I have a simple function as written below and I want to compute the partial derivative of it against an element u[k] in a vector variable u. I intentionally left k unspecified because it is not a set number and I don't really want to put it there to generate a bunch of specific output. But when I run it in Maple 12, it gives me the wrong result (sum((x-a[k])*(y-b[k]),k) instead of the correct result (x-a[k])*(y-b[k]).

restart;
with(PDEtools):
m:=(x,y,u)->sum(u[k]*(x-a[k])*(y-b[k]),k);
diff(m(x,y,u),u[k]);
 

Hi all,

I have a function defined as a sum:

with(PDEtools): mfx:=(x,y,ufx)->sum(ufx[k]*(x-x[k])*(y-y[k]),k);

I want to declare mfx(x,y,ufx) so that it would appear as mfx in subsequent displays. However, when I tried

declare(mfx(x,y,ufx));

Maple tells me that "Error, (in PDEtools:-declare) cannot declare objects as sum(ufx[k]*(x-x[k])*(y-y[k]), k)".

How can I solve this problem?

Thanks.

I am a newbie and this is the second post I am making. The previous follow-ups I received was very helpful and I appreciate it.

I am interested in using maple to derive derivatives of implicit functions. I have a function f(x,y) which I want to compute the gradients of it agaist r and theta. x and y are both functions of r and theta. I don't have a explicit form of f(x,y). My goal is to use this kind of operation to compute complicated higher order gradients of implicit functions so that I don't need to derive them by hand.

What is the best way to do this?