
From:  M. Edward (Ed) Borasky 
Subject:  Re: [Axiomdeveloper] Re: AMS Notices: Open Source Mathematical Software 
Date:  Mon, 26 Nov 2007 20:06:35 0800 
Useragent:  Thunderbird 2.0.0.9 (X11/20071031) 
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 closedsource commercial, "academic free but industrial users pay", GPL, BSD, MIT, etc., why would a nonprofit 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 reinvented. The FFT is another example  radio engineers were doing 24point 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 sentyou 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 reinvented.
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