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.

Kiwi is an efficient C++ implementation of the Cassowary constraint solving algorithm. Kiwi has been designed from the ground up to be lightweight and fast. Kiwi ranges from 10x to 500x faster than the original Cassowary solver with typical use cases gaining a 40x improvement. Memory savings are consistently > 5x.

This DUNE module provides interface and implementation for shape functions defined on the DUNE reference elements. In addition to the shape function, interpolation operators and special keys are provided which can be used to assemble global function spaces on finite-element grids.

This package provides an interface and implementation for shape functions defined on the DUNE reference elements. In addition to the shape function, interpolation operators and special keys are provided which can be used to assemble global function spaces on finite-element grids.

Calc is an arbitrary precision arithmetic system that uses a C-like language. It can be used as a calculator, an algorithm prototyper and as a mathematical research tool, and it comes with built in mathematical and programmatic functions.

HighFive is a header-only C++11 friendly interface for libhdf5. It supports STL vector/string, Boost::UBLAS, Boost::Multi-array and Xtensor; and handles C++ from/to HDF5 with automatic type mapping. HighFive does not require additional libraries.

Veusz is a scientific plotting and graphing program with a graphical user interface, designed to produce publication-ready 2D and 3D plots. In addition it can be used as a module in Python for plotting. It supports vector and bitmap output, including PDF, Postscript, SVG and EMF.

CCOLAMD is library for computing a permutation vector for a matrix with which the LU factorization becomes sparser. It is a variant of COLAMD which has the the option to apply constraints to the ordering.

Bitwise is a multi base interactive calculator supporting dynamic base conversion and bit manipulation. It's a handy tool for low level hackers, kernel developers and device drivers developers.

Some of the features include:

• Interactive ncurses interface.

• Command line calculator supporting all bitwise operations.

• Individual bit manipulator.

• Bitwise operations such as NOT, OR, AND, XOR, and shifts.

optizelle is a software library designed to solve nonlinear optimization problems. Four types of problem are considered: unconstrained, equality constrained, inequality constrained and constrained. Constraints may be applied as values of functions or sets of partial differential equations (PDEs).

Solution algorithms such as the preconditioned nonlinear conjugate gradient method, sequential quadratic programming (SQP) and the primal-dual interior-point method are made available. Interfaces are provided for applications written in C++ and Python. Parallel computation is supported via MPI.

SUNDIALS is a family of software packages implemented with the goal of providing robust time integrators and nonlinear solvers that can easily be incorporated into existing simulation codes.

SoftFPU is a C++ library implementing concrete and symbolic semantics for floating point numbers as defined in the IEEE-764 Standard for Floating-Point Arithmetic. It is templated in terms of the bit-vectors, propositions, floating-point formats and rounding mode types used. This allow the same code to be executed as an arbitrary precision library or to be used to build symbolic representations of floating-point operations.

This package provides a range of SAT solvers, including the sequential lingeling and its parallel variants plingeling and treengeling. A bounded model checker is also included.

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.

CAMD is a set of routines for ordering a sparse matrix prior to Cholesky factorization (or for LU factorization with diagonal pivoting). It is a variant of AMD which has the the option to apply constraints to the ordering.

orthopy provides various orthogonal polynomial classes for lines, triangles, quadrilaterals, disks, spheres, hexahedra, and n-cubes. All computations are done using numerically stable recurrence schemes. Furthermore, all functions are fully vectorized and can return results in exact arithmetic.

feedgnuplot is a tool to plot realtime and stored data from the command line, using gnuplot. It can read data from a pipe or file, make a variety of transformations, and render the result in the terminal or with an external viewer.

SLEEF (SIMD Library for Evaluating Elementary Functions) is a library that implements vectorized versions of all C99 real floating point math functions. It can utilize SIMD instructions that are available on modern processors.

Ceres Solver is a C++ library for modeling and solving large, complicated optimization problems. It is a feature rich, mature and performant library which has been used in production since 2010. Ceres Solver can solve two kinds of problems:

1. non-linear least squares problems with bounds constraints;

2. general unconstrained optimization problems.

CXSparse is a collection of sparse matrix algorithms for direct methods on both real and complex matrices.

reduceLCS is an implementation of the Reduce-Expand algorithm for LCS. It is a fast program to compute the approximate Longest Commons Subsequence of a set of strings.

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

Gmsh is a 3D finite element grid generator with a built-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. Gmsh is built around four modules: geometry, mesh, solver and post-processing. The specification of any input to these modules is done either interactively using the graphical user interface or in ASCII text files using Gmsh's own scripting language.

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.

PETSc, pronounced PET-see (the S is silent), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.