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.

PariTwine is a glue library between the system for computer algebra and number theory PARI/GP and a number of other mathematics libraries, currently GMP, GNU MPFR, GNU MPC, FLINT and CMH.

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). Single-precision version.

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.

PyNormaliz provides an interface to Normaliz via libNormaliz. It offers the complete functionality of Normaliz, and can be used interactively from Python.

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.

FLINT is a C library for number theory. It supports arithmetic with numbers, polynomials, power series and matrices over many base rings, including multiprecision integers and rationals, integers modulo n, p-adic numbers, finite fields (prime and non-prime order) and real and complex numbers (via the Arb extension library).

Operations that can be performed include conversions, arithmetic, GCDs, factoring, solving linear systems, and evaluating special functions. In addition, FLINT provides various low-level routines for fast arithmetic.

NTL is a 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.

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. This package also includes parform, a version of FORM parallelized using OpenMPI.

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.

The CM software implements the construction of ring class fields of imaginary quadratic number fields and of elliptic curves with complex multiplication via floating point approximations, and the elliptic curve primality proving algorithm (ECPP). It consists of libraries that can be called from within a C program and of executable command line applications.

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.

Gappa is a tool intended to help verifying and formally proving properties on numerical programs dealing with floating-point or fixed-point arithmetic. It has been used to write robust floating-point filters for CGAL and it is used to certify elementary functions in CRlibm. While Gappa is intended to be used directly, it can also act as a backend prover for the Why3 software verification platform or as an automatic tactic for the Coq proof assistant.

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).

This package provides a simple Python interface to the Singular computer algebra system.

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.

fpylll is a Python wrapper for fplll.

This package provides Python bindings for the Littlewood-Richardson Calculator.

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.

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

Kiss FFT attempts to be a reasonably efficient, moderately useful FFT that can use fixed or floating data types and can easily be incorporated into a C program.

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.

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.

GAP is a system for computational discrete algebra, with particular emphasis on computational group theory. It provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects.