Editing Axiom (computer algebra system) (section)

== 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 specialized interaction mode for [[Emacs]], as well as a plugin for the [[TeXmacs]] editor.

<gallery>
Image:AxiomHyperDoc.png|HyperDoc displaying the available operations for a domain
Image:AxiomGraphics.png|Axiom displaying a surface
Image:Axiomfirefox.jpg|Axiom Firefox Browser Interface
Image:Heatequation.jpg|Axiom simplifying a heat equation
Image:Matrixinmatrix.jpg|Axiom matrix manipulation
Image:RischIntegration.jpg|Axiom computing a Risch integral
</gallery>

Axiom has an implementation of the [[Risch algorithm]] for elementary integration, which was done by Manuel Bronstein and Barry Trager. While this implementation can find most elementary antiderivatives and whether they exist, it does have some non-implemented branches, and raises an error when such cases are encountered during integration.<ref>{{Cite web |last=Bronstein |first=Manuel |date=September 5, 2003 |title=Manuel Bronstein on Axiom's Integration Capabilities |url=https://groups.google.com/g/sci.math.symbolic/c/YXlaU8WA2JI/m/1w1MxrSpm6IJ |access-date=2023-02-10 |website=groups.google.com}}</ref><ref>{{Cite web |date=Oct 15, 2020 |title=integration - Does there exist a complete implementation of the Risch algorithm? |url=https://mathoverflow.net/questions/374089/does-there-exist-a-complete-implementation-of-the-risch-algorithm |access-date=2023-02-10 |website=MathOverflow |language=en}}</ref>