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Awesome Python Math Packages Awesome

Python packages for mathematics, from algebra and analysis to geometry, statistics, optimization, and topology.

Contributions are welcome! Read the contribution guidelines first.

Contents

Algebra

  • clifford - Geometric Algebra (Clifford algebra) for Python.
  • fxpmath - A Python library for fractional fixed-point (base 2) arithmetic and binary manipulation.
  • galgebra - Symbolic Geometric Algebra/Calculus package for SymPy.
  • Galois - A performant NumPy extension for Galois fields and their applications.
  • kingdon - A symbolically optimized Geometric Algebra library with PyTorch/NumPy/SymPy compatibility and ganja.js visualization.
  • pixell - A rectangular pixel map manipulation and harmonic analysis library derived from Sigurd Naess' enlib.
  • Plabic - Cluster algebraic/geometric structures related to plabic graphs.
  • PyQuaternion - A fully featured, pythonic library for representing and using quaternions.
  • multivar_horner - Python package implementing a multivariate Horner scheme for efficiently evaluating multivariate polynomials.
  • Quaternion - Add built-in support for quaternions to NumPy.

Analysis

  • chaospy - Toolbox for performing uncertainty quantification with polynomial chaos expansions.
  • chebpy - A Python implementation of Chebfun.
  • dedalus - A flexible framework for solving PDEs with modern spectral methods.
  • devito - DSL and compiler framework for automated finite-differences and stencil computation.
  • diffrax - Numerical differential equation solvers in JAX; autodifferentiable and GPU-capable.
  • dolfinx - Next generation FEniCS problem solving environment for solving PDEs with the finite element method.
  • findiff - Python package for numerical derivatives and partial differential equations in any number of dimensions.
  • FiPy - A finite volume PDE solver written in Python.
  • firedrake - An automated system for the portable solution of partial differential equations using the finite element method.
  • foof - Parameterizing neural power spectra into periodic & aperiodic components.
  • harmonica - Forward modeling, inversion, and processing gravity and magnetic data.
  • MutatorMath - Python library for piecewise linear interpolation in multiple dimensions with multiple, arbitrarily placed, masters.
  • NGSolve - High performance multiphysics finite element software with a flexible Python interface.
  • numdifftools - Solve automatic numerical differentiation problems in one or more variables.
  • PyAbel - A Python package for Abel and inverse Abel transforms.
  • pyFFTW - A pythonic wrapper around FFTW, the fast Fourier transform library.
  • pykoopman - A package for computing data-driven approximations to the Koopman operator.
  • py-pde - Python package for solving partial differential equations using finite differences.
  • PyWavelets - Wavelet transforms in Python.
  • quadpy - Numerical integration (quadrature, cubature) in Python.
  • scikit-fem - Simple finite element assemblers.
  • scikit-fmm - A Python extension module implementing the fast marching method.
  • sfepy - Software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D.
  • SHTOOLS - Spherical Harmonic Tools.
  • torchdiffeq - Differentiable ODE solvers with full GPU support and O(1)-memory backpropagation.
  • torchquad - Numerical integration in arbitrary dimensions on the GPU using PyTorch / TF / JAX.

Animations and Images

  • Hyperbolic wythoff - Draw the Wythoff construction of uniform tilings in hyperbolic plane.
  • ManimGL - 3Blue1Brown's animation engine for explanatory math videos.
  • Manim - A community-maintained Python framework for creating mathematical animations.

Dynamical Systems

  • dysts - A database of hundreds of chaotic systems and strange attractors.
  • jitcdde - Just-in-time compilation for delay differential equations.
  • jitcode - Just-in-time compilation for ordinary differential equations.
  • nolds - Nonlinear measures for dynamical systems (Lyapunov exponents, correlation dimension, Hurst exponent, ...).
  • parcels - Main code for Parcels (Probably A Really Computationally Efficient Lagrangian Simulator).
  • PyDMD - Dynamic Mode Decomposition in Python.
  • PyNamical - Modeling and visualizing discrete nonlinear dynamical systems, chaos, and fractals.
  • PySINDy - Sparse identification of nonlinear dynamical systems from data.

