Thanks for the news, William. I will hold off on this chain rule business till the new symbolics arrive.
Alex On Apr 24, 3:43 pm, William Stein <[email protected]> wrote: > On Thu, Apr 23, 2009 at 7:18 PM, Alex Raichev <[email protected]> wrote: > > > Hmm, implementing the chain rule is trickier than i thought. My > > straightforward plan of attack was to write a function that > > differentiates a symbolic expression as usual but when it comes to a > > composition f o g, it uses the chain rule and returns the appropriate > > entry of the matrix (Df o g)Dg. Problems: > > > (a) How do you split apart a symbolic expression to scan for > > compositions? > > (b) How do you construct Df so that you can compose it with g? > > > Both thwart me and my white belt Sage-fu. > > > Any helpful suggestions for (a), (b), or the general project? > > > Alex > > Picking apart expressions will change significantly soon in Sage, when > we switch over to using Pynac for basic symbolic manipulation. The > plan is to do this switch by May 15. > > -- William > > > > > > > On Apr 23, 1:43 pm, Alex Raichev <[email protected]> wrote: > >> Never mind. I'll just right a short recursive function. It's easy > >> enough. > > >> Alex > > >> On Apr 23, 11:10 am, Alex Raichev <[email protected]> wrote: > > >> > Hi all: > > >> > Do any of you know how to get Sage to use the chain rule and expand > >> > the derivative of a composition involving one or two callable symbolic > >> > functions? Here's an example with one callable symbolic function. > > >> > ---------------------------------------------------------------------- > >> > | Sage Version 3.4, Release Date: 2009-03-11 | > >> > | Type notebook() for the GUI, and license() for information. | > >> > ---------------------------------------------------------------------- > >> > sage: var('x,y,t') > >> > (x, y, t) > >> > sage: f= function('f',x,y) > >> > sage: g= exp(I*t) > >> > sage: diff(f(g,g^2),t).expand() > >> > diff(f(e^(I*t), e^(2*I*t)), t, 1) > > >> > ------------------------------------------------------------------------ > > >> > The reason i ask is that i have to take higher-order derivatives of a > >> > composition f o g of two callable symbolic multivariate functions. I > >> > want the expanded form so that i can evaluate at a certain point c > >> > and solve a linear system to get the derivatives of f at g(c). (I > >> > know the values of the derivatives f o g and g at c.) I could write a > >> > Sage function to expand the derivatives of f o g using Faà di Bruno's > >> > formula, but before i do so, i was wondering if there's an easier > >> > way. > > >> > Alex > > -- > William Stein > Associate Professor of Mathematics > University of Washingtonhttp://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
