Ask for the syntax of representing operators in Common-Lisp

Thank you for your reply.  I decided to go with the simplification
rules as you suggested.  I was hoping for some sort of pure operator
calculus because then, at every stage of the operation, the program
doing the analysis would be able to use all the identities and
knowledge it had about the function.  However, for me it's more
important that the underlying software be regularly maintained and
documented (thank you everybody!), so I'm sticking with regular
maxima.

I must add that I had never thought to make the derivative terms into
parameters in the renamed function.  I don't know how I missed that
one.  It's so simple once you see it.  Thank you again.

On 7/12/06, Richard Fateman <fateman at cs.berkeley.edu> wrote:
> Here's what you can do..
>
>  matchdeclare([a,b,n],true);
>  tellsimp('diff(f(a),a,n), g(a,n));
>
>
> Thus for your particular examples,
> tellsimp('diff(MyExp(a),a,n), MyExp(a));
>
> tellsimp('diff(MyAtan(a,b),a,1,b,1),  (a^2-b^2)/(a^2+b^2)^2)
>
> There have been several proposals, some implemented, for introducing a "pure
> operator" calculus in Macsyma. I think one was written up by Jeff Golden,
> maybe 20 years ago.
> Generally there are choices to be made about semantics that kind of depend
> on the circumstances, so there is no universal resolution of all that you
> might want to do. If you can't do what you want with simple patterns, you
> may have to change your representation more substantially and do a more
> functional style of manipulation.
>
> Oh, there is also the deftaylor facility, which doesn't really do what you
> say you want to do, but might in fact be useful, since it allows you to
> define derivatives as used by taylor expansions.
>
> RJF
>
>
>
> -----Original Message-----
> From: maxima-admin at math.utexas.edu [mailto:maxima-admin at math.utexas.edu] On
> Behalf Of James Hart
> Sent: Wednesday, July 12, 2006 3:53 PM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Ask for the syntax of representing operators in
> Common-Lisp
>
> Hello.
>
> I've discovered an extremely useful feature of Mathematica and I was
> wondering if it exists in some form in Maxima as well.  I am writing a
> GUI that can use either Maxima or Mathematica as a back-end, and this
> feature of Mathematica has saved me a lot of trouble and potential
> bugs, and I was wondering if something similar existed in Maxima.  It
> could avoid some tricky problems if it did.
>
> The feature I'm talking about is the ability Mathematica has to define
> functions which are "the nth derivative of f with respect to parameter
> 1 in f, the mth derivative of f with respect to parameter 2 in f",
> etc.  For instance, Derivative[1][Sin] is Cos, and Derivative[n][Exp]
> is Exp, and Derivative[1,1][ArcTan] is (#1^2-#2^2)/(#1^2+#2^2)^2 &.
> This works even for functions which have not been explicitely defined
> and which have no form.
>
> Is there similar notation for such functions in maxima?  So far I've
> been obfuscating the function names so maxima can swallow them, and
> restoring them on input, but this is less than ideal.
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
>