Editing Axiom (computer algebra system) (section)

== Design ==

In Axiom, each object has a type. Examples of types are mathematical structures (such as [[ring (mathematics)|rings]], [[field (mathematics)|fields]], [[polynomial]]s) as well as data structures from computer science (e.g., [[list (computing)|list]]s, [[tree (data structure)|tree]]s, [[hash tables]]).

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