On Sep 19, 3:03 pm, TianWei <[email protected]> wrote: > On Sep 19, 9:44 am, Nils Bruin <[email protected]> wrote: > > > > > > > On Sep 18, 6:43 pm, kcrisman <[email protected]> wrote: > > > > Actually, the subject of your email now makes a little more sense. > > > But I don't think that one can define an inverse function quite this > > > easily! That would indeed be *very* obscure notation! I don't know > > > if we can define a symbolic inverse of this kind yet, or whether that > > > would even be easy - much less to differentiate it. Anyone? > > > Finding an expression for the derivative of an inverse is part of most > > first calculus courses: > > > Suppose that f : R -> R is a differentiable function and that y=f(x). > > Suppose that g : R -> R is an inverse to f, i.e., x=g(y). > > Find an expression for g'(y) in terms of f'(x). [HINT: use the chain > > rule on f(g(y) or g(f(x))] > > > One usually continues with stating the inverse function theorem to > > conclude that if this computation doesn't rule out the existence of a > > differentiable inverse, then the inverse exists locally, an expression > > for which you can now find by integration [so, probably rather hard to > > do in general on a symbolic level] > > I might be misunderstanding this whole thread, but I think kcrisman is > looking for a generic way to express the inverse of a symbolic > function, perhaps similarly to the way Mathematica's "InverseFunction" > works: > > http://reference.wolfram.com/mathematica/ref/InverseFunction.html > > I don't know what sort of features are available in Sage or any of its > standard packages that could provide this sort of functionality.
Well, the original poster's reply was pretty concise, so I'm not even sure whether I understood the point of the thread :) But hopefully I did. It seemed that this is what the poster wanted. - kcrisman -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
