The GLPK (GNU Linear Programming Kit) package is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems.
The gmp library is the GNU Multiple Precision Arithmetic Library. This is a set of routines for doing high accuracy calculations.
The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. It is free software under the GNU General Public License.
LAPACK is a Linear Algebra PACKage. It is used to compile many scientific and mathematical software packages.
Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
Maxima is a system for the manipulation of symbolic and numerical expressions.
MKL is a Math Kernel Library sold by Intel. It has standard math functions such as BLAS and LAPACK in an optimized, thread safe format.
Octave is a public domain clone of matlab. It is about 95% compatible with Matlab.