Talk:Derivation (differential algebra)

message: I'm not sure, but shouldn't this article be merged into Derivative? Jon Harald Søby \ no na 07:05, 4 November 2005 (UTC)
replies: text: No - it is too abstract and the concept is important enough in its own right. Charles Matthews 09:58, 4 November 2005 (UTC)

text: Jessica writes On the other hand, I think derivation should be concatenated with differential algebra.  I'm going to make the change, although I am open to discussion with anyone who wants to change it back. Shellgirl 15:19, 5 April 2007 (UTC)
thread_title: Untitled

message: Should fox derivative be linked?198.189.194.129 (talk) 19:09, 10 April 2012 (UTC)
replies: text: No. The Fox derivative has some vague superficial similarities, but it is really a different thing. 67.198.37.16 (talk) 20:36, 24 May 2024 (UTC)
thread_title: [[Fox derivative]]

message: In many differential geometry texts -- such as Sharpe's Differential Geometry, Gallot's Riemannian Geometry, as well as in "Natural Operations in Differential Geometry", which is referenced in this article, and in the article "Tangent Space", under "See also" -- derivations on the Algebra C_p^∞(M) of smooth germs at p are defined not as a an endomorphism, but as a function onto the underlying field, D:C_p^∞(M) -> R, satisfying the slightly modified Leibniz Rule
D(fg) = D(f)g(p) + f(p)D(g)
Admittedly, in the last text cited above, "Natural Operations in Differential Geometry", "Derivation of an algebra" is later defined as in this article. Nonetheless, I find that the concept of "derivation at a point" is widespread enough for its complete omission in this article to be quite confusing (it certainly confused me).  — Preceding unsigned comment added by Jslam (talk • contribs) 15:55, 16 April 2013 (UTC)
replies: text: I added a single sentence to the lede, to try to say this in a very informal way, but perhaps I was too simplistic. I can't find any WP page to link to, that would provide a clear demo of derivations "at a point". Yes, this article could benefit from a simpler, less formal lede. 67.198.37.16 (talk) 20:55, 24 May 2024 (UTC)
replies: text: I'll revert this added sentence. Fisrtly, it is too vague for being useful for anybody. Also it is confusing, as the standard derivative is defined for the derivation at a point, and the sentence suggests that the derivation at a point is a concept specific to manifolds. Also, there is a confusion between "manifold" (used in the edit) and "germ" (used above). Finally, I am not sure whether Jslam's complaint deserves to be implemented. Indeed, if their assertion is correct, it must appear in Germ (mathematics). This assertion (that the derivation of a germ is a number) is doubtful, since it does not allow to define higher order derivatives and Taylor series of a germs. In any case, since constant functions are germs, the above Jslam's definition is an endomorphism of the algebra of germs. D.Lazard (talk) 08:24, 25 May 2024 (UTC)
thread_title:  Derivations at a point 

message: I'm familiar with the concept, though not, it appears, enough with the English language. In other people, this may be vice versa. => It would be helpful information if the article said whether the verb for the thing, as in "derivXXX x^3 and you get 3x^2", is derive or derivate.--2001:A61:260D:6E01:412F:2D0F:6B21:83F7 (talk) 00:54, 31 January 2018 (UTC)
replies: text: There's no verb for this. Linguists have a joke that you can always "verbize your nouns", but for the noun "derivative", this is not generally done. 67.198.37.16 (talk) 21:07, 24 May 2024 (UTC)
thread_title:  seemingly stupid question