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 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.

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

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.