Fwd: [Maxima-users] How does impdiff work?

Thanks for your reply!

On Sat, Aug 04, 2007 at 10:24:39AM -0600, Robert Dodier wrote:
> Oliver, I've taken the liberty of forwarding your message to
> maxima at math.utexas.edu, the primary Maxima mailing list.
>

alright.
 
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I just subscribed.
 
> About impdiff, I don't see how it is supposed to work.
> There is an example at the end of share/contrib/impdiff.mac
> 
> /* the following example will fill the array f with derivatives
> array(f,2,3,function)
> f[0,0]:x^2+y^3-z^4=0
> implicit_derivative(f,[x,y],[2,3],z) */
> 
> but when I try that (after loading impdiff and makeOrders) I get an error.

perhaps some of part of maxima has changed since the implementation of that package?

> Maybe someone can help out here.
>

In general it seems to me that the maxima documentation has some
space for further improvements (;-)); for example the maxima-book, I would
guess it would take only a few more weeks for somebody knowledgeable
with it to complete it. 

So well, will compute the derivatives myself.

Thanks again.

Oliver


> Sorry I can't be more helpful,
> Robert Dodier
> 
> 
> ---------- Forwarded message ----------
> From: Oliver Kullmann <O.Kullmann at swansea.ac.uk>
> Date: Aug 3, 2007 11:45 AM
> Subject: [Maxima-users] How does impdiff work?
> To: maxima-users at lists.sourceforge.net
> 
> 
> Hello,
> 
> I would like to use the package impdiff,
> but documentation only says
> 
> -------------
> 53.1 Definitions for impdiff
> Function: implicit_derivative (f,indvarlist,orderlist,depvar)
> This subroutine computes implicit derivatives of multivariable
> functions. f is an array function, the indexes are the derivative
> degree in the indvarlist order; indvarlist is the independent variable
> list; orderlist is the order desired; and depvar is the dependent
> variable.
> To use this function write first load("impdiff").
> --------------
> 
> which I don't understand: A simple example would likely explain it (and could
> be added to the documentation; perhaps even two ...).
> 
> What does "order" refer to? Which "indexes" (apparently they are not
> arguments)??
> Why "array function"??? (What has efficiency of computation by memoisation to do
> with computing derivatives of implicitly defined functions?)
> 
> For example I try
> 
> (%i3) implicit_derivative(x+y^2,[x],[1,2],[y]);
> Second argument to `fillarray' must be an array or list:
> makeOrders([x], [1, 2])
> #0: implicit_derivative(f=y^2+x,indvarlist=[x],orderlist=[1,2],depvar=[y])(impdiff.mac
> line 36)
>  -- an error.  To debug this try debugmode(true);
> 
> but (as seems usual) the error message doesn't tell much (since
> "fillarray" is apparently
> not connected to "makeOrders") ?
> 
> Perhaps
> 
> load("makeOrders")$
> 
> is needed (shouldn't the package do that?). Now I get:
> 
> (%i15) implicit_derivative(x+y^2,[x],[1],[y]);
> Argument to `first' is empty.
> #0: implicit_derivative(f=y^2+x,indvarlist=[x],orderlist=[1],depvar=[y])(impdiff.mac
> line 47)
>  -- an error.  To debug this try debugmode(true);
> 
> But what is "first"?
> 
> Yet I never managed to get something out of the debugmode: Always the context is
> missing (when I write a function f(x), and check the argument, then in
> case argument
> x=5 is not allowed, I wouldn't return "5 is bad" (as maxima apparently
> does), but
> would say "The function f, used for ..., doesn't want input 5,
> *because of* ...";
> this is especially important for nested uses).
> 
> 
> 
> Thanks in any case.
> 
> Oliver
> 
> P.S. I use Maxima 5.12, from the Sage system (2.7.2); could this cause problems?
> 
> 
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