PARI/GP is a computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions.

Singular is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.

Its main computational objects are ideals, modules and matrices over a large number of baserings. These include

* polynomial rings over various ground fields and some rings (including the integers),
* localizations of the above,
* a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra),
* quotient rings of the above,
* tensor products of the above.

Singular's core algorithms handle

* Grobner resp. standard bases and free resolutions,
* polynomial factorization,
* resultants, characteristic sets, and numerical root finding.

A high performance parallel ray tracing system supporting MPI and multithreaded implementations.

Tachyon implements all of the basic geometric primitives such as triangles, planes, spheres, cylinders, etc. Some of the goals in developing Tachyon were to make it fast and for it to parallelize well. These are what set it apart from more full-featured programs like POV-Ray, Rayshade, and others. Tachyon supports enough features to be an excellent alternative to slower programs for demanding animation and scientific visualization tasks.