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.
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| Sage Version 3.4, Release Date: 2009-03-11 |
| Type notebook() for the GUI, and license() for information. |
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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)
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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
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