Re: [Axiom-developer] Axiom, FriCAS, forks and teeth

[C Y]

--- Gabriel Dos Reis <address@hidden> wrote:

> Multicore are no longer supercomputers myths you would find in
> highly financed National Labs.  They are the reality today.  

Sure.

> If you order a machine from Dell, the probability that you
> get a multicore is very high.  How do you we wisely and efficiently
> use that computational power?

As I said, that is an interesting and important question - just not my
primary area of interest.

> Clearly Waldek has an example where Axiom is making a dumb use of
> resource.  No matter how correct the answer
> is.  How would you react to computation of determinant of
> an nxn matrix with complexity O(n!)?

Better than I would to a complexity O(1) computation whose
implementation I couldn't trust.  Correctness first, then performance. 
Both are important, but in my personal opinion correctness is more so. 
Of course, you want to use the best algorithms available, but not at
the expense of adding risk of incorrect answers.  And right now, the
view seems to be that all existing CASs have risk of incorrect answers.
 
> Many things that were considered absolute truths or theorems a decade
> ago are no longer valid.  We have to retthink the algorithms we
> implement; we have to rethink the core system.

That's an interesting direction to go, and I hope it bears fruit, but
it is not my first concern.  I would rather have the computer spend a
few extra minutes using verified, trustable routines to check that my
answer to a problem being published in a paper is correct, although
obviously the BEST case is to be both fast and trustworthy.

Cheers,
CY


      
____________________________________________________________________________________
Fussy? Opinionated? Impossible to please? Perfect.  Join Yahoo!'s user panel 
and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7