NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields.

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.

The Parma Polyhedra Library (PPL) is a library for the manipulation of (not necessarily closed) convex polyhedra and other numerical abstractions. The applications of convex polyhedra include program analysis, optimized compilation, integer and combinatorial optimization and statistical data-editing. The Parma Polyhedra Library comes with several user friendly interfaces, is fully dynamic (available virtual memory is the only limitation to the dimension of anything), written in accordance to all the applicable standards, exception-safe, rather efficient, thoroughly documented, and free software. This package provides all what is necessary to run applications using the PPL through its C and C++ interfaces.

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.