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

[Gabriel Dos Reis]

On Wed, 11 Jul 2007, C Y wrote:

| --- 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. 

In  the context of situation where O(n^3) algorithms are known?

| Both are important, but in my personal opinion correctness is more so. 

Yes, but when I say algorithm, there is the implied assumption that the
algorithm was answering the question, i.e. giving the answer.  So, 
correctness is not at issue.  We are talking about choising efficient answers
between correct answers.

| Of course, you want to use the best algorithms available, but not at
| the expense of adding risk of incorrect answers. 

Nobody is suggesting that the system should not give correct answer.
The issue is *efficiently* computing the answer.  Not just giving
the answer.  


-- Gaby