General Mathematics

  • AxiomPy - A Python library for advance mathematics operations.
  • cypari2 - Python interface to the number theory library PARI/GP.
  • diofant - A Python computer algebra system (CAS), originally a fork of SymPy.
  • gmpy2 - General multiple-precision arithmetic for Python (GMP, MPFR, MPC).
  • Mathics - A free, general-purpose computer algebra system featuring Wolfram Language compatibility.
  • mpmath - A Python library for arbitrary-precision floating-point arithmetic.
  • passagemath - A modularized, pip-installable fork of SageMath.
  • pymbolic - A simple package to do symbolic math (focus on code generation and DSLs).
  • Sage - SageMath, a free open-source mathematics software system (computer algebra system).
  • SciPy - Open-source software for mathematics, science, and engineering, with modules for statistics, optimization, integration, linear algebra, Fourier transforms, signal and image processing, ODE solvers, and more.
  • SimPy - A computer algebra system written in pure Python.
  • SymEngine - Python wrappers for SymEngine, a fast symbolic manipulation library written in C++.

Geometry

  • boule - Reference ellipsoids for geodesy and geophysics.
  • CGAL bindings - Python bindings for CGAL, the Computational Geometry Algorithms Library.
  • COMPAS - Core library of the COMPAS framework for research in architecture, engineering and digital fabrication.
  • geomstats - Computations and statistics on manifolds with geometric structures.
  • gpytoolbox - A collection of utility functions to prototype geometry processing research in Python.
  • libigl - Python bindings for libigl, a geometry processing library.
  • Manifold - Geometry library for topologically robust mesh Boolean operations.
  • NURBS-Python - Object-oriented pure Python B-Spline and NURBS library.
  • polytope - Geometric operations on polytopes of any dimension.
  • potpourri3d - 3D geometry tools in Python: geodesic distances, heat methods, mesh and point cloud processing.
  • pymanopt - Python toolbox for optimization on Riemannian manifolds with support for automatic differentiation.
  • pytransform3d - 3D transformations for Python.
  • roma - A lightweight library to deal with 3D rotations in PyTorch.
  • shapely - Manipulation and analysis of geometric objects in the Cartesian plane.
  • trimesh - Python library for loading and using triangular meshes.

Graph Theory

  • cuGraph - RAPIDS GPU-accelerated graph analytics library.
  • EasyGraph - A network analysis library covering structural hole spanners, network embedding, and classic network analysis.
  • GraKeL - A scikit-learn compatible library for graph kernels.
  • graph-theory - A simple graph library.
  • graphblas-algorithms - Graph algorithms written in GraphBLAS.
  • Graphillion - Fast, lightweight library for operations on huge sets of graphs.
  • networkit - A toolkit for large-scale network analysis.
  • networkx - Creation, manipulation, and study of the structure, dynamics and functions of complex networks.
  • PrRGG - Python Random Graph Generator.
  • python-igraph - Python interface for the igraph high-performance graph library.
  • rustworkx - A high-performance Python graph library implemented in Rust.

Group Theory

  • bella - New computational package for small-rank matrix groups.
  • e3nn - A modular framework for neural networks with Euclidean symmetry (irreducible representations of O(3)).
  • jaxlie - Rigid transforms and Lie groups (SO(2), SE(2), SO(3), SE(3)) for JAX.
  • Liegroups - Python implementation of SO2, SE2, SO3, and SE3 matrix Lie groups using NumPy or PyTorch.
  • manif - A small library for Lie theory with Python bindings.
  • Permuta - A native Python library for permutation pattern research.
  • Permutation - Permutations of finitely many positive integers.
  • spglib - A library for finding and handling crystal symmetries (space groups).
  • spgrep - On-the-fly generator of space-group irreducible representations.
  • symmetria - An intuitive, thorough, and comprehensive framework for interacting with the symmetric group and its elements.

