Talk:Closed-form expression
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In Fluid dynamics, the closure form of the governing equations is called for the boundary layer approximation or the parabolic approximation.
I'd thought that closed-form solutions were possible for quintic equations, although there is no general formula for them? Could someone more knowledgeable edit this article?
- You can of course find closed form solutions to quintics such as x5 − 1 = 0 (the five roots of one). There is even a general process to solve quintics by introducing a new radical (The Bring radical). --njh 12:12, 12 July 2006 (UTC)
[edit] This article title is not so good
Why the word "solution"?? Some cases of closed-form expressions in mathematics are in some sense "solutions", and others are not. This seems to me like one of those cases where someone picks a word like "equation" or "solution" as a sort of catch-all term to be used when they don't know the right nomenclature. This happens frequently in math, when, for example, lay persons promiscuously use the word "equation" to denote anything at all that is written in mathematical notation.
Since closed form seems to be a disambiguation page, I propose that this article be moved to closed-form expression. Michael Hardy 00:05, 26 November 2005 (UTC)
- I agree with your basic point. I have a general problem with the notion of "closed form", as I think it's a bit difficult to define "closed form" in the abstract, or to differentiate "expressed in closed form" from "expressed analytically". For example, one can often solve (in)equalities by using inverse functions, but whether or not the resulting expression would be said to be "in closed form" depends on what the basic inventory of functions and expressions is. I'm not sure if e.g. Lambert's W function would be considered part of that inventory, but it's obviously very convenient for expressing solutions of certain equations in a form that can easily be evaluated by numerical software. I have the feeling that large aspects of this notion of "closed form" are very much a remnant of a past time when only a small number of expressions could be conveniently evaluated by hand or looked up in a table. --MarkSweep (call me collect) 01:27, 26 November 2005 (UTC)
I am inclined to suspect that the concept does admit some precise definition, but I am skeptical of the claims even of some fairly sophisticated mathematicians to have done that definitively. But the fact that it is not yet fully precise doesn't mean there should be no article on it. Michael Hardy 22:33, 26 November 2005 (UTC)
- So, let's move it, shall we? Regarding the content, here are some external links, which may or may not shed further light on the meaning of "closed form":
- Also note that these articles all talk about solutions (though I agree with you now that that's too limited). --MarkSweep (call me collect) 10:58, 29 November 2005 (UTC)
