Sollya is a computer program whose purpose is to provide an environment for safe floating-point code development. It is particularly targeted to the automated implementation of mathematical floating-point libraries (libm). Amongst other features, it offers a certified infinity norm, an automatic polynomial implementer, and a fast Remez algorithm.

The Littlewood-Richardson Calculator (lrcalc) is a program designed to compute Littlewood-Richardson coefficients. It computes single Littlewood-Richardson coefficients, products of Schur functions, or skew Schur functions. In addition it computes products in the small quantum cohomology ring of a Grassmann variety. The software package also includes a program that performs fast computation of the more general multiplicative structure constants of Schubert polynomials.

M4RI is a library for fast arithmetic with dense matrices over finite fields of characteristic 2. So it extends the functionality of M4RI from F_2 to F_2^e.

lmfit is a C library for Levenberg-Marquardt least-squares minimization and curve fitting. It is mature code, based on decades-old algorithms from the FORTRAN library MINPACK.

Clac is a command line, stack-based calculator with postfix notation that displays the stack contents at all times. As you type, the stack changes are reflected immediately.

JLargeArrays is a Java library of one-dimensional arrays that can store up to 263 elements.

JTransforms is a multithreaded FFT library written in pure Java. Currently, four types of transforms are available: Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Discrete Sine Transform (DST) and Discrete Hartley Transform (DHT).

Mpfrcx is a library for the arithmetic of univariate polynomials over arbitrary precision real (mpfr) or complex (mpc) numbers, without control on the rounding. For the time being, only the few functions needed to implement the floating point approach to complex multiplication are implemented. On the other hand, these comprise asymptotically fast multiplication routines such as Toom–Cook and the FFT.

Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. It provides an elegant API based on "expression templates". It is versatile: it supports all matrix sizes, all standard numeric types, various matrix decompositions and geometry features, and more.

msolve is a C library implementing computer algebra algorithms for solving polynomial systems (with rational coefficients or coefficients in a prime field).

Currently, with msolve, you can basically solve multivariate polynomial systems. This encompasses:

• the computation of Groebner bases

• real root isolation of the solutions to polynomial systems

• the computation of the dimension and the degree of the solution set.

PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorisations, algebraic number theory, elliptic curves...), but it 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. PARI is also available as a C library to allow for faster computations.

M4RI is a library for fast arithmetic with dense matrices over F2. The name M4RI comes from the first implemented algorithm: The Method of the Four Russians inversion algorithm published by Gregory Bard. This algorithm in turn is named after the Method of the Four Russians multiplication algorithm.

The eclib package includes mwrank (for 2-descent on elliptic curves over Q) and modular symbol code; it has been written by John Cremona to compute his elliptic curve database.

FORM is a symbolic manipulation system. It reads symbolic expressions from files and executes symbolic/algebraic transformations upon them. The answers are returned in a textual mathematical representation. The size of the considered expressions in FORM is only limited by the available disk space and not by the available RAM.

GiNaC is a C++ library for symbolic computation. Contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities.

The la4j library is a Java library that provides Linear Algebra primitives (matrices and vectors) and algorithms. The key features of the la4j library are:

• No dependencies and tiny size

• Fluent object-oriented/functional API

• Sparse (CRS, CCS) and dense (1D/2D arrays) matrices

• Linear systems solving (Gaussian, Jacobi, Zeidel, Square Root, Sweep and other)

• Matrices decomposition (Eigenvalues/Eigenvectors, SVD, QR, LU, Cholesky and other)

• MatrixMarket/CSV IO formats support for matrices and vectors

xtensor is a C++ library meant for numerical analysis with multi-dimensional array expressions.

xtensor provides:

• an extensible expression system enabling lazy broadcasting.

• an API following the idioms of the C++ standard library.

• tools to manipulate array expressions and build upon xtensor.

FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data---i.e. the discrete cosine/ sine transforms or DCT/DST). With OpenMPI parallelism support.

This package provides functions for 1D and 2D Discrete Cosine Transform (DCT), Discrete Sine Transform (DST) and Discrete Hartley Transform (DHT).

libsemigroups is a C++14 library containing implementations of several algorithms for computing finite, and finitely presented, semigroups and monoids.

Spectra stands for Sparse Eigenvalue Computation Toolkit as a Redesigned ARPACK. It is a C++ library for large scale eigenvalue problems, built on top of Eigen. It is implemented as a header-only C++ library and can be easily embedded in C++ projects that require calculating eigenvalues of large matrices.

Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. It provides an elegant API based on "expression templates". It is versatile: it supports all matrix sizes, all standard numeric types, various matrix decompositions and geometry features, and more.

FFLAS-FFPACK is a C++ template library for basic linear algebra operations over a finite field. FFLAS (Finite Field Linear Algebra Subprograms) provides the implementation of a subset of routines of the numerical BLAS; it also supports sparse matrix-vector products. FFPACK (Finite Field Linear Algebra Package) is inspired by the LAPACK library to provide functionalities of higher level, using the kernel of a BLAS. Additionally, it provides routines specific to exact linear algebra, such as the row echelon form.

Kiss FFT is a mixed-radix Fast Fourier Transform based up on the principle, 'Keep It Simple, Stupid.'