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.

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.