William Stein wrote:
> Cool!!  Do they explain why Sage gets a relatively low rating, e.g.
> Scilab gets 9 but Sage 6?   Is it because of the relative lack of our
> focus on numerics?

Not quite, although it must be noted that the primary focus of Will
Tribbey, the reviewer, was numerical computing. As far as I understand,
the tests had nothing to do with symbolic capabilities of the five
targeted systems. One surprise is that only Sage is praised for its
symbolic capability as well as not inventing its own programming
language. Page 35 concludes:

<quote>
Sage and the Euler Math Toolbox were only included as a matter of
diversity and choice, since one person's numerical nirvana is usually
another's sixth circle of hell. We were therefore pleasantly surprised
to find Sage a worthy contender not only for numerical computing but for
doing symbolic computing too. It stood out as the only platform to make
direct use of an existing programming language, Python. Since you can
directly create mathematics documents on the web with Sage, don't be
surprised if maths blogging becomes the next cool thing on the internet.
And remember, you read it here first...
</quote>

The evaluation of the Euler Math Toolbox (EMT), Matlab, Octave, Sage and
Scilab were conducted with the following factors in mind:

(1) ease of installation

(2) user interface

(3) documentation

(4) community support

(5) available toolboxes

Matlab was held to be the "gold standard" (an expression from the
review) against which the other four systems were measured.

A recurring theme throughout tests on the above five systems was the
issue of algorithmic performance, as measured "by computing the singular
value decomposition (SVD) and fast Fourier transform (FFT) of a 500x500
real-valued matrix 100 times and calculating the average and standard
deviation of those 100 trials" (page 30). And on page 31, we have the
following performance evaluation:

<quote>
Performance is one area where Matlab had difficulty maintaining a
commanding lead. For the SVD test --- an important matrix decomposition
in many statistical and numerical algorithms --- Matlab performance was
slightly more than 20% better than Scilab and Octave. The surprise was
that the Numpy algorithm used from within Sage was on average over 250%
faster than Matlab. It's not included in this Roundup, but this
performance difference indicates that the Numpy library for Python
deserves a closer look when performance matters. Matlab comes out the
winner in the fast Fourier transform.
</quote>

In the end, Scilab comes out with a score of 9/10. Matlab has the same
score: "[Matlab's] score was taken down because of its cost" (p.31).
Here's a list of reasons why, as a contender against Matlab, Scilab is
ahead of EMT, Octave and Sage:

(1) the large number of toolboxes

(2) visual system modelling (the Metanet toolbox) and simulation (the
Scicos toolbox)

(3) the number of built-in functions

(4) a Matlab IDE-like command window for developing and debugging functions


-- 
Regards
Minh Van Nguyen

Web: http://nguyenminh2.googlepages.com
Blog: http://mvngu.wordpress.com

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