Axiom Computer Algebra System

Registered 2006-04-24 by Bill Page

Axiom is a general purpose system for doing mathematics by computer. It is especially useful for mathematical research and for development of mathematical algorithms. Axiom has a strongly-typed high-level programming language for expressing abstract mathematical concepts. Over 1,000 mathematical domains and categories are collected in the Axiom Library.


Axiom has been in development since 1971. At that time, it was called Scratchpad. Scratchpad was a large, general purpose computer algebra system that was originally developed by IBM under the direction of Richard Jenks. The project started in 1971 and evolved slowly. Barry Trager was key to the technical direction of the project. Scratchpad developed over a 20 year stretch and was basically considered as a research platform for developing new ideas in computational mathematics. In the 1990s, as IBM's fortunes slid, the Scratchpad project was renamed to Axiom, sold to the Numerical Algorithms Group (NAG) in England and became a commercial system. As part of the Scratchpad project at IBM in Yorktown Tim Daly ( worked on all aspects of the system and eventually helped transfer the product to NAG. For a variety of reasons it never became a financial success and NAG withdrew it from the market in October, 2001.

Open Source

NAG agreed to release Axiom as free software, under the Modified BSD License. The basic motivation was that Axiom represents something different from other programs in a lot of ways. Primarily because of its foundation in mathematics the Axiom system will potentially be useful 30 years from now. In its current state it represents about 30 years and 300 man-years of research work. To strive to keep such a large collection of knowledge alive seems a worthwhile goal.

Development Emphasis

Efforts are underway to extend this software to:

    * develop a better user interface

    * make it useful as a teaching tool

    * develop an algebra server protocol

    * integrate additional mathematics

    * rebuild the algebra in a Literate Programming style

    * integrate logic programming

    * develop an Axiom Journal with refereed submissions.

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trunk series 

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Programming Languages:
Simplified BSD Licence

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