Learning Math

  • MathGenerator - A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.
  • PyWonderland - A tour in the wonderland of math with Python.

Linear Algebra

  • CoLA - Compositional linear algebra for large-scale structured matrices.
  • lineax - Linear solvers in JAX and Equinox.
  • matfree - Matrix-free linear algebra in JAX.
  • NumPy - The fundamental package for scientific computing with Python.
  • opt_einsum - Optimizing einsum functions in NumPy, TensorFlow, Dask, and more with contraction order optimization.
  • PyAMG - Algebraic multigrid solvers in Python.
  • python-graphblas - Python library for GraphBLAS: high-performance sparse linear algebra for scalable graph analytics.
  • scikit-sparse - Sparse matrix tools extending scipy.sparse (CHOLMOD sparse Cholesky decomposition).
  • sparse - Multi-dimensional sparse arrays for the PyData ecosystem.
  • Spatial Maths for Python - Create, manipulate and convert representations of position and orientation in 2D or 3D using Python.
  • PentaPy - A Python toolbox for pentadiagonal linear systems.
  • PyLops - A Linear-Operator Library for Python.
  • PyParadiso - Python interface to the Intel MKL Pardiso library to solve large sparse linear systems of equations.
  • Poisson-solver-2D - Finite difference solution of 2D Poisson equation. Can handle Dirichlet, Neumann and mixed boundary conditions.
  • scikit-spatial - Spatial objects and computations based on NumPy arrays.
  • TensorLy - Tensor decomposition, tensor algebra and tensor regression in Python.

Number Theory

  • continuedfractions - Object-oriented continued fractions with Python.
  • primesieve-Python - Fast prime number generator. Python bindings for the primesieve C++ library.
  • pyadic - P-Adic numbers and finite fields in Python.
  • python-flint - Python bindings for FLINT (Fast Library for Number Theory) and Arb.
  • oeis - Newcomer friendly project implementing a few oeis.org sequences.

Optimization

  • BayesianOptimization - A Python implementation of global optimization with Gaussian processes.
  • BoTorch - Bayesian optimization in PyTorch.
  • CasADi - A symbolic framework for numeric optimization with algorithmic differentiation.
  • CVXOPT - Python software for convex optimization.
  • cvxpy - A Python-embedded modeling language for convex optimization problems.
  • DEAP - Distributed Evolutionary Algorithms in Python.
  • GEKKO - Optimization suite for mixed-integer, nonlinear and dynamic optimization.
  • HiGHS - High performance linear, mixed-integer and quadratic optimization software with a Python interface (highspy).
  • linopy - Linear optimization with N-D labeled arrays in Python.
  • Nevergrad - A Python toolbox for gradient-free optimization.
  • NLopt - A library for nonlinear optimization, wrapping many algorithms for global and local, constrained or unconstrained optimization.
  • optax - A gradient processing and optimization library for JAX.
  • optimistix - Nonlinear optimisation (root-finding, least squares, minimisation) in JAX and Equinox.
  • OR-Tools - Google's operations research tools for combinatorial optimization, linear programming and constraint programming.
  • OSQP - Python interface for OSQP, the Operator Splitting Quadratic Program solver.
  • PuLP - A Python linear programming API.
  • pymoo - Multi-objective optimization in Python (NSGA-II, NSGA-III, MOEA/D, and more).
  • Pyomo - An object-oriented algebraic modeling language in Python for structured optimization problems.
  • PySCIPOpt - Python interface for the SCIP Optimization Suite.
  • Python-MIP - Python tools for the modeling and solution of mixed-integer linear programs.
  • qpsolvers - Quadratic programming solvers in Python with a unified API.

