Axiom (computer algebra system)

Axiom
Developer(s) independent group of people
Stable release November 2011
Operating system cross-platform
Type computer algebra system
License Modified BSD License
Website axiom-developer.org

Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed, mathematically (mostly) correct type hierarchy.

Contents

History

Axiom has been in development since 1971,[1] originally as Scratchpad by researchers at IBM under the direction of Richard Dimick Jenks.[2] Other key early developers were Barry Trager, Stephen Watt, James Davenport, Robert Sutor, and Scott Morrison.

In the 1990s it was sold to NAG and given its current name. In 2001 it was withdrawn from the market and re-released under the Modified BSD License. Since then, the project lead developer has been Tim Daly.

In 2007, Axiom was forked into two different open-source projects: OpenAxiom,[3] and FriCAS.[4]

Documentation

Axiom is a literate program. The source code is becoming available in a set of volumes which are available on the axiom-developer.org[5] website. These volumes contain the actual source code of the system.

The currently available documents are:

Videos

The Axiom project has a major focus on providing documentation. Recently the project announced the first in a series of instructional videos, which are also available on the axiom-developer.org[6] website. The first video[7] provides details on the Axiom information sources.[8]

Philosophy

The Axiom project focuses on the “30 Year Horizon”. The primary philosophy is that Axiom needs to develop several fundamental features in order to be useful to the next generation of computational mathematicians. Knuth's literate programming technique is used throughout the source code. Axiom plans to use proof technology to prove the correctness of the algorithms (such as Coq and ACL2).

Design

In Axiom, all objects have a type. Examples of types are mathematical structures (such as rings, fields, polynomials) as well as data structures from computer science (e.g., lists, trees, hash tables).

A function can take a type as argument, and its return value can also be a type. For example, Fraction is a function, that takes an IntegralDomain as argument, and returns the field of fractions of its argument. As another example, the ring of 4\times 4 matrices with rational entries would be constructed as SquareMatrix(4, Fraction Integer). Of course, when working in this domain, 1 is interpreted as the identity matrix and A^-1 would give the inverse of the matrix A, if it exists.

Several operations can have the same name, and the types of both the arguments and the result are used to determine which operation is applied (cf. function overloading).

Axiom comes with an extension language called SPAD. All the mathematical knowledge of Axiom is written in this language. The interpreter accepts roughly the same language. SPAD was further developed under the name A# and later Aldor. The latter can still be used as an alternative extension language. It is, however, distributed under a different license.

Features

Within the interpreter environment, Axiom uses type inference and a heuristic algorithm to make explicit type annotations mostly unnecessary.

It features 'HyperDoc', an interactive browser-like help system, and can display two and three dimensional graphics, also providing interactive features like rotation and lighting. It also has a specialised interaction mode for Emacs, as well as a plugin for the TeXmacs editor.

Axiom has an implementation of the Risch algorithm for elementary integration, which was done by Manuel Bronstein and Barry Trager.

See also

References

External links

Software forks: