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. Then again, I might have gotten this all wrong. -- Tianwei -- 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
