Singular is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry and singularity theory.

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.

IML is a C library implementing algorithms for computing exact solutions to dense systems of linear equations over the integers. Currently, IML provides the following functionality:

• Nonsingular rational system solving: compute the unique rational solution X to the system AX=B, where A and B are integer matrices, A nonsingular.

• Compute the right nullspace or kernel of an integer matrix.

• Certified linear system solving: compute a minimal denominator solution x to a system Ax=b, where b is an integer vector and A is an integer matrix with arbitrary shape and rank profile.

In addition, IML provides some low level routines for a variety of mod p matrix operations: computing the row-echelon form, determinant, rank profile, and inverse of a mod p matrix. These mod p routines are not general purpose; they require that p satisfy some preconditions based on the dimension of the input matrix (usually p should be prime and should be no more than about 20 bits long).

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.

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).

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

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.

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

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.

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.

bc is an arbitrary precision numeric processing language. It includes an interactive environment for evaluating mathematical statements. Its syntax is similar to that of C, so basic usage is familiar. It also includes "dc", a reverse-polish calculator.

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

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

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.

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.

Normaliz is a tool for computations in affine monoids, vector configurations, rational polyhedra and rational cones. Normaliz now computes rational and algebraic polyhedra, i.e., polyhedra defined over real algebraic extensions of QQ.

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).

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

This package provides a tool for manipulating old Android Boot Images. abootimg can work directly on block devices, or, the safest way, on a file image.

Androguard is a full Python tool to manipulate Android files. It is useful for reverse engineering, analysis of Android applications and more.

This package provides a tool to create Android Boot Images.

This package provides fastboot, a tool to upload file system images to Android devices.

While the Android client integrates with the system with regular update checks and notifications, this is a simple command line client that talks to connected devices via ADB.