Re: RE: Comparison between Mathematica and other

*To*: mathgroup at smc.vnet.net*Subject*: [mg92537] Re: [mg92527] RE: [mg92378] Comparison between Mathematica and other*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 3 Oct 2008 06:41:39 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200809301133.HAA21932@smc.vnet.net> <200810022248.SAA28999@smc.vnet.net>*Reply-to*: murray at math.umass.edu

I'd exercise caution before presenting such an example to people whom you're trying to convince to turn to Mathematica. all the vertical strokes, including those in the brackets, make this look like a jumble of incomprehensible symbols. The effect could be precisely the opposite of what you intend. Ingolf Dahl wrote: > 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. -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**RE: Comparison between Mathematica and other symbolic systems***From:*"Ingolf Dahl" <ingolf.dahl@telia.com>