Re: [Reduce-algebra-developers] problem with depend that seems erroneous

[Rainer S. <rai...@gm...>]

On Wed, 15 May 2013 at 08:10 +0930, Tony Roberts wrote:

 > the following code causes me grief with derivatives and dependencies,
 > and looks like an error that needs fixing.
 > operator x; operator pp;
 > % for j:=1:2 do depend pp,x(j); % why is this not needed?
 > let df(pp,x(~j))=>pp(j);
 > thisIsOK:=df(pp^2,x(1));
 > shouldBeZero:=df(pp^2,t);
 > end;
 > 
 > On my Reduce it generates
 > thisisok := 2*pp(1)*pp
 > shouldbezero := 2*df(pp,t)*pp
 > and the second is certainly not what I want, and causes me grief.
 > Further, why is the "depend pp,x(j)" statement not needed?

When you add a rule for differentiation, a suitable dependency is added 
automatically, ie.

 let df(pp,x) => something;

effectively adds

 depend pp,x;

The exception is the case of differentiation w.r.t. a free variable, eg.,

 let df(pp,~y) => x(y);

since a dependency on a free variable doesn't make sense.

What happens here is that your rule defines differentation w.r.t. an expression 
containing a free variable. Unfortunately, this general case is not checked, and 
you end up with a dependency of pp on x(~j).

Now, when you enter 

 df(pp,t);

Reduce checks whether x depends on t; if that happens to be the case, the 
correct answer would either be

 df(pp,t);

(if the switch expanddf is off), or

 df(pp,x)*df(x,t);

if the switch expanddf is on.

In your case it checks whether x(~j) depends on t. A free variable may be 
replaced by an arbitrary expression, and therefore x(~j) is treated as being 
dependent on anything.

I'll test a correction in the next few days.

  Rainer