Python-flint is a Python extension module wrapping FLINT (Fast Library for Number Theory) and Arb (arbitrary-precision ball arithmetic). It supports integers, rationals, modular integers, real and complex ball arithmetic, polynomials and matrices over all these types and other mathematical functions.

LinBox is a C++ template library for exact linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields.

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.

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.

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.

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.

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

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.

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

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.

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.

The gf2x library provides arithmetic of polynomials over finite fields of characteristic 2. It implements the multiplication, squaring and greatest common divisor operations.

REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations but also provides a full programming language, with a syntax similar to other modern programming languages. REDUCE supports alternative user interfaces including Run-REDUCE, TeXmacs and GNU Emacs. This package provides the Codemist Standard Lisp (CSL) version of REDUCE. It uses the gnuplot program, if installed, to draw figures.

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.

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.

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.

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.

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.

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

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.

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.

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.

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).