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D. Lazard Operators Questions[edit]

Dr. Lazard: In working on a polynomial computing article I was shocked to find there also is no article or section on Polynomial operators! As I'm sure you know, many researchers and students, in structuring or working on linear equations and nonlinear systems, fail to notice the underlying polynomial nature of the problems. Multivariate polynomial operators are very important in polynomial computing, special functions, numerical methods and other algorithms for CAS, but I think they might be less known when seen only as a footnote to tough nonlinear systems or even linear equations, which of course are actually a subset of PO's. Do you think an article or at least a section is warranted? Recent work also is applying sytems of PO's to Latin squares for new approaches to research design methodology (as a statistical generality / approach). Pdecalculus (talk) 16:41, 29 December 2013 (UTC)

Thanks to db for comment on being careful of techniques. I've been zinged before on articles for giving technique instead of theory because there is a wiki caveat against "how to's" I guess. Because of this I'm shy about applications, but have combed a bunch of them on the site looking for (not totally how to) connections between polys, computing and linear algebra, with a view toward perhaps compiling a list of polynomial operators if not an article. These include but are not limited to related articles on linear algebra, polynomial algorithm generation, functional methods and shift operators, signal processing, of course numerical LA, Bezoutian and Hankel forms (eg. what wiki would call polynomial stability testing ala Bézout matrix or Hankel matrix-- although even the ortho poly section there is incomplete), control theory, etc. On the current wiki, the relevant operators are scattered thoughout the site, some with individual articles, others buried "as" an application. I don't know the site rules enough to know if a comprehensive article explaining them, or a list tying them to polynomial computing and algos is warranted, and I don't want to spend a week writing it if it's just going to be removed. I don't mind it being heavily edited, but removal just kills the idea under the rubric it's covered elsewhere, which is true, but you need a trail of bread crumbs to find it!Pdecalculus (talk) 17:25, 29 December 2013 (UTC)
Forum update db: I'm cracking up at your idea that a list obviates the covered elsewhere argument because, by nature, a list IS what's "covered elsewhere." If other editors agree, maybe I'll start there! And thanks for the encouragement. — Preceding unsigned comment added by Pdecalculus (talkcontribs) 22:19, 29 December 2013 (UTC)
Calc: thanks! I've moved my operator efforts to Operator (mathematics) which had ZERO references or cites, and no mention of polynomials. It's pretty much an orphan.Pdecalculus (talk) 21:41, 3 January 2014 (UTC)
@Pdecalculus: An orphan is an article without incoming links. With more than 50 incoming links (their list may be obtained with the button "What links here" at the left of the page), Operator (mathematics) is far to be an orphan. D.Lazard (talk) 16:54, 6 January 2014 (UTC)

Merger proposal[edit]

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
The result of this discussion was to merge Brirush (talk) 05:08, 7 November 2014 (UTC)

I propose that Polynomial expression be merged into Polynomial. This is a bad way to distinguish the two terms "polynomial expression" and "polynomial"; even if there were a better title for the first article, it's unlikely to be expanded. (It was created in 2010 by one user and has received no substantial edits since that day.) I think that its content could go well at the end of the Definition section here; we wouldn't need the introductory context, just a simple statement and the examples. (On a related note, the entire Definition section here needs refactoring, but that's a bigger job, and the refactoring will go better if the merging is done first.) —Toby Bartels (talk) 16:07, 13 April 2014 (UTC)

Since I was that user, I just like to let know that I don't oppose to the proposed merge. A main motivation for creating the polynomial expression article was to have a destination for links that would not just (and confusingly) point to polynomial; however this concern might be taken care of by a specific redirect (if a target is available). I think the term "polynomial expression" is fairly well understood by mathematicians in the field, any often freely used without defining it; as it is not something one writes books about, so it does not surprise me that finding sources is hard/impossible. Sometimes it is used without the "expression", although this usage contradicts the definition of polynomial (see for instance matrix polynomial). Good luck with trying to find the right angle/tone for discussing this in the context of the Polynomial article (which is more aimed at a broad public, I think).Marc van Leeuwen (talk) 16:57, 13 April 2014 (UTC)
  • Support: I support the merge. However, care should be taken that polynomial expression has two slightly different meanings. The article to be merged here call polynomial expression the result of substituting the indeterminate(s) of a polynomial by some mathematical object (called here "entity"). As far as I know, in most mathematical texts, "polynomial expression" is not used for this purpose, but the authors use instead something like "polynomial in cos(x)", for example. In other contexts, "polynomial expression" is used for expressions that may eventually be simplified into a polynomial, while "polynomial" is reserved for the expanded form of the polynomial. D.Lazard (talk) 17:38, 13 April 2014 (UTC)
I share D.Lazard's concern about the two different senses of "polynomial expression". (Actually, I'm not sure that I'm familiar with either sense, Marc's or Lazard's, as a term to be used specifically in preference to "polynomial", although in both cases I can see that it's being used for something slightly different than a polynomial exactly.) This means that redirecting polynomial expression to a place within the polynomial article wouldn't work either. Perhaps there could be some very brief mention of Marc's sense of "polynomial expression" in the lede. —Toby Bartels (talk) 03:04, 17 April 2014 (UTC)
OK, here's another idea. Maybe we have a little section in this article discussing the term "polynomial expression" in all of its senses. This would be in addition to merged text handling things like polynomials in cos x and matrix polynomials (not to mention the current material handling expressions that reduce to polynomials upon algebraic simplification). But then we would need citations. —Toby Bartels (talk) 03:09, 17 April 2014 (UTC)
I support this proposal. --JBL (talk) 23:27, 12 June 2014 (UTC)
I'm prepared to sit on board with this proposal as well, although I'm still a little skeptical about referring to polynomial-like expressions as "polynomial expressions" (but then that's just me). --JB Adder | Talk 22:15, 13 September 2014 (UTC)
  • Support: As far as I remember, I've always seen polynomials and polynomial expressions in the same section in a majority of my mathematics text books. As far as Polynomial expression is considered as a standalone article, it's still a stub and viewing from an encyclopaedic point of view, I do not see anything more meaningful that could be added, other than stuff for highly targeted audiences. However, as D.Lazard mentioned above, care must be taken to clearly mention the contexts of usage of the term "polynomial expression" Amitosh.swain (talk) 05:57, 1 November 2014 (UTC)

