Talk:Algebraic equation

message: I'm not familiar with the usage of "algebraic equation" to mean an equation with rational coefficients. If anything, it should be "a polynomial equation (with coefficients in whatever the working base field is)". Do you have a source for the definition given? Dmharvey 02:27, 6 July 2006 (UTC)
replies: text: Yes, algebraic is also a relation between fields: E is algebraic over F iff all elements of E are roots of algebraic polynomials over F. Hence the extension of meaning. Septentrionalis 13:16, 7 July 2006 (UTC)

text: Yes. (Do see if the article is clear; this is one reason non-mathematicians are needed in editing mathematical articles.) Septentrionalis 17:27, 7 July 2006 (UTC)

text: I am surprised by the claim that this is redundant. The algebraic nature of the equation also implies that the coefficients of the equation lie in the given field, or equivalently, in the algebraic closure of the field. I revert generally. Rob Har has made several other tweaks, but  they seem to me indifferent; if they are put back, I don't care either way. Septentrionalis PMAnderson 22:31, 19 December 2006 (UTC)
replies: text: Thanks for commenting on this, it has made me look further into the subject. Upon searching google and mathscinet for "algebraic polynomial" it does indeed appear that the term algebraic polynomial is used. However it does not appear to be used in a context germane to this article. Further, the generality of the definition of this article appears to be never used. I found my way to this article from articles related to algebraic geometry and that's why I made the claim that the term was redundant since in algebraic geometry (at least in my opinion) it is (one generally fixes a base field in algebraic geometry, and if one is speaking about more than one field, one would generally say the polynomial was "rational" over whichever field one wants). From searching the web, the term algebraic polynomial seems to be exclusively used to describe polynomials whose coefficients are algebraic numbers over the rationals. They seem to be mainly discussed when talking about approximating functions by such algebraic polynomials (for example Hermite polynomials), as on would approximate functions by trigonometric polynomials such as Fourier polynomials or Chebyshev polynomials. For this reason, I would suggest removing the definition of algebraic polynomial from this article and creating an article on its own, since it occurs in a different field of math. Anyone have any opnions? RobHar 19:37, 22 December 2006 (UTC)

text: I will however modify the two last paragraphs: for example, not every equation is alegebraic (the extent to which this is true would be techinically hard to describe, for example " True = not False" is not algebraic over any field). —The preceding unsigned comment was added by RobHar (talk • contribs) 19:50, 22 December 2006 (UTC)
thread_title: Untitled

message: 2x+3y=7;3x-4y=2  —Preceding unsigned comment added by 119.155.103.175 (talk) 16:52, 1 April 2010 (UTC)
thread_title:  2x+3y=7;3x-4y=2 

message: It seems that this article has clearly long since moved beyond stub quality; I'm going to provisionally re-rate it as C-class, and I'd love to hear any other opinions. -Bryanrutherford0 (talk) 01:47, 18 July 2013 (UTC)
thread_title: Article is beyond stub quality

message: See x^1/3+y^1/3=0 is algebraic equation or polynomial equation Prankher31 (talk) 02:04, 24 January 2021 (UTC)
replies: text: See the new section . D.Lazard (talk) 15:34, 24 January 2021 (UTC)
thread_title:  Confusion 

message: When one time it is written that generally algebraic equation refers to univariate and polynomial equation refers to multivariate what is use of writing the line again.
Is it written for people who consider algebraic and polynomial equation as same? Prankher31 (talk) 18:33, 24 January 2021 (UTC)
replies: text: I do not see any duplicate assertion in the lead of the article. You must be more specific and quote the exact sentence that is disputed. D.Lazard (talk) 19:05, 24 January 2021 (UTC)

text: What I wrote here does not matter. This talk page is for discussing the article. If you have concerns with the article, express them clearly. Otherwise stop arguing. D.Lazard (talk) 20:25, 24 January 2021 (UTC)

text: Please stop wasting your time for talking about what you see in the article, and instead – as  asked you before – quote the exact sentence (or sentences) you consider unnecessary duplication. --CiaPan (talk) 12:32, 3 February 2021 (UTC)
thread_title:  Regarding deletion of line