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>
- Reply-to: <ingolf.dahl at telia.com>
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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