The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

Section Polynomial equations[edit]

At present, this section has two subsections. Allegedly, the division between the subsections is between introductory material and material on solving polynomial equations. In fact, both sections contain definitions of polynomial equations and both sections contain material on solutions of polynomial equations, but the notation, style, level, etc. is completely different between the two sections. (In particular, the first section is much more approachable and does not introduce unnecessary subtleties like the difference between a polynomial and its associated function.) I tentatively propose to rewrite this section to remove redundancy; I will probably aim for a level closer to the level of the first, smaller, subsection. What do others think? --JBL (talk) 23:25, 12 June 2014 (UTC)

Reciprocal equations[edit]

This is a term mentioned in some good treatments of polynomials yet it doesn't seem to be mentioned on wikipedia. Would it be appropriate to mention it on this page? If so, how should it be incorporated?

SewerCat (talk) 18:51, 21 September 2014 (UTC)

See Reciprocal polynomial. D.Lazard (talk) 19:30, 21 September 2014 (UTC)

Polynomial Calculator External Link[edit]

Hello Sirs,

Thanks for the explanation. Those software are kind of charity provided for free usage of public. I believed could be helpful promoting them in a convenient place frequented by relevant pupils and scholars. I couldn't find any other way.

Therefore I insist putting it here improves useability of wikipwdia entry.

Regards (talk) 11:33, 1 November 2014 (UTC)

The explanation referred to in the preceding post is here, and concern the inclusion of this external link by this and this edit. I have reverted these edits, as, IMO, they do not satisfy the requirements for an external link. Other opinions are welcome. D.Lazard (talk) 14:29, 1 November 2014 (UTC)
I agree with D. Lazard. --JBL (talk) 14:56, 1 November 2014 (UTC)
Sirs, it is similar to Derek's Virtual Slide Rule Gallery link that I found on Wikipedia Slide Rule page. Were not that link on Wikipedia I never could know such a thing should exist by software. That slide rule is in java script codes. The Dysprosium Polynomial Calculator Software is in Java. (talk) 18:34, 18 November 2014 (UTC)

Merged from Talk:Polynomial expression[edit]

Examples? Tutorial? Explanation to general audience?[edit]

So many of these science, tech, and math (especially math) articles are written exclusively to an audience that already knows the material – people who don't need the article in the first place. In order to be truly useful wikipedia must be more than an archive of compressed insider information. I am more and more of the opinion that this problem is (at least partially) rooted in the actual editing environment (the editing interface) which feels custom built to exclusively filter for a particular class of computer nerd, a class of people who are notoriously uninterested in teaching or of expending any effort to make technical information cognitively available to non-nerds. This filter excludes the very category of potential contributors that could transform wikipedia from an archive of coded insider information - and into a true information transference medium. The entreaty, "Did you know that you can edit this page?" isn't honest. Only those with HTML editing experience will be comfortable contributing within the wikipedia page editing environment. This is either a gross oversight (highly unlikely), or a persistently and aggressively arrogant form of direct and purposeful filtering of potential contributors. Feels for all the world like social engineering gone terribly wrong (is there some other way for social engineering to go?). Change the interface to a simple and direct WYSIWYG content editor and watch as wikipedia content becomes friendlier and more instructive.

Note: I realize that much work has been done to make the wikipedia editing and contribution environment more "humane", but the legacy of nerd-facing tools and attitude presents a considerable wall to overcome. Wikipedia fights an uphill battle to attract and keep the non-nerd contributor. The overall look and feel of the wikipedia interface seems very much more an attribute of the underlying page description protocol and very much less an attribute of the purpose - that of making it intuitive and slippery smooth for ANYONE to contribute and edit content.

Randall Lee Reetz — Preceding unsigned comment added by Randall Lee Reetz (talkcontribs) 17:57, 20 May 2012 (UTC)


While I think there are some valid points in your dissertation, it is not part of a discussion about Polynomial Expressions. You would probably get a larger audience and some support if you considered a different location. Les Hayden (talk) 13:55, 3 June 2012 (UTC)