Probability and Statistics

  • arch - Autoregressive conditional heteroskedasticity (ARCH) and other volatility models in Python.
  • ArviZ - Exploratory analysis of Bayesian models.
  • Bambi - BAyesian Model-Building Interface (Bambi) in Python.
  • BlackJAX - A Bayesian inference library designed for ease of use, speed and modularity.
  • CmdStanPy - A lightweight Python interface to Stan.
  • dynesty - Dynamic nested sampling package for computing Bayesian posteriors and evidences.
  • emcee - The Python ensemble sampling toolkit for affine-invariant MCMC.
  • GPJax - Gaussian processes in JAX and Equinox.
  • icepool - Python dice probability package.
  • lifelines - Survival analysis in Python.
  • linearmodels - Instrumental variable and panel data models missing from statsmodels.
  • lmfit - Non-linear least-squares minimization and curve fitting.
  • NumPyro - Probabilistic programming with NumPy powered by JAX for autograd and JIT compilation.
  • obscure_stats - A small collection of lesser-known statistical measures.
  • OpenTURNS - Probabilistic modelling and uncertainty quantification library.
  • particles - Sequential Monte Carlo in Python.
  • pgmpy - Python toolkit for causal and probabilistic reasoning with graphical models.
  • Pingouin - Statistical package in Python based on Pandas.
  • pomegranate - Fast, flexible and easy to use probabilistic modelling in Python.
  • PyAutoFit - Classy probabilistic programming.
  • pyGAM - Generalized Additive Models in Python.
  • PyMC - Bayesian modeling and probabilistic programming in Python.
  • Pyro - Deep universal probabilistic programming with Python and PyTorch.
  • SALib - Sensitivity analysis library in Python (Sobol, Morris, FAST, and other methods).
  • sbi - A Python package for simulation-based inference.
  • scikit-posthocs - Multiple pairwise comparisons (post hoc) tests in Python.
  • Statsmodels - Statistical modeling and econometrics in Python.
  • thejoker - A custom Monte Carlo sampler for the (gravitational) two-body problem.
  • UltraNest - Fit and compare complex models reliably and rapidly with advanced nested sampling.

Topology

  • Dionysus - Library for computing persistent homology.
  • GUDHI - A generic library with a Python interface for topological data analysis and higher-dimensional geometry.
  • kepler-mapper - A flexible Python implementation of the Mapper algorithm for topological data analysis.
  • persim - Distances and representations of persistence diagrams.
  • Regina - Software for low-dimensional topology: 3-manifolds, 4-manifolds, knots and normal surfaces.
  • ripser.py - A lean persistent homology library for Python.
  • scikit-tda - Topological data analysis for Python.
  • SnapPy - A package for studying the topology and geometry of 3-manifolds, with a focus on hyperbolic structures.
  • Spherogram - Planar diagrams arising in 3-dimensional topology, such as link and Heegaard diagrams.
  • TopoNetX - Computing on topological domains: simplicial, cell and combinatorial complexes.

Others

  • autograd - Efficiently computes derivatives of NumPy code.
  • Axelrod - A research tool for the Iterated Prisoner's Dilemma and other game-theoretic tournaments.
  • Gambit - Software tools for computation in game theory.
  • handcalcs - Convert Python calculations into rendered LaTeX.
  • LaTeX-OCR - Convert images of equations into LaTeX code using a vision transformer.
  • LeanDojo - Tool for data extraction and interacting with the Lean theorem prover programmatically.
  • MathTranslate - Translate scientific papers with math.
  • Nashpy - A Python library for the computation of equilibria of 2-player strategic games.
  • Pint - Operate and manipulate physical quantities (units of measurement) in Python.
  • portion - Data structure and operations for intervals.
  • PySAT - A toolkit for SAT-based prototyping in Python.
  • pySMT - A library for SMT formulae manipulation and solving.
  • PySymmPol - Manipulation of various symmetric polynomials, and Young diagrams.
  • quicktions - Fast fractions reimplementation in Cython.
  • uncertainties - Transparent calculation of uncertainties (error propagation) on the quantities involved.
  • unyt - Handle, manipulate, and convert data with units in Python.
  • Z3 - The Z3 theorem prover, with a Python API.

Footnotes

Packages that are archived, no longer available, or without activity in the last two years are listed in unmaintained.md.