The introduction of zero into the decimal system in the 13th century was the most significant achievement in the development of a number system, in which calculation with large numbers became feasible. Without the notion of zero, the descriptive and prescriptive modeling processes in commerce, astronomy, physics, chemistry, and industry would have been unthinkable.

GiNaC is a C++ library. It is designed to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation- intense numeric applications, graphical interfaces, etc.) under one roof.

Axiom is a general purpose Computer Algebra system. It is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.

Giac/Xcas is a free computer algebra system for Windows, Mac OS X and Linux/Unix. It has a compatibility mode for maple, mupad and the TI89. Xcas is an interface to perform computer algebra, geometry (2-d and 3-d), and spreadsheet. Giac is a free (GPL) C++ library, it does all the computations, it may be used inside other C++ programs.