On Nov 24, 2009, at 12:10 PM, rjf wrote:

> David Kirby's comments on competition stuck in my mind as I was doing
> some errands this morning, and his repeating them suggested to me that
> maybe I should comment again.
>
> For a start, the healthy competition he refers to between Intel and
> AMD. Perhaps he has not noticed the substantial amount of money spent
> on lawyers and suits?  Intel settles a lawsuit for 1.25 BILLION
> dollars.  That's not an indication of health.

No one is claiming that there aren't (gross) inefficiencies in the  
system, but I am one of many who subscribe to the belief that most of  
the time completion provides better results than the lack thereof.

My goal is not to put the Ma's out of business, but I strongly feel  
having an open alternative is important.

> And it is
> also hard to give much credit to a system that advertises itself as a
> new viable alternative to Maple and Mathematica when the fact is that
> it often just calls Maxima, already a viable alternative to Maple and
> Mathematica, a reality that it attempts to conceal (see NSF proposal
> draft).  Until something goes wrong, and then it blames Maxima.(see
> Sage-support).

The fact that you're chosen field doesn't require any math beyond what  
Maxima can do greatly colors your perspective. Sage, and even Maple  
and Mathematica are about much more than symbolic manipulation.

The fact that Maxima comes up so often in sage-support is both due to  
the popularity of doing calculus (nearly every college freshman out  
there) and the fact that doesn't work well (sometimes because of the  
wrapper, sometimes because of deficiencies in the underlying system).

> I think that any company that chooses to use Sage instead of buying
> Mathematica would be unlikely to do so because Sage is open-source and
> can therefore be "verified".  While Sage might be free, the expense of
> that company in hiring a person to check the verification would be
> substantial, and probably pointless.  Proving that a program matches a
> specification or some other indication of correctness is not something
> done casually or cheaply.  Verifying a program's result (whether from
> Mathematica, Maple, or Maxima)
> is typically done by quite other means than examining the code that
> produced it.

I've looked at code, and not just Sage code, to decide if I want to  
trust the results. Sometimes I don't. Of course, trust start's  
somewhere (I trust my FPU...) but at least I have a choice. Most  
companies don't care about proofs, but researchers, especially in  
mathematics, do.

Openness is more than about verification (formal or not), it's about  
being able to understand, extend, adapt, and fix as well. We're  
targeting researchers, teachers, and students, not just commercial  
companies.

> I can recall no instance of a published program proof
> in symbolic computation for any non-trivial algorithm.  Repeated
> proofs of the Extended Euclidean Algorithm (GCD) don't make the grade.

Again, you're limiting yourself to thinking about symbolic computation.

> Someone who has the choice between Mathematica and Sage may very well
> think:
>
> Oh Mathematica or Matlab or ... costs $X and I just load it on my
> machine(s).
> Oh Sage costs $0, and I have to designate a technician to compile and
> install it on my machines at expense $Y.  Is Y>X ?

I am offering my services to download a tarball and type "make" on  
anyone's system for half the cost of a Mathematica or Matlab license-- 
your money back if it doesn't install correctly. X/2 < X (for positive  
values of X, which is a safe assumption here). That wouldn't just be  
altruistic, it'd be a pretty good hourly rate :).

Look at Maxima and Macsyma, which one is alive and well now?

> more likely a decision will be made on the basis of persons in the
> company asking for one or the other, based on the availability of
> library of application code, or programs written by colleagues in that
> particular language (mathematica, python, matlab).
> Thus someone doing signal processing calculations will likely choose
> the system with the best signal processing library.

I would hope so.

> Is that Sage?

For signal processing, probably not yet (though SciPy, included in  
Sage, is widely used), but I hope some day it will be. But for other  
areas (e.g. computations related to elliptic curves) I would say yes.

- Robert

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