RE: Comparison between Mathematica and other symbolic systems

• To: mathgroup at smc.vnet.net
• Subject: [mg92527] RE: [mg92378] Comparison between Mathematica and other symbolic systems
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Thu, 2 Oct 2008 18:48:54 -0400 (EDT)
• Organization: Goteborg University
• References: <200809301133.HAA21932@smc.vnet.net>

```Hi,
I do not know how this is example is interesting or how it is done in other
systems, but once, 14 years back, it convinced me that I should use
Mathematica for a specific problem. I wanted to sort the eigenvectors of a
real matrix according to decreasing size of the real part of the
eigenvalues. For complex eigenvalue pairs I wanted the eigenvalue with
positive imaginary part sorted first. I just wanted to specify the sorting
rule, and did not feel for writing the sorting algorithm from scratch. This
is how I solved it in Mathematica

Transpose[
Sort[Transpose[Eigensystem[RandomReal[{-1, 1}, {6, 6}]]],

Re[#2[[1]]] < Re[#1[[1]]] ||
Re[#2[[1]]] == Re[#1[[1]]] && Im[#2[[1]]] < Im[#1[[1]]] &]]

I think this also is a good example of the use of functional programming,
and it helped me to get in to it.
In Mathematica we are thus able to sort any kind of "objects" with any kind
of sorting criteria, thanks to the generality of the language.
Best regards

Ingolf Dahl
Sweden

-----Original Message-----
From: Paolo Bientinesi [mailto:pauldj at aices.rwth-aachen.de]
Sent: 30 September 2008 13:34
To: mathgroup at smc.vnet.net
Subject: [mg92527] [mg92378] Comparison between Mathematica and other symbolic systems

Hi everybody,

As part of a presentation to students, I will have to support the claim that
"Mathematica is better than other systems when it comes to symbolic
computations". Some experts in other systems will be giving a 15 min
presentation to convince the audience of the contrary, and then it will be
my turn.

At this point I am quite clueless on how to make my point across.
First of all, I am not at all familiar with any other system's symbolic
toolboxes, so I don't know what are the weaknesses. Also, I am not sure what
kind of demo could really make an impression on graduate students and
colleagues.

Has any of you any experience on this? Ideas? Suggestions?

Thank you!
--
Prof. Paolo Bientinesi, Ph.D.
RWTH Aachen University, AICES
pauldj at aices.rwth-aachen.de
pauldj at alumni.cs.utexas.edu

```

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