Lazy evaluation of derivatives of an unknown function
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) print(g) D[0, 1](f)(x, y) h = D[0, 1](f)(x, y) print(h) 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.