Re: [Axiom-developer] Re: AMS Notices: Open Source Mathematical Software

[M. Edward (Ed) Borasky]

root wrote:
> The NSF, INRIA, and others cover it.
> These are the same people who won't fund Axiom because "it competes
> with commercial software". Which shows that they don't understand
> that Axiom is NOT trying to compete; and that funding competition
> to commercial software implies funding BOTH sides of the effort.

Ah, but given the difficulty of writing said software with any licensing 
scheme, whether it be closed-source commercial, "academic free but 
industrial users pay", GPL, BSD, MIT, etc., why would a non-profit 
organization like the NSF want to get dragged into licensing disputes, 
questions about tax exemptions, intellectual property battles, and other 
things that a society full of attorneys "features"? The world is 
littered with the corpses of organizations that sued other organizations 
bigger than they were. I don't know about INRIA, but I really doubt the 
NSF could withstand a lawsuit from Wolfram or Maplesoft.

> In the long term (think next century) does it benefit computational
> mathematics if the fundamental algorithms are "black box"?

Mathematics has a long history of independent discoveries by researchers 
working on different problems. Think of Gauss and Legendre, for example, 
and least squares. In other words, fundamental algorithms will get 
re-invented. The FFT is another example -- radio engineers were doing 
24-point DFTs using essentially the FFT algorithm long before Cooley and 
Tukey, and both Runge and Lanczos published equivalents.

> Suppose someone creates a
> closed, commercial, really fast Groebner basis algorithm, does not
> publish the details, and then the code dies. It can happen. Macsyma
> had some of the best algorithms and they are lost.

1. What do you think the real chances are of a "really fast Groebner 
basis algorithm" are? I'm by no means an expert, but I thought the 
computational complexity odds were heavily stacked against one.

2. What did Macsyma have that Vaxima and Maxima didn't/don't?
> Way back in history there are stories of people who found algorithms
> (can't remember any names now) but they didn't publish them. In order
> to prove they had found one you sent them your problem and they sent
> you a solution. How far would mathematics have developed if this 
> practice still existed today?

I think I've made the case that they would get re-invented.