Re: [Axiom-math] About rewrited expressions for power, log, exp and so.

[Martin Rubey]

Francois Maltey <address@hidden> writes:

> Hello,
> 
> I try to understand how axiom is sure in Expression domain.
> and what suppositions axiom does.
> 
> It seems that axiom makes a lot of fuzzy simplifications.

yes.

> But then how can I test if standard exemples of axiom continue to be right
> with a new elemntry.spad ?

Well, I'm still hoping for a unit testing package. But in fact, I wouldn't mind
if some "standard example" stops working, but in exchange a dozen others start
working.

The "simplifier" in EXPR is nearly non-existent, and those bits that do exist
are quite broken.

>     sqrt (u^2)  ---> sqrt (u^2) I agree  sqrt ((-1)^2) = 1
> but (u^a)^(1/a) ---> u          not coherent with a=2

quite right. In fact, I believe I corrected this behaviour in "hackroot"
once. I didn't realize that there were other places with that nonsense, too.

> What rules might apply axiom for expressions ?  Is there a reason that theses
> rules aren't usual mathematic rules ?  What is the axiom policy ? What is
> your advice ?

My advice is: look at MuPaD and see how things are done there. I think they got
it right.

Apart from that, implement many good computable domains.


Great that you are working on this stuff.


Martin