ExprTk is a C++ headers only library for mathematical expression parsing and evaluation.

Lis is a parallel software library for solving discretized linear equations and eigenvalue problems that arise in the numerical solution of partial differential equations using iterative methods.

This package provides a computer algebra module for Lie groups. Documentation is available on http://www-math.univ-poitiers.fr/~maavl/pdf/LiE-manual.pdf.

4ti2 implements algorithms for solving algebraic, geometric and combinatorial problems on linear spaces. Among others, it solves systems of linear equations, computes extreme rays of polyhedral cones, solves integer programming problems and computes Markov bases for statistics.

More than 1500 numerical integration schemes for line segments, circles, disks, triangles, quadrilaterals, spheres, balls, tetrahedra, hexahedra, wedges, pyramids, n-spheres, n-balls, n-cubes, n-simplices, and the 1D/2D/3D/nD spaces with weight functions exp(-r) and exp(-r2) for fast integration of real-, complex-, and vector-valued functions.

Boolector is a SMT solver for the theories of fixed-size bit-vectors, arrays and uninterpreted functions.

HDF-EOS5 is a software library built on HDF5 to support the construction of data structures used in NASA's Earth Observing System (Grid, Point and Swath).

KLU is a method for computing the LU factorization of sparse for real and complex matrices.

LibPoly is a C library for manipulating polynomials to support symbolic reasoning engines that need to reason about polynomial constraints.

This package provides a C++ interface to the NetCDF library for scientific data storage.

Deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. The main aim of deal.II is to enable rapid development of modern finite element codes, using among other aspects adaptive meshes and a wide array of tools often used in finite element programs.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods.

This is the iterative solver template library which provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

CryptoMiniSat is an incremental SAT solver with both command line and library (C++, C, Python) interfaces. The command-line interface takes a CNF as an input in the DIMACS format with the extension of XOR clauses. The library interfaces mimic this and also allow incremental solving, including assumptions.

MUMPS (MUltifrontal Massively Parallel sparse direct Solver) solves a sparse system of linear equations A x = b using Gaussian elimination.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD).

Bitwise is a multi base interactive calculator supporting dynamic base conversion and bit manipulation. It's a handy tool for low level hackers, kernel developers and device drivers developers.

Some of the features include:

• Interactive ncurses interface.

• Command line calculator supporting all bitwise operations.

• Individual bit manipulator.

• Bitwise operations such as NOT, OR, AND, XOR, and shifts.

Cbc (Coin-or branch and cut) is a mixed integer linear programming solver written in C++. It can be used as a library or as a standalone executable.

libensemble is a complete toolkit for dynamic ensembles of calculations. It connects deciders to experiments or simulations.

GNU Octave is a high-level interpreted language that is specialized for numerical computations. It can be used for both linear and non-linear applications and it provides great support for visualizing results. Work may be performed both at the interactive command-line as well as via script files.

Armadillo is a C++ linear algebra library, aiming towards a good balance between speed and ease of use. It is useful for algorithm development directly in C++, or quick conversion of research code into production environments. It can be used for machine learning, pattern recognition, signal processing, bioinformatics, statistics, econometrics, etc. The library provides efficient classes for vectors, matrices and cubes, as well as 150+ associated functions (e.g., contiguous and non-contiguous submatrix views).

mCRL2 (micro Common Representation Language 2) is a formal specification language for describing concurrent discrete event systems. Its toolset supports analysis and automatic verification, linearisation, simulation, state-space exploration and generation, and tools to optimise and analyse specifications. Also, state spaces can be manipulated, visualised and analysed.

SPEX is a set of routines for sparse exact linear algebra. It contains the SPEX Left LU library for computing a sparse exact left-looking LU factorization for solving unsymmetric sparse linear systems.

GNU XaoS is a graphical program that generates fractal patterns and allows you to zoom in and out of them infinitely in a fluid, continuous manner. It also includes tutorials that help to explain how fractals are built. It can generate many different fractal types such as the Mandelbrot set.

A pure Ruby AsciiMath parsing and conversion library. AsciiMath is an easy-to-write markup language for mathematics.