Axiom stellt dem Anwender eine Programmiersprache zur Verfügung, mit der
Elementary Programming
which comprises essentially the definition of functions.
Advanced Programming
which includes the specification of algebraic entities. An algebraic entity is remotely similar to an abstract datatype. Axiom provides a lot of predefined algebraic entities. The more frequently used algebraic entities are Integer, Fraction, AlgebraicNumber, UnivariatePolynomial, Monoid, Ring, Field.
Advanced Programming requires at least a basic understanding of contemporary algebra.