Talk:Rational function

message: I presume an irrational function is one that is algabraic but not rational. Is this correct? Brianjd
:I don't think irrational function is a standard term. Charles Matthews 09:13, 8 Dec 2004 (UTC)
replies: text: No one says 'rational expression'. Rational function is the standard term, and should be the article name. We should not mess with traditional terminology, even though there is the point you make, and also the lack of definition at values for which the denominator vanishes. Charles Matthews 08:30, 22 December 2005 (UTC)

text: No disagreement from me that 'function' here is a misnomer. Policy is to use the common name. "Rational function" has five times the Google hits. I'm quiter happy for the article to have a full discussion of all those points. But in a sense the functional notation runs counter to the argument that this is not a function ... Charles Matthews 16:10, 22 December 2005 (UTC)

text: All functions that cannot be written in the form f(x) = P(x)/Q(x) are not rational.  If this isn't clear, maybe we need to say it explicitly.  Rick Norwood (talk) 14:50, 19 January 2010 (UTC)
thread_title: Irrational function

message: I've just created these three images for this article
http://en.wikipedia.org/wiki/Image:RationalDegree2byXedi.gif
http://en.wikipedia.org/wiki/Image:RationalDegree3byXedi.gif
http://en.wikipedia.org/wiki/Image:RationalDegree4byXedi.gif
Feel free to add them, as I do not know how to. 
Xedi 17:30, 30 August 2006 (UTC)
replies: text: Just added two of them, don't really know where to fit the third so didn't put it in. Xedi 18:08, 30 August 2006 (UTC)
thread_title:  New Images 

message: Just moved the paragraph beginning "These objects are first encountered in school algebra" to this section where it more properly belongs.  I am also removing the reference to an alternative construction for hyperreal numbers, a reflection of my own original research that does not belong in Wikipedia, Alan R. Fisher 01:01, 5 July 2007 (UTC)
thread_title:  Application 

message: The examples section states that the limit of a certain function as x goes to infinity is... another function. Instead of limit, it should say asymptote, I guess. Also, there was something about the "negation" of the imaginary unit. I took the liberty of changing "negation" to "negative".  —Preceding unsigned comment added by 24.232.19.210 (talk) 12:39, 21 August 2008 (UTC)
thread_title:  Examples 

message: This article doesn't address rational functions as defined in algebraic geometry, as elements of the function field of a variety... anyone care to aa  —Preceding unsigned comment added by 99.231.110.182 (talk) 01:05, 15 November 2009 (UTC)
replies: text: I've added a brief paragraph, based on the Springer reference. Charles Matthews (talk) 09:43, 15 November 2009 (UTC)

text: Rational functions are not morphisms to the projective line, since the numerator and the denominator can vanish simultaneously.  —Preceding unsigned comment added by 79.119.109.101 (talk) 16:38, 21 June 2010 (UTC)
thread_title:  Algebraic geometry 

message: The recent edits have clarified the distinction between rational function, rational fraction, and rational expression. This is very welcome, but I'd prefer the lead sentence to define rational function rather than rational fraction:
:In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
Note that "rational fraction" is not written in bold here since rational fraction does not redirect to this article. Moreover, I'm not sure whether "rational expression" should redirect to this article. Wouldn't algebraic expression be a more straightforward target in analogy with rational fraction redirecting to algebraic fraction? Isheden (talk) 21:24, 1 June 2013 (UTC)
replies: text: I can accept these modifications. My only concern is that the reader that arrive to any of these pages would be provided with definitions that are accurately correct. D.Lazard (talk) 21:42, 1 June 2013 (UTC)
thread_title:  Lead 

message: A section is needed on ordering and total orders, since I believe that, for example, the Levi-Civita field is a totally ordered subfield of the rational functions, but I'm not entirely clear on the details. Clearly, the power series F^G can be totally ordered whenever F is a field, and G is an abelian group, and the coefficients of the power series are totally ordered. That is, when the series \sum_g a_g X^g has the property that the set of non-zero coefficients \{a_g\} can be totally ordered; one can then impose a lexicographic order on such series (that is, X behaves as if it were infinitessimal).  However, how to extend this to a rational series is not obvious: am I supposed to "divide things out", to get an ordinary series, and then order things?? Is there some other ordering?
Also, the lead to the article surreal number suggests that rational functions can be totally ordered; clicking through to here provides no such discussion.67.198.37.16 (talk) 17:29, 5 July 2016 (UTC)
thread_title:  total order 

message: I believe there's a mistake in the first paragraph: a rational function can be a fractional of polynomials defined over rings and not only fields.  — Preceding unsigned comment added by 79.179.6.85 (talk) 19:32, 8 August 2016 (UTC)
replies: text: No, there is no mistake. Probably some authors generalize the definition for coefficients in a ring, but this is too marginal to be mentioned in the lead. In fact, if the ring of coefficients is an integral domain R, then the field of fractions of the polynomials over R (see the new second paragraph of the lead) is the field of the rational fractions over the field of fractions of R. So, in this case, there is no need for a definition of rational functions over R. For other rings of coefficients, there is no definition, which is widely accepted in the literature. D.Lazard (talk) 08:10, 9 August 2016 (UTC)
thread_title:  Ring 

message: User:D.Lazard you may think that this term has a more common meaning (and I doubted myself at first because I got it from a control systems source, not a maths source) but the first page of gbooks results agree with my definition, and many of those are books on some field of mathematics.  So it is for you to provide a source. SpinningSpark 21:11, 24 December 2016 (UTC)
thread_title:  Proper rational function 

message: The use of biquadratic function in the network theory sense may have first been used by mathematician Ronald M. Foster who did some of the early work in the fied in the 1920s.  See this 1963 paper for instance. SpinningSpark 23:07, 9 April 2020 (UTC)
thread_title:  Biquadratic function