Maxima Computeralgebra System (CAS)

Maxima is one of the oldest computeralgebra systems (CAS), with its roots going back to the legendary LISP-based computeralgebra system Macsyma (see http://maxima.sourceforge.net/ ).

Computeralgebra systems, first and foremost of all are full-fledged programming languages – usually with the following properties:

Modularity
Recursion
List processing
Symbol processing
High precision arithmetic
Graphics support
Interactivity
Expandability

The following text is an elementary German language introduction to Maxima:

In the following Maxima worksheets elementary, mostly historically motivated algorithms are treated – usually in a straightforward, „natural“ way. Sometimes, for the sake of methodological comparison, different versions of an algorithm are given; e.g. (as in Euclids algorithm or in the Fibonacci number algorithm) a recursive and an iterative implementation or (as in the sieve of Eratosthenes) an implementation using arrays as opposed to lists. The worksheets originally were stored in the wxmx worksheet format and then exported to the pfd format for portability reasons. in some of the worksheets Maxima's timing-facilities are used for run-time comparison. For further support (in particular for the wxmx files) please contact ziegenbalg.edu@gmail.com

Some historical algorithms:

• Heron’s algorithm (The Babylonian-Sumerian root-algorithm)
• Euclid’s algorithm
• The Sieve of Eratosthenes
• The Sieve of Eratosthenes: programs in Maxima and Mathematica
• Archimedes‘ algorithm for approximating Pi
• The Egyptian multiplication algorithm
• Fibonacci numbers – case studies in recursion and iteration

More Maxima programs:

• Simulation des Disko-Problems mit Hilfe von Maxima
  (vgl. Problembeschreibung)
• Independent subsets of a finite set
• Maxima wxmx-file: independent subsets of a finite set
• A stochastic simulation: Waiting time for complete sets
• Cobweb diagrams / Cobweb Diagramme
• Wachstumsprozesse (Growth Processes)
• Kleine Studie zur Korrektheit der Arithmetik in Maxima