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.

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 CMake build offers the file FFTW3LibraryDepends.cmake required by some dependent packages, absent in the gnu build version.

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 CMH software computes Igusa (genus 2) class polynomials, which parameterize the CM points in the moduli space of 2-dimensional abelian varieties, i.e. Jacobians of hyperelliptic curves. It can also be used to compute theta constants at arbitrary precision.

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.

Giac/Xcas is a computer algebra system. It has a compatibility mode for maple, mupad and the TI89. It is available as a standalone program (graphic or text interfaces) or as a C++ library.

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.

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

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.

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.

fplll contains implementations of several lattice algorithms. The implementation relies on floating-point orthogonalization, and LLL is central to the code, hence the name.

It includes implementations of floating-point LLL reduction algorithms, offering different speed/guarantees ratios. It contains a wrapper choosing the estimated best sequence of variants in order to provide a guaranteed output as fast as possible. In the case of the wrapper, the succession of variants is oblivious to the user.

It includes an implementation of the BKZ reduction algorithm, including the BKZ-2.0 improvements (extreme enumeration pruning, pre-processing of blocks, early termination). Additionally, Slide reduction and self dual BKZ are supported.

It also includes a floating-point implementation of the Kannan-Fincke-Pohst algorithm that finds a shortest non-zero lattice vector. For the same task, the GaussSieve algorithm is also available in fplll. Finally, it contains a variant of the enumeration algorithm that computes a lattice vector closest to a given vector belonging to the real span of the lattice.

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).

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.

GP2C, the GP to C compiler, translates GP scripts to PARI programs.

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.

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

GMP-ECM factors integers using the elliptic curve method (ECM) as well as the P-1 and P+1 algorithms. It provides a library and a stand-alone binary.

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.

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.

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.

This package provides a Python wrapper for Fourier Local Correlation Tracking.

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.

This library provides a Python wrapper to SymEngine, a fast C++ symbolic manipulation library.