On Sep 28, 2009, at 5:37 PM, Nils Bruin wrote:
> Would you have suggestions for printing derivatives using partials? I
> think the main problem here is that one needs to "name" the formal
> variables, whereas mathematical notation otherwise identifies
> arguments by position.
>
> For instance, suppose we have a function f(x,y) for which we want to
> evaluate the derivative with respect to x at the point (x,y)=(x0,y0).
> Using partials, we'd need
> $$\left . \frac{\partial f}{\partial x} \right |_{(x,y)=(x0,y0)}$$
> As you see, one has to "introduce" local variables x and y and bind
> them.
Considering that the function f(x,y) is a function of x and y, I'd
be completely happy with that.
> In this particular case, there would be little confusion if we were to
> write instead $\frac{\partial f}{\partial x}(x0,y0)$, but this would
> already get much less clear if we would want to evaluate at $(x,y)=
> (y0,x0)$.
I prefer the notation using the bar to indicate the evaluation point
that way the variables are explicit, not implicit. Plus, it's how I
(and basically all the people I work with) do it.
>
> What we could do, but this still looks funny, is be explicit about the
> variable names and write
> $$\left . \frac{\partial f(x_0,x_1,x_2}{\partial x_0} \right |_
> {(x_0,x_1,x_2)=(a,b,c)}$$
> That is at least an unambiguous way of writing $(D[0]f)(a,b,c)$.
>
I like this. It isn't compact, but it's clear. The D notation loses
information in an attempt to be compact. Plus, using D isn't
interoperable
with Maxima (or most other systems).
> Perhaps with some heuristic rules, one could cut down on some of these
> elements if the formula is sufficiently simple.
> Do other programs produce easier to read derivatives while
> guaranteeing that the representation they produce is unambiguous?
The D notation is used in Maple as an option, but almost always allows
conversion to the standard notation.
Cheers,
Tim.
---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://www.linkedin.com/in/timlahey
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