Lazy evaluation of derivatives of an unknown function

asked 2013-06-10 05:27:40 -0500

nosneros gravatar image


I am using Sage to check some solutions to partial differential equations. I am wondering if a have an unknown function f, can I somehow form the PDE in terms of its derivatives and then substitute in the assumed solution and evaluate the derivatives after the fact?

Here is what I tried so far:

var('x y')
f = function('f', x, y)
g = derivative(f, x, y) 


D[0, 1](f)(x, y)
h = D[0, 1](f)(x, y)

Traceback (click to the left of this block for traceback)
TypeError: 'sage.symbolic.expression.Expression' object has no
attribute '__getitem__'

I figured out that D[0, 1] represents the derivatives with respect to the ith indepent variable of the function (is this a Maxima expression?), but I'm not sure then how to use these types of expressions when I finally want to substitute in the known form of f. I.e., since the output of the expression for g is in terms of D[], and when I try to reuse that expression as h, I get an error (since D is actually some other type of object). Any help would be appreciated. Let me know if my question is not clear.

Many thanks!

edit retag flag offensive close merge delete


Could you provide a specific example? Why not just plug in the putative solutions to original DE to check them?

rickhg12hs gravatar imagerickhg12hs ( 2013-06-13 20:21:31 -0500 )edit

That is what I'm doing for now, but I was thinking it would be convenient to be able to construct the system of pdes with an arbitrary unknown function and then substitute in the trial solutions to check them. I will play with it a bit more and see if I can come up with a better example use case. Thanks!

nosneros gravatar imagenosneros ( 2013-06-14 10:45:42 -0500 )edit