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

Oliver, I've taken the liberty of forwarding your message to
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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.
Maybe someone can help out here.

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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