Talk:Polynomial

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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 86.31.47.92 (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.86.31.47.92 (talk) 18:34, 18 November 2014 (UTC)

Number of coefficients in multivariable polynomials[edit]

I think this article would benefit from mentioning the maximum number of terms a multivariable polynomial may have. I've seen a proof using the stars and bars method from combinatorics that shows it is something like: \binom{n+d}{d} for a polynomial of degree d with n variables. I do not have any sources, but I assume someone can dig this up. — Preceding unsigned comment added by 65.129.216.147 (talk) 02:50, 10 February 2015 (UTC)

You are right: \binom{n+d}{d}=\binom{n+d}{n} is the number of monomials of degree at most d in n variables. This is said in Monomial#Number. This would be worth to mention this here, as well as in Polynomial ring and in Monomial basis. D.Lazard (talk) 09:16, 10 February 2015 (UTC)