Mathematics

• JuliaMath organization
• JuliaApproximation organization

See also

• Symbolic computation
• Linear Algebra
• Digital signal processing

General Mathematics packages

• Dualization.jl : Automatic dualization feature for MathOptInterface.jl conic optimization problems.
• FastPow.jl : @fastpow speeds up the computation of integer powers in any Julia expression by transforming them into optimal sequences of multiplications, with a slight sacrifice in accuracy.
• GSL.jl : Julia interface to the GNU Scientific Library - GSL.
• Manifolds.jl : a unified interface to define and use manifolds as well as a library of manifolds to use for your projects.
• Tau.jl : A simple module providing definition of the Tau constant = 2pi.

Numeric data types

• BitIntegers.jl : This package implements fixed-width integer types similar to standard built-in ones like Int or UInt128.
• CustomUnitRanges.jl : This Julia package supports the creation of array types with “unconventional” indices.
• DualNumbers.jl: Julia package for representing dual numbers for differentiation.
• FixedPointNumbers.jl : This library exports fixed-point number types.
• Infinity.jl : Representation of infinity in Julia.
• Measures.jl : Unified measure and coordinates types.
• Quaternions.jl : Quaternions, octonions and dual-quaternions for 3D rotational orientation.
• Ratios.jl : Faster Rational-like types for Julia at the risk of greater risk of overflow.

Units

• DynamicQuantities.jl : Lightweight and fast physical quantities in Julia to supplement Unitful.jl.
• Unitful.jl : A Julia package for physical units.
• UnitSystems.jl: Physical unit systems (Metric, English, Natural, Planck, etc…). See also Similitude.jl: Dimensions and Quantities for UnitSystems.jl.

Floating-point numbers

• ArbNumerics.jl : extended precision math, accurate and performant
• BFloat16s.jl : This package defines the BFloat16 data type. The only currently available hardware implementation of this datatype are Google’s Cloud TPUs.
• DecFP.jl : The package provides 32-bit, 64-bit, and 128-bit binary-encoded decimal floating-point types following the IEEE 754-2008, implemented as a wrapper around the (BSD-licensed) Intel Decimal Floating-Point Math Library.
• Decimals.jl : Pure Julia decimal arithmetic library.
• DoubleFloats.jl : Numbers with 85 accurate bits.
• LogarithmicNumbers.jl : A logarithmic number system for Julia. Provides the signed ULogarithmic and unsigned Logarithmic types for representing real numbers on a logarithmic scale.

Intervals

Julia intervals

• IntervalArithmetic.jl : Rigorous floating-point calculations using interval arithmetic in Julia.
• Measurements.jl : Error propagation calculator and library. It supports real and complex numbers with uncertainty, arbitrary precision calculations, and operations with arrays.
• MonteCarloMeasurements.jl : Error propagation using Monte-Carlo simulation. Similar to Measurements.jl, but more accurate for highly nonlinear functions at the expense of longer execution time.

Computer Arithmetic

• Wikipedia: Computer Arithmetic
• ent : Primes, Congruences, and Secrets.

Floating Point numbers

Wikipedia: Floating Point

• ErrorfreeArithmetic.jl : Error-free transformations for arithmetic ops.
• FastRounding.j : Faster directed rounding for inline arithmetic.

Algebra

adeles algebraic number theory

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• Hecke.jl : A package for algebraic number theory that works on top of Nemo.jl by Tommy Hofmann and Claus Fieker.
• Mods.jl : Easy modular arithmetic for Julia.
• Nemo.jl : A computer algebra package for the Julia programming language.
• OEIS.jl : A basic wrapper to allow access to OEIS integer sequences from within Julia.
• SemiringAlgebra.jl : Semiring Algebra. A linear algebraic approach to graph algorithms that exploits the sparse adjacency matrix representation of graphs can provide a variety of benefits.

Boolean Algebra

Boolean Algebra

• ShowSet.jl : Nicer output for Set and IntSet objects.

Approximations

• AMD.jl : Given a square sparse matrix, compute an approximate minimum degree ordering.
• ChebyshevApprox.jl : Julia code to approximate continuous functions using Chebyshev polynomials.
• FastGaussQuadrature.jl : A Julia package to compute n-point Gauss quadrature nodes and weights to 16-digit accuracy and in O(n) time.
• FastTransforms.jl : Julia package for fast orthogonal polynomial transforms.
• Remez.jl : Remez algorithm for computing minimax polynomial approximations.
• Simplices.jl : Compute exact simplex intersections in N dimensions.
• Sobol.jl : is a generation of Sobol low-discrepancy sequence (LDS) implementation, that generates quasi-random sequences of points in N dimensions which are equally distributed over an N-dimensional hypercube.

