Computer Algebra Systems

These have become an interesting subject area in their own right. The possibility to perform complex mathematics at the algebraic level on a desktop PC can hold a certain fascination. Of course, the setting up of such a system to solve a problem can take just as long as pen and paper. Often a judgment on the most efficient method to use based on experience is taken. At a basic level they are very good at finding a simple integral, better than ploughing through a three inch book full of integral tables.

Macsyma - not available at present, but my favourite and the one I trust - written in a variant of LISP

- a free version called Maxima is available, but I cannot vouch for it.

Derive - a good "algebraic calculator" - now owned by Texas Instruments - discontinued 2006

Maple - up to date system written in C++ and well supported, great graphics

Mathematica - similar to Maple but more features and wider support with better graphics

Reduce - an old favourite I used on a mainframe years ago, it is still available for a PC

Axiom - this system is interesting, I want to know if it is any good - discontinued 2001 - passed to open-source consortium

MuPAD and MathCAD - not as heavy weight as Maple or Mathematica - never seen them used

Numerical Systems

MATLAB - simply the best, does advanced number crunching and graphics very efficiently and allows access to the vast number of routines included. Only low level functions are precompiled.

There are still situations where I use Basic, Fortran and C, but rarely. To get decent graphics you also need an additional graphics library.

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