Talk:Budan's theorem

Needs Wikification
Please research related Wikipedia articles and Wikify this article. For example, in the first sentence under History, you mention F. D. Budan and J. B. J. Fourier. I presume these refer to Ferdinand François Désiré Budan de Boislaurent and Jean Baptiste Joseph Fourier. Fourier theory redirects to Harmonic analysis but this article seems closer to Fourier series. Relevant and related articles should be linked using Wikimarkup.

I can't comment on the content or formulas. I am NOT a mathematician (barely earned grade D in college algebra and trig). In my opinion, this article isn't yet ready for Wikipedia main pages.DocTree (talk) 18:22, 2 April 2012 (UTC)


 * I totally agree with you. I mostly work on the mathematics part (and the required citations) on this article but I believe that it requires a more unbiased and encyclopaedic approach. SurferBuffer


 * Many thanks for your improvements to this article, SurferBuffer. DocTree (talk) 16:51, 19 April 2012 (UTC)

History section
This section (and parts of others) gives WP:UNDUE attention to the research of a few authors. The history is interesting and encyclopedic, but I think it should be reviewed for excessive detail (and WP:COI). At the very least, I think it will be prudent to move the 700+ word discussion on history below the main topic of the article. Rschwieb (talk) 18:29, 20 April 2012 (UTC)

The new ordering of topics is nice! Akritas2 (talk) 07:37, 21 April 2012 (UTC)


 * As far as "UNDUE attention to the research of a few authors", a Professor of the History of Mathematics told me there is nothing undue here as I am the only one who dealt with the topic under discussion. As much as he tried with other sources (Dieudonne and English, French & Russian encyclopedias) he was unable to find anything. Ditto for the COI. Nonetheless, I have reduced the number of references to the absolutely minimum number required for the narrative to have "verifiable evidence".
 * Akritas2 (talk) 12:42, 24 April 2012 (UTC)


 * I don't know why you think the opinion of an unnamed professor of the history of mathematics is what determines compliance with WP standards. I can only attribute it to your unfamiliarity with the standards. Verifiability is the relevant policy.
 * As for COI, let me try to explain myself so that it sounds like less of an accusation. Simply put, self-citation is always a likely suspect for self-promotion. It is what self-promoters do. I don't think this is your motivation, but I think you just want to include information you believe is true and peer reviewed, and you have few sources outside of your own papers. But the fact that you are forced to cite your own papers so much indicates that there are not many independent resources and this is not easily verified. This is why the WP policy is "verifiability, and not truth", it's a stronger policy than truth.
 * New editors are often surprised and dismayed by this fact at first, but objectively it is a good policy. I don't intend to remove material myself, but don't be surprised if some of your material is removed by other editors for the policy I outlined above.
 * How many authors in the citations independently supported your argument? On the surface it only looks like your papers. Rschwieb (talk) 13:26, 24 April 2012 (UTC)
 * You precisely described my motives above. The authors in the citations are mostly of the 19th century. Our contemporaries are Massimo Galuzzi (University of Milan, Italy), Adam Strzeboński (Wolfram Research), Panagiotis Vigklas (got his Ph.D. with me) and Hourya, Benis-Sinaceur (a Hiastorian of Mathematics). I have shown the article (in various stages) to the first three of them and they all found it (to quote Adam, to whom I showed it last) very good. Adam also pointed out (today) an important omission on our part in the theorems and I corrected them immediately ("sharpened them" is the term I used in the comments).
 * Akritas2 (talk) 15:04, 24 April 2012 (UTC)


 * BTW, I have contacted two Professors of the History of Mathematics (their names are at your disposal) and we are in the process of contacting Hourya, Benis-Sinaceur mentioned above. If you have any further ideas ...Akritas2 (talk) 15:17, 24 April 2012 (UTC)


 * Last but not least! I believe that in our times (when everything has been digitized -- except, maybe, for things that have to do with government corruption) there does not exist anything that is not easily verified. As an example I mention our intervention in the Encyclopedia of Mathematics http://www.encyclopediaofmath.org/index.php/Budan-Fourier_theorem. The editor there was astonished and told us that if you type Budan there are almost 100 hits in Math Reviews; indeed there were, and they all had Fourier's statement of the theorem. So I believe that everything can be verified.Akritas2 (talk) 14:23, 25 April 2012 (UTC)

Definition of sign variations
This definition is used by both theorems and so I believe the best place for it is in the lead -- and not in Budan's theorem. Open to any suggestions for a better place.

Akritas2 (talk) 06:30, 21 April 2012 (UTC)

Nice!! Akritas2 (talk) 09:15, 21 April 2012 (UTC)


 * As I have mentioned it many times before, please at least glance at MOS:MATH. I'll point out for you this time MOS:MATH so that you can read on appropriate lead material. A definition of terminology should not appear in the lead: the lead is for a broad overview of the topic. A defintion on conventions is really too specific, and should be below, but it doesn't have to be where I moved it. I just glanced at the article as it is now, and that current position looks fine. Rschwieb (talk) 13:21, 23 April 2012 (UTC)

Slight disagreement with Mathworld's article
Currently, the article states that just the right side of the interval cannot be a zero of the polynomial. However http://mathworld.wolfram.com/Fourier-BudanTheorem.html states that neither the left nor the right can be a zero of the polynomial. Mathworld also uses a closed interval rather than an open interval. That might be justification enough for this difference. Regardless, this article needs more references.Mouse7mouse9 01:09, 4 June 2015 (UTC) — Preceding unsigned comment added by Mouse7mouse9 (talk • contribs)
 * Edit - this article needs more references in English.Mouse7mouse9 01:11, 4 June 2015 (UTC) — Preceding unsigned comment added by Mouse7mouse9 (talk • contribs)

Comments about two section
In the present state of the article, sections "History" and "The most significant application of Budan's theorem" are far to be conform to Wikipedia policies and guidelines (see below for a list of the main issues). I intend fixing this. However, this will remove several reference that may be useful in the future. Therefore, I keep here a link to the present version.

The main issues of these sections are the following D.Lazard (talk) 15:46, 20 November 2018 (UTC)
 * Section "The most significant application of Budan's theorem" consists essentially of a description and an history of Vincent's theorem. This is misplaced here, and I'll replace it with a few sentence about the relationship between Budan's andVincent's theorems.
 * WP:COI and non-neutral point of view: These sections haven been written by an editor who is also the author of many references. This is a true problem, since this editor uses this article for pushing its own point of view, which is not shared by most modern authors working or having written on the subject (none is cited). A witness of this bias is that the editor cites only his thesis in section "Comeback of Budan's theorem", without citing his advisor Georges Collins, who gave him his thesis subject, and co-autored the paper that made Budan's and Vincent's theorems known to the community of computer algebra. Several others former students of Collins have also worked on the problem of real root isolation, and this shows that Collins was deeply involved in this subject, and must be credited of the "come back of Budan's theorem".
 * These sections are over detailed on many points of minor historical importance.


 * I finished to rewrite this article. D.Lazard (talk) 12:04, 21 November 2018 (UTC)

Typos
I think the proof requires proof-reading. There are some 'h' exponents that should probably be 'm', "either of m – 1 or m – 1". — Preceding unsigned comment added by 85.171.184.78 (talk • contribs) 13:20, 5 May 2019 (UTC)
 * . Good catch, thanks. D.Lazard (talk) 14:06, 5 May 2019 (UTC)