expand(), was: derivatives of matrix functions

I wrote:
> > Hmm, well, I have to say I found it quite surprising that
> > sum and integrate, for example, are not automatically 
> > declared linear.
 
--- Stavros Macrakis <stavros.macrakis@verizon.net> wrote:
> But what if (a+b) is integrable as a sum, but a and b are not
> integrable separately, e.g. 1/LOG(x)-1/LOG(x)^2?  You really
> don't want linearity applied!

If I entered "'integrate(1/log(x)-1/log(x)^2,x);expand(%);"
then I asked for linearity to be applied, and I should get it.

I agree that Maxima should not immediately turn 'integrate(a+b)
into 'integrate(a)+'integrate(b). But expand(%) should be 
taken as sufficient evidence of intent to do just that.

> > What about having a global linearity flag? E.g., 
> > DECLARE_LINEAR_ALL_USUAL_SUSPECTS or something.
> 
> You can put together a batch file to define all your 
> favorite settings, [...]

Yes, I could do that -- now. It wouldn't help me while I'm
figuring out (over a period of weeks) how to make Maxima
do what I want. 

As a general goal, Maxima should try to do the "right
thing" out of the box. Yes, that is vague and ill-defined.
I hope people are interested in defining it and making 
it happen.

[...]
> There is more than one definition of "simplest".  It depends
> on what you want to do with the expression, [...]
> Do you want f((a+b)/c) (linear f) to automatically become
> f(a/c)+f(b/c)? The answer is surely "sometimes".

Sometimes, sure. How can Maxima tell if "this time"
it's supposed to try hard to expand an expression?
I propose that if I execute "expand(expr)", that is 
enough evidence that I really want expansion, and it 
should go ahead and apply whatever it knows.
 
At present, expand(expr) might or might not actually
expand something. I can't believe that this is how 
people expect an algebra system to work.

> [...] Perhaps there should be a generic Expand that 
> knows about all possible kinds of expansion.  But to 
> control its application, it should only operate on the
> top level of an expression. [...]

That is an interesting idea: if I want to expand some 
complex expression, I'll apply expand() repeatedly.
That seems like a useful operation.

best,
Robert Dodier

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