Walking Randomly

It’s been a great week for Open Source maths software this week with new releases of both Maxima and Scilab.

Maxima is a computer algebra system written in lisp that runs on most operating systems including Linux, Mac OS X and Windows.  The latest version, Maxima 5.20.1,  was released on Sunday 13th December and the full list of changes can be found here.  Highlights include improvements to the calculation of special functions, faster fourier transform routines and a general mechanism for functions to distribute over operators.

This last item is pretty cool since it allows you to map functions over lists in a similar manner to Mathematica.  For example, if you apply the sin function to a list in Maxima then you’ll now get a list containing the sines of each element of that list:

(%i1) sin([1,2,3]);
(%o1) [sin(1),sin(2),sin(3)]

Here are some examples of this new functionality for two-argument functions such as expintegral_e (taken from a post of Dieter Kaiser’s) include :

(%i2) expintegral_e([1,2,3],x);
(%o2) [expintegral_e(1,x),expintegral_e(2,x),expintegral_e(3,x)]

(%i3) expintegral_e(1,[x,y,z]);
(%o3) [expintegral_e(1,x),expintegral_e(1,y),expintegral_e(1,z)]

(%i4) expintegral_e([1,2,3],[x,y,z]);
(%o4) [[expintegral_e(1,x),expintegral_e(1,y),expintegral_e(1,z)],
       [expintegral_e(2,x),expintegral_e(2,y),expintegral_e(2,z)],
       [expintegral_e(3,x),expintegral_e(3,y),expintegral_e(3,z)]]

Head over to sourceforge to download Maxima for your operating system of choice. Now, onto Scilab….

Scilab is a fantastic open source numerical mathematics environment that always seems to come top of the list when people start discussing free MATLAB alternatives.  December 17th saw the release of Scilab 5.20 and the list of changes is epic (warning:pdf file).

The first new Scilab feature that caught my eye is the addition of a module called Xcos.  Xcos 1.0 is based on Scicos 4.3 which is a “graphical dynamical system modeler and simulator.”  Now I’ve not used any of this stuff before but as far as I can tell it could be considered as a free version of Simulink.  A bit of googling turned up a paper by M.G.J.M. Maassen, a student at the Eindoven University of Technology, who looked at the issue of migrating from Simulink to Scicos with respect to real time programs.  Written in 2006, this paper is slightly out of date but is a great start for anyone who is considering moving away from Simulink.

Along with other free mathematical software applications such as Octave, Sage, Python/Numpy and freemat, these new releases demonstrate that the world of free, open source mathematical applications has never looked better.