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

From: William Stein
Subject: Re: [Axiom-developer] Re: AMS Notices: Open Source Mathematical Software
Date: Mon, 26 Nov 2007 20:53:37 -0800

On Nov 26, 2007 8:06 PM, M. Edward (Ed) Borasky <address@hidden> wrote:
> 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.

(1) The NSF does fund research that directly results in open source
mathematical software development.    They've funded Macaulay2,
they've funded me, and they've funded other scientists. NIH also
funds software development:

(2) Regarding NSF withstanding a lawsuit -- I don't know.
NSF is a very powerful and impressive foundation.  They have
a 6 billion dollar annual budget:
compared to Mathematica which probably has maybe $150
million per year in revenue.

(3) People at the NSF do think about issues such as
"licensing disputes, questions about tax exemptions, intellectual
property battles, and other things", and take them seriously.

> > 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.

I think has a point; though there are examples like yours, there are also
many interesting powerful algorithms that do exist only in closed proprietary
software, and it could be a long time until they are rediscovered and

> > 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.

Since "really fast" isn't well defined, I'll just give you a practical example
of exactly this.   For the last 5 years there have been exactly
two implementations of a "really fast Groebner basis algorithm", namely
F4 (and its variant F5).  One implementation is closed source and is
only available via purchasing Magma.  The other is closed source and
is only available via purchasing Maple.     The one in Magma took
Allan Steel (who is in my mind easily one of the top 5 mathematical
software coders in the world today) about 5 years to implement, even with
full access to all the papers that Faugere wrote on his algorithm.  The
one in Maple was implemented by Faugere, and is of course also closed
source.   There have been numerous (maybe a dozen?) attempts by
open source authors to implement a really usable F4, but nobody has
yet come close so far as I can tell.   (Ralf Phillip Weinmann is working
on a promising open source one right now, maybe...)

The F4 in Magma is really incredibly fast at many standard benchmark
problems.   See the timings here:


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