Talk:Monic polynomial

The article Monic polynomial has some history of (unsuccessful) attempts at creating short texts, and (successful) redirects. The latest text attempt by Ettrig (and Michael Hardy) was reverted with a (IMHO not completely consistent) reference to both WP:DICDEF (i.e., "The stuff may be worthy of a wict article, but has no wp interest") and WP:CFORK (i.e., "The stuff interesting to wp is already present in an alternative article, and this is a duplication off efforts").

I disagree. I think that the 'monicity' proper does not have top rank priority, but that there are enough mathematical properties of monic polynomials, which they do not share with all other polynomials. This makes the subject worth more than a lexical definition. This does not mean that I think that the attempted short texts formed good and interesting finished articles; but the text should be given a fair chance to grow to one. There are a lot of scattered references to monic plynomials (vide infra); and in e.g. coding theory and the theory of algebraic integers and (more generally) integral closures, the property of being monic is crucial.

Actually, a clearer exposition is given in Algebraic number field#Algebraicity and ring of integers, where it should be easier to find the term monic, and where at least one of its crucial properties is given. Unhappily, the editors of that article seemed to believe that there was a wp article worth linking to.

There is an extra complication. The redirect, that has been restored, links to a rather obscure mention of monic in the section Polynomial#Classifications. This should not be a great help for readers following one of the over 50 links to Monic polynomial (and, of course, the matter would not be improved by bypassing the redirect). Moreover, 'bots insist in restoring iw-links from our svwp article sv:Monisk to that section in Polynomial.

My recommendation:: Allow the creation of a stand-alone article Monic polynomial, where not only the definition, but also the most important properties are collected. Link to this article from the occurrence in Polynomial#Classification, and from other places where now there are no links or only external links. Then, restore an appropriate iw linking. JoergenB (talk) 14:34, 23 June 2011 (UTC)Reply

Since no-one has complained, and Ettrig's latest attempt has been left unreverted for two weeks, I'll try to realise a little of the suggested programme. JoergenB (talk) 13:39, 3 July 2011 (UTC)Reply

There are a little more than 50 links to Monic polynomial. Interestingly, there are 343 occurrences of "monic" in articles, and a quick sampling indicates that roughly half of them are to "monic as in monic polynomial". (This is true for 22 of the first 40 occurrences. The other 18 include different uses of the term in category theory and linguistics, and a few others.)

I was curious of the discrepancy: By these numbers, there ought to be at least a houndred links to Monic polynomial. Some sampling showed that in some articles (like Finite field), the concept was unlinked and also unexplained. In at least one case, where a link to "Monic polynomial" did exist, closer examination showed that it wasn't to wp. In Coding theory approaches to nucleic acid design#1. Code construction using complex Hadamard matrices, the link goes to the "dictionary-like" item http://mathworld.wolfram.com/MonicPolynomial.html. (However, given the state of wp's treatment of the subject, this seems reasonable; at least, a reader does not have to scroll down the mathwolrld stub article past some tables in order to find the lexical definition embedded as a small part of a long sentence.) JoergenB (talk) 14:34, 23 June 2011 (UTC)Reply

An editor has changed "If a polynomial has only one variable" into "If a polynomial has only one independent variable", without providing any source for this terminology in the case of polynomials.In forty years of work in algebra and theory of polynomials, I have never encountered this terminology. Thus, I have reverted this edit. The same editor restored it, without any justification. As I do not want to enter into an edit war, I'll replace "variable" or "independent variable" by "indeterminate", which, in any case is more correct here. D.Lazard (talk) 22:18, 20 November 2013 (UTC)Reply