Re: [Reduce-algebra-developers] An inconsistency in computing derivatives?

[Francis W. <f.j...@qm...>]

> From: Rainer Schöpf [mailto:rai...@gm...]
> Sent: Thursday, September 08, 2011 9:21 PM
> To: Francis Wright
> Cc: red...@li...
> Subject: RE: [Reduce-algebra-developers] An inconsistency in computing
> derivatives?
> 
> Some more border cases in differentiation:
> 
> 1. This one has nothing to do with expanddf and the recent changes:
> 
> depend cos(y),x;
> 
> df(cos(y),x) => 0
> 
> because df(cos(y),x) simplifies to
> 
> -sin(y) * df(y,x)
> 
> and y doesn't depend on x.
> 
> This looks wrong to me.

Yes. But the only way that cos(y) can depend on x is if y depends on x, so I
think REDUCE should either regard "depend cos(y),x; " as an error or interpret
it to mean "depend y,x; ". But you can't do this for all functions, because an
arbitrary function f(y) could reasonably have some implicit dependence on other
variables. Off hand, the only way I can see to distinguish the cases would be to
flag known operators in some way.

> 2. With expand set to on:
> 
> depend r,x;
> df(f(r,cos(x)),x);
> 
> gives
> 
> df(f(r,cos(x)),r)*df(r,x) + df(f(r,cos(x)),cos(x))*df(cos(x),x)
> 
> 
> I believe it is correct, but possibly not what one expects.

Yes. I would suggest leaving this and waiting for users to complain if it's not
what they expect. (I presume that df(cos(x),x) actually simplifies.)

> BTW, I think there is an error in the procedure diffp, both in the original
one and
> the one in odesolve/odepatch.red: The else clause
> 
>            else if eqcar(cadr u, 'int) then
> 
> is not an alternative to the then clause
> 
>            if cadr u eq v then
> 
> (as the indentation suggests), but part of that then clause, ie there is a
> 
> <<
> ...
> >>
> 
> missing.

As far as odesolve/odepatch.red is concerned, I clearly missed this problem,
partly because I try not to reformat existing code that I'm modifying. So can
you change odesolve/odepatch.red as well, please, if you change the main code?

Thanks, Francis