Talk:Algebraic function

In reference to an older version
This is just wrong. Charles Matthews 14:50, 14 February 2007 (UTC)

You are all nerds

Algebraic expression
It would be useful with a definition of an algebraic expression. The article Expression (mathematics) is quite vague regarding this. Isheden (talk) 12:25, 18 October 2011 (UTC)

A solution in radicals is not the same as any solution
I wish people would cease making this error. Gene Ward Smith (talk) 07:01, 17 April 2012 (UTC)

Incomprehensible
This article fails to convey any clear concept of what an algebraic expression is to non-mathematicians. Relying on even more obscure definitional technicalities is not good enough. I am no mathematician, but I am trained in analytic philosophy and formal logic, and I cannot understand what the hell you people are talking about at all. One suspects that the authors of this article don't have a full grasp of their topic. If you do, then prove it, and make it clear to all of us. Larry oh larry (talk) 16:48, 25 February 2013 (UTC)

Rearrange
(Dis. - I am neither a mathematician nor an experienced Wiki user) I'm quite sure the editor-by-author is adequately versed on the subject, and as a student the information doesn't seem at all odd. However, I still feel that the problem remains concerning the article's method of conveying the information. Wikipedia's math section has many great broad-topic articles, and a recurring theme I notice is that the simplified approach is always put first. As of now, this is not the case for this article, and this is a considerably important subject. Yes, it may be somewhat informal to refer "a polynomial whose coefficients are themselves rational-coefficient polynomials", given a rigorous context of algebra. However, an even more intuitive approach would rather refer "a function which can be represented using only addition, multiplication, division, and root-taking in a finite number of steps", or something of the like. This is more easily understood to non-mathematicians, and less intimidating than the approach provided now. From there, one may clarify any shortcomings or technicalities for due formalism, and then continue with the more technical and rigorous definitions. This is simply a conventional standard that seems ubiquitous in math entries, so I'm just suggesting a rearrangement. — Preceding unsigned comment added by 71.22.207.207 (talk) 03:28, 5 March 2013 (UTC)

Regarding the previous two comments
I have attempted to clarify parts of the article. Part of it was done after the first comment above but before the second. I also rephrased the lead in line with the ideas in the second comment. Hopefully the article is a bit more comprehensible now. Isheden (talk) 20:59, 5 March 2013 (UTC)

Name of function
Does $$f(x)^5+f(x)^4+x=0$$ have a name? RJFJR (talk) 02:53, 13 June 2016 (UTC)
 * Yes, it is called Bring radical. However it seems not really useful (and possibly confusing) to mention it in this article. D.Lazard (talk) 09:36, 13 June 2016 (UTC)
 * Maybe use a footnote with a link? RJFJR (talk) 12:39, 13 June 2016 (UTC)
 * OOOPS, this function is not the Bring radical. I have edited the article for taking the Bring radical as an example, and linking to it. I have also changed the link for the impossibility of solving by radicals. D.Lazard (talk) 13:12, 13 June 2016 (UTC)

Further requirements?
Though I'm not deeply into the field, I fear that something is missing in the current definition of "algebraic function" here. According to the definition, something like
 * $$f(x) = \begin{cases}

-1, & \mbox{if } x \in \mathbb{Q} \\ 1, & \mbox{if } x \in \mathbb{R} \setminus \mathbb{Q} \end{cases} $$ would be an algebraic function, since it satisfies the polynomial equation:
 * $$f(x)^2=1$$.

Is this actually correct? The wikipedia definition of a "transcendental function" explicity requires the function to be analytic, which is very strong... Doesn't the "algebraic" concept (which should be more strict) need some continuity specification? Furthermore, the article affirms that "As an equation of degree n has n roots, a polynomial equation does not implicitly define a single function, but n functions, sometimes also called branches". This is not true, as infinitely many functions satisfying the same equation can be built by exploiting tricks similar to the one adopted for constructing the example function above. Additional requirements about continuity could fix the issue. --Il wage (talk) 14:15, 27 September 2018 (UTC)
 * . Good catch. As an algebraic equation has, in general, several solutions, one can get a lot of uninteresting functions by jumping many times from solution to another one. If continuity is assumed, it can be proved that the solution is analytic at any point where the root is not multiple. D.Lazard (talk) 16:13, 27 September 2018 (UTC)

Opt maths
Algebraic function 202.51.89.69 (talk) 01:56, 26 July 2022 (UTC)

Math
Funvtiond 197.212.183.32 (talk) 01:15, 9 November 2022 (UTC)