CVXOPT is a package for convex optimization based on the Python programming language. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python’s extensive standard library and on the strengths of Python as a high-level programming language.

SLEPc, the Scalable Library for Eigenvalue Problem Computations, is based on PETSc, the Portable, Extensible Toolkit for Scientific Computation. It employs the MPI standard for all message-passing communication. slepc4py provides Python bindings to almost all functions of SLEPc.

SuiteSparse is a suite of sparse matrix algorithms. This package contains a library with common configuration options.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods.

This is the iterative solver template library which provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

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.

LAPACK is a Fortran 90 library for solving the most commonly occurring problems in numerical linear algebra.

GNU Dionysus is a convenient system for quickly retrieving the values of mathematical constants used in science and engineering. Values can be searched using a simple command-line tool, choosing from three databases: universal constants, atomic numbers, and constants related to semiconductors.

The Parma Polyhedra Library (PPL) provides numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems. These abstractions include convex polyhedra, defined as the intersection of a finite number of (open or closed) halfspaces, each described by a linear inequality (strict or non-strict) with rational coefficients; some special classes of polyhedra shapes that offer interesting complexity/precision tradeoffs; and grids which represent regularly spaced points that satisfy a set of linear congruence relations. The library also supports finite powersets and products of (any kind of) polyhedra and grids, a mixed integer linear programming problem solver using an exact-arithmetic version of the simplex algorithm, a parametric integer programming solver, and primitives for termination analysis via the automatic synthesis of linear ranking functions.

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

HYPRE is a software library of high performance preconditioners and solvers for the solution of large, sparse linear systems of equations. It features multigrid solvers for both structured and unstructured grid problems.

This package provides a Cython interface to the C++ library primecount.

Ruy is a matrix multiplication library. Its focus is to cover the matrix multiplication needs of neural network inference engines. Its initial user has been TensorFlow Lite, where it is used by default on the ARM CPU architecture.

ExprTk is a C++ headers only library for mathematical expression parsing and evaluation.

The General Cartographic Transformation Package (GCTP) is a system of software routines designed to permit the transformation of coordinate pairs from one map projection to another. The GCTP is the standard computer software used by the National Mapping Division for map projection computations.

The C-library cddlib implements the Double Description Method of Motzkin et al. for generating all vertices (i.e. extreme points) and extreme rays of a general convex polyhedron given by a system of linear inequalities in arbitrary dimension. It can also be used for the converse operation of computing convex hulls.

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

CGLM is an optimised 3D maths library for graphics software based on the GLSL specifications.

It's similar to the original C++ GLM library but written in C99 and compatible with C89.

This package provides a C++ implementation of the Louvain community detection algorithm.

HiGHS provides serial and parallel solvers for large-scale sparse linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP) models

Why3 provides a language for specification and programming, called WhyML, and relies on external theorem provers, both automated and interactive, to discharge verification conditions. Why3 comes with a standard library of logical theories (integer and real arithmetic, Boolean operations, sets and maps, etc.) and basic programming data structures (arrays, queues, hash tables, etc.). A user can write WhyML programs directly and get correct-by-construction OCaml programs through an automated extraction mechanism. WhyML is also used as an intermediate language for the verification of C, Java, or Ada programs.

CLP is a high quality linear programming solver. Its main strengths are its dual and primal Simplex algorithms. It also has a barrier algorithm for linear and quadratic objectives. There are limited facilities for nonlinear and quadratic objectives using the Simplex algorithm.

libensemble is a complete toolkit for dynamic ensembles of calculations. It connects deciders to experiments or simulations.

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

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.