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.
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