Interpolations

• ApproxFun.jl : Julia package for function approximation using Chebyshev basis.
• CoordinateSplittingPTrees.jl : Accurate and efficient full-degree multidimensional polynomial interpolation.
• DataInterpolations.jl: A library of data interpolation and smoothing functions.
• Dierckx.jl : Julia package for 1-d and 2-d splines, a wrapper for the dierckx Fortran library.
• GridInterpolations.jl : Multi-dimensional grid interpolation in arbitrary dimensions on a recti-linear grid.
• Interpolations.jl : Fast, continuous interpolation of discrete datasets in Julia.
• PiecewiseInterpolation.jl : A simple interface for interpolations on timeseries with first order discontinuities (using Dierckx.jl).
• RationalFunctionApproximation.jl : approximation by ratios of polynomials. JuliaCon 2025 video

Polynomials

Wikipedia: Polynomials

• FastPolynomialRoots.jl : Fast and backward stable computation of roots of polynomials by Fortran in Julia.
• Jacobi.jl : Jacobi polynomials and Gauss quadrature related functions.
• MultivariatePolynomials.jl : Multivariate polynomials and multivariate moments.
• PolynomialRoots.jl : Fast complex polynomial root finder, with support for arbitrary precision calculations.
• Polynomials.jl : Basic arithmetic, integration, differentiation, evaluation, root finding, and fitting for univariate polynomials in Julia.
• SemialgebraicSets.jl : Extension of MultivariatePolynomials to semi-algebraic sets.
• TaylorModels.jl : A numerical mathematics package to treat the high-order scaling property of the remainder bound interval in a Taylor polynomial. 📹 JuliaCon 2018.

Functions

Wikipedia: Functions

Evaluation and approximations of functions

• ApproxFun.jl : Julia package for function approximation.
• BasisFunctions.jl : A collection of routines for working with a number of standard basis functions. For more complete software packages to manipulate numerical function approximations, please consider ApproxFun.
• Elliptic.jl : Elliptic integral and Jacobi elliptic special functions.
• FrameFun.jl : Exploring practical possibilities of approximating functions with frames rather than with a basis.
• LambertW.jl : A package implementing the Lambert_W function and associated omega constant.
• LogExpFunctions.jl: Julia package for various special functions based on log and exp.
• NaNMath.jl : Implementations of basic math functions which return NaN instead of throwing a DomainError.
• SpecialFunctions.jl : Special mathematical functions in Julia.
• Struve.jl : Struve functions for Julia.

Calculus

• Riemann Hypothesis book with the source code on github.
• Calculus With Julia : Introductory Calculus with the Julia Programming Language.
• An IJulia notebook showing Taylor’s method integration of the pendulum.

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• Calculus.jl : Calculus package.
• Cuba.jl : Library for multidimensional numerical integration with the Cuba library.
• Cubature.jl : Oneand multi-dimensional adaptive integration routines for the Julia language.
• FastGaussQuadrature.jl : Computes Gauss quadrature rules to 16-digit precision (so far Legendre, Jacobi, Lobatto, Radau).
• FiniteDifferences.jl : estimating derivatives with finite differences.
• FiniteDiff.jl : Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support.
• FractionalCalculus.jl : High performance and high precision numerical fractional calculus computing.
• HCubature.jl : Pure-Julia multidimensional h-adaptive integration.
• Integrals.jl : A common interface for quadrature and numerical integration.
• RiemannComplexNumbers.j : The RiemannComplexNumbers module is an alternative Complex type for Julia (with a single complex infinity value).
• Roots.jl : Root finding functions for Julia.
• TaylorSeries.jl : A julia package for Taylor expansions in one independent variable.
• WiltonInts84.jl : Integrals of arbitrary powers of R over flat triangles.

Automatic Differentiation

• ADOLC.jl : A Julia wrapper of the automatic differentiation package ADOL-C. JuliaCon 2024 video
• ChainRules.jl : forward and reverse mode automatic differentiation primitives.
• DifferentiationInterface.jl : An interface to various automatic differentiation backends in Julia. JuliaCon 2024 video
• Diffractor.jl : An experimental next-generation, compiler-based AD system for Julia.
• DualNumbers.jl : Julia package for representing dual numbers and for performing dual algebra.
• Enzyme.jl : Julia bindings for the Enzyme automatic differentiator. The Enzyme project is a tool for performing reverse-mode automatic differentiation (AD) of statically-analyzable LLVM IR.
• ForwardDiff.j : Forward Mode Automatic Differentiation for Julia.
• HyperDualNumbers.jl : Hyper-dual numbers can be used to compute first and second derivatives numerically without the cancellation errors of finite-differencing schemes.
• ReverseDiff.jl : Reverse Mode Automatic Differentiation for Julia.
• StochasticAD.jl : automatic differentiation of programs containing discrete randomness. JuliaCon 2023 video
• Yota.jl : Reverse-mode automatic differentiation for static and dynamic graphs.
• Zygote.jl : Source-to-source automatic differentiation (AD) in Julia, and is the next-gen AD system for the Flux differentiable programming framework.

Mathematical Analysis

Wikipedia: Mathematical Analysis

• Complementarity.jl : This package provides a modeling and computational interface for solving Mixed Complementarity Problems (MCP), modeling by JuMP.jl and computing by PATHSolver.jl.
• Fatou.jl : Fatou/Julia sets in Julia (Fractals, Newton basins, Mandelbrot).
• PATHSolver.jl : This package provides a Julia wrapper of the PATH Solver for solving linear Mixed Complementarity Problems (MCP).
• Wilkinson.jl : Toolkit for studying numerical analysis and floating point algebra round-off error in Julia.

Discrete math

• Wikipedia: Discrete math
• Wikipedia: Combinatorics
• See also graph theory

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• Collatz.jl : The Collatz conjecture.
• PermPlain.jl : Permutations of integers.
• Permutations.jl : Permutations class for Julia.
• SimplePosets.jl : Simple partially ordered sets for Julia.
• ZChop.jl : Replaces small numbers with zero.

Information theory

Wikipedia: Information theory

• InformationMeasures.jl : Entropy, mutual information and higher order measures from information theory, with various estimators and discretization methods.