Who wouldn’t want to type tables in LaTeX without worrying about how text is treated in each column. Something as simple as:
bla blaaaa & bleee bleeeeh & babble babble \\
Well, it can be almost as simple!
This is quite nice. Despite some gloomy forecasts for LaTeX (along the lines “new kids just want power point and word”, ref. below), wikipedia has been using it as the basis for its mathematical language. Now, along comes the powerfull google corporation. In google docs, formulas are also inserted in LaTeX (the documentation is not too abundant on this, btw). Just make a new document, then insert, then formula.
Typical problem in computational geometry: given a set of points, what is its shape? This may often be intuitive for a human being, but try to define this concept mathematically, then implement it numerically.
One of the proposals is called the “α shape”, and is closely related to the Delaunay triangulation. More details below.
See also alpha shapes, for a recent application of this concept to molecular simulation. Check out the movie too!
I have been following and using this project for some years now, on and off. In my opinion, a very remarkable cooperative effort of several research centers, coordinated at INRIA Sophia Antipolis. They provide very robust implementations of algorithms on computational geometry: Delaunay triangulations, Voronoi diagrams ski sums, meshes, alpha shapes, convex hulls, all that. Warning: very abstract C++ is needed (I actually learned C++ because of these libraries).
A brief post, on two notable mathematical databases I have recently come across:
The amount of work the maintenance of these pages must demand (not to talk about the actual writing!)
A brief survey of the ones I have tried, with the student version price (as of mid 2008).
- Computer algebra systems (see wikipedia comparison)
- derive. Very simple, very easy. Unfortunately, it seems discontinued.
- Mathematica. Incredibly powerful. But: crazy syntax, annoying graphic interface (it used to be impossible to rotate 3D objects, I don’t know if this has been fixed). Owned by Wolfram Research, founded by visionary Dr. Wolfram (see his humble book A New Kind of Science). 145$
- maple. Really powerful, nicer syntax than Mathematica, much better graphics (rotating 3D figures since the early 90s at least). Owned by a spinoff from a university (Waterloo, Canada, hence the name). 99$
- mupad. Used to be free, not any longer. I never had the time to play with it much. 88€
- sage. I have not tried, but it’s very high on my to-try list. Open source, powerful (it seems), and a project based at the University of Washington, where I spent three years of my life (my wife and very good friends were actually at the Department of Mathematics, where the project is hosted, but I never met anyone working on this).
- Numerical analysis (see wikipedia comparison)
- matlab. Very powerful, very popular. Quite simple syntax. Specially useful for linear algebra. 99$
- octave. A matlab clone: an open source program whose syntax mimics matlab’s (but with different underlying code, hence no copyright infringements). Of course it lacks many advanced matlab features, but, hey, it’s free. 0$