HDF5 is a suite that makes possible the management of extremely large and complex data collections.

LibPoly is a C library for manipulating polynomials to support symbolic reasoning engines that need to reason about polynomial constraints.

Qalculate! is a multi-purpose calculator; this package contains its command line interface qalc and library libqalculate. Features include:

• arbitrary precision and interval arithmetic

• currency conversion

• physical constants

• plotting via gnuplot

• symbolic calculations (including integrals and equations)

• uncertainty propagation

• unit calculations and conversions

• user-defined functions

Aris is a program for performing logical proofs. It supports propositional and predicate logic, as well as Boolean algebra and arithmetical logic. In addition to its predefined inference and equivalence rules, Aris also supports references to older proofs. Its use of standard logical symbols and its natural deduction interface make it easy to use for beginners.

Bitwuzla is a SMT solver for the theories of fixed-size bit-vectors, floating-point arithmetic, arrays, uninterpreted functions and their combinations.

Metamath is a tiny formal language and that can express theorems in abstract mathematics, with an accompyaning metamath executable that verifies databases of these proofs. There is a public database, set.mm, implementing first-order logic and Zermelo-Frenkel set theory with Choice, along with a large swath of associated, high-level theorems, e.g.: the fundamental theorem of arithmetic, the Cauchy-Schwarz inequality, Stirling's formula, etc. See the Metamath book.

Arcane is a development environment for parallel numerical calculation code. It supports the architectural aspects of a calculation code, such as data structures for meshing and parallelism, as well as more environment-related aspects such as dataset configuration.

SYMPOW is a mathematical program to compute special values of symmetric power elliptic curve L-functions; it can compute up to about 64 digits of precision.

HDF5 is a suite that makes possible the management of extremely large and complex data collections.

Giza is a lightweight scientific plotting library built on top of cairo that provides uniform output to multiple devices.

Gfan is a software package for computing Gröbner fans and tropical varieties.

The dune-functions module provides an abstraction layer for global finite element functions. Its two main concepts are functions implemented as callable objects, and bases of finite element spaces.

The ELPA library provides efficient and scalable direct eigensolvers for symmetric matrices.

Openspecfun provides AMOS and Faddeeva. AMOS (from Netlib) is a portable package for Bessel Functions of a Complex Argument and Nonnegative Order; it contains subroutines for computing Bessel functions and Airy functions. Faddeeva allows computing the various error functions of arbitrary complex arguments (Faddeeva function, error function, complementary error function, scaled complementary error function, imaginary error function, and Dawson function); given these, one can also easily compute Voigt functions, Fresnel integrals, and similar related functions as well.

HPCombi is a C++17 header-only library using the SSE and AVX instruction sets, and some equivalents, for very fast manipulation of combinatorial objects such as transformations, permutations, and boolean matrices of small size.

SLEPc is a software library for the solution of large sparse eigenproblems on parallel computers. It can be used for the solution of linear eigenvalue problems formulated in either standard or generalized form, as well as other related problems such as the singular value decomposition. The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations.

Matio is a library for reading and writing MAT files. It supports compressed MAT files, as well as newer (version 7.3) MAT files.

Elemental is a modern C++ library for distributed-memory dense and sparse-direct linear algebra, conic optimization, and lattice reduction.

MUMPS (MUltifrontal Massively Parallel sparse direct Solver) solves a sparse system of linear equations A x = b using Gaussian elimination.

Gosl is a set of tools for developing scientific simulations using the Go programing language. It provides numerical methods and solvers for differential equations but also present some functions for Fast Fourier Transforms, the generation of random numbers, probability distributions, and computational geometry.

Gosl includes the following Go packages:

• chk - to check numerical results and for unit testing

• fun - special functions, DFT, FFT, Bessel, elliptical integrals, orthogonal polynomials, interpolators

• gm - geometry algorithms and structures

• hb - pseudo hierarchical binary (hb) data file format

• io - input/output, including printing to the terminal and handling files

• la - linear algebra: vector, matrix, efficient sparse solvers, eigenvalues, decompositions

• num - fundamental numerical methods such as root solvers, non-linear solvers, numerical derivatives, and quadrature

• ode - solvers for ordinary differential equations

• opt - numerical optimization: Interior Point, Conjugate Gradients, Powell, Grad Descent

• pde - solvers for partial differential equations (FDM, Spectral, FEM)

• rnd - random numbers and probability distributions

• utl - to generate series (e.g., linspace) and other functions as in pylab/matlab/octave

The dSMFT package speeds up Fast Mersenne Twister generation by avoiding the expensive conversion of integer to double (floating point). dSFMT directly generates double precision floating point pseudorandom numbers which have the IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985) format. dSFMT is only available on the CPUs which use IEEE 754 format double precision floating point numbers.

SCOTCH is a set of programs and libraries which implement the static mapping and sparse matrix reordering algorithms developed within the SCOTCH project. Its purpose is to apply graph theory, with a divide and conquer approach, to scientific computing problems such as graph and mesh partitioning, static mapping, and sparse matrix ordering, in application domains ranging from structural mechanics to operating systems or bio-chemistry.

libflame is a portable library for dense matrix computations, providing much of the functionality present in LAPACK, developed by current and former members of the SHPC group in the Institute for Computational Engineering and Sciences at The University of Texas at Austin. libflame includes a compatibility layer, lapack2flame, which includes a complete LAPACK implementation.

GNU Octave is a high-level interpreted language that is specialized for numerical computations. It can be used for both linear and non-linear applications and it provides great support for visualizing results. Work may be performed both at the interactive command-line as well as via script files.