Galois group, trigonometric solutions, etc.
• Which summary of the splitted article must be kept in Cubic function? The summary provided in your edit is not convenient, as being wrong in all cases where cubic roots are not well defined. In other words, it is correct only in the case of real coefficients and a single real root.

My opinion is that it is worth to split away the cubic formula, but that, before splitting, one must reorganize the article for making a correct split simpler. This means having a single section "Cubic formula (for depressed cubics) and its derivations", and the other results regrouped in other sections. D.Lazard (talk) 09:04, 6 September 2019 (UTC)