Axiom (computer algebra)

Axiom is an open-source computer algebra system for symbolic computation, algebraic manipulation, and mathematical programming. Its strongly typed language represents mathematical structures explicitly and supports interactive computation.

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Axiom type system: Axiom’s type system uses categories, domains, and packages to organize mathematical objects and operations. It determines which operations are valid for each mathematical structure.
Domain (Axiom): A domain in Axiom is a concrete type that implements operations for a mathematical structure. Domains provide the values and executable operations used in Axiom programs.
Scratchpad: Scratchpad was an interactive symbolic mathematics system developed at IBM Research beginning in the 1960s. Axiom developed from this earlier system and inherited its broad mathematical ambitions.
Computer algebra: Computer algebra uses algorithms to manipulate mathematical expressions exactly or in symbolic form. Axiom applies these methods across a broad range of mathematical domains.
SageMath: SageMath is an open-source mathematics software system that integrates many specialized libraries through a common interface. Both are open-source, but SageMath emphasizes integrating external systems while Axiom centers its own typed algebraic framework.
Axiom interpreter: Axiom’s interactive environment parses and evaluates expressions, displays results, and supports mathematical programming. It is the main interface for running computations and exploring the language.
Category (Axiom): A category in Axiom is an interface specifying operations and properties shared by domains. Categories let Axiom state algebraic requirements independently of particular representations.
IBM Research: IBM Research is the industrial research organization that developed Scratchpad, Axiom’s predecessor. The system originated as an IBM project before its release as Axiom.
Polynomial: A polynomial is a finite sum of variables raised to nonnegative integer powers with coefficients. Polynomial arithmetic is a basic symbolic task supported by Axiom’s algebraic domains.
Maple: Maple is a commercial computer algebra system for symbolic computation, visualization, and mathematical programming. Maple offers a commercial alternative with a different language and product model.