Re: [Maxima-discuss] diff of a block generated by optimize

[Richard F. <fa...@gm...>]

there is an area of study called "automatic differentiation"  which
addresses techniques for
taking an algorithm for computing f(x) at some point x0 and creating an
algorithm for computing
df(x)  at a point x0.  Google finds many hits.  Oddly this is quite
different from differentiating
a symbolic expression.  It is more closely allied with expansion of a
function in a Taylor series.
Your use of gradef seems to be defining the function a(x)  as a solution to
a differential equation that looks, at first sight, as unpleasant.

I don't know if auto diff would be useful, or if a reformulation using
Taylor series might help.
Just 2 thoughts.
RJF



On Sat, Jul 30, 2022 at 3:32 PM Andrei Zorine <zoa...@gm...> wrote:

> Gentlemen,
> can DIFF function be taught to deal with a BLOCK generated by OPTIMIZE?
> Consider an example:
>
> depends(a,x);
> gradef(a,x,(a+x)/(a^2+a*x-1));
> diff( (x*a-a^2)/(a+x+1)^3,x);
> diff( (x*a-a^2)/(a+x+1)^3,x,2);
>
> Here the second call produces a lengthy expression. If we ask for 20th
> derivative instead, the answer will blow up memory.
> Instead, the first I'd like to have something like
> diff( optimize(diff((x*a-a^2)/(a+x+1)^3, x)), x)
> in an efficient and concise form.
> If I remember correctly, Maple can do this.
>
> Andrei Zorine
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