MPIR is an open source multiprecision integer library derived from version 4.2.1 of the GMP (GNU Multi Precision) project (which was licensed LGPL v2+).

MPIR is constructed by a developer and vendor friendly community of professional and amateur mathematicians, computer scientists and hobbyists.

muParser is an extensible high performance math parser library written in C++. It works by transforming a mathematical expression into bytecode and precalculating constant parts of the expression.

A C++ Library for Parsing Expressions with Strings, Complex Numbers, Vectors, Matrices and more.

programs for computing automorphism groups of graphs and digraphs

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.

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.