Mathematics Packages

SparseDiffTools.jl201Fast jacobian computation through sparsity exploitation and matrix coloring

Sundials.jl188Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

LinearSolve.jl178LinearSolve.jl: HighPerformance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

BandedMatrices.jl129A Julia package for representing banded matrices

Grassmann.jl415⟨LeibnizGrassmannClifford⟩ differential geometric algebra / multivector simplicial complex

QuadGK.jl210Adaptive 1d numerical Gauss–Kronrod integration in Julia

CoordinateTransformations.jl158A fresh approach to coordinate transformations...

RootedTrees.jl34A collection of functionality around rooted trees to generate order conditions for RungeKutta methods in Julia for differential equations and scientific machine learning (SciML)

Oscar.jl208A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory.

MolecularGraph.jl167Graphbased molecule modeling toolkit for cheminformatics

ImplicitDifferentiation.jl86Automatic differentiation of implicit functions

LinearAlgebra.jl131Generic numerical linear algebra in Julia

GenericLinearAlgebra.jl131Generic numerical linear algebra in Julia

Measurements.jl415Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration.

ShiftedArrays.jl49Lazy shifted arrays for data analysis in Julia

SymbolicNumericIntegration.jl93SymbolicNumericIntegration.jl: SymbolicNumerics for Solving Integrals

Nemo.jl133Julia bindings for various mathematical libraries (including flint2)

Finch.jl58Write Loops Dense! Run Loops Sparse!

CategoricalArrays.jl118Arrays for working with categorical data (both nominal and ordinal)

BifurcationKit.jl240A Julia package to perform Bifurcation Analysis

AbstractFFTs.jl96A Julia framework for implementing FFTs

SymbolicUtils.jl454Expression rewriting and simplification

Symbolics.jl1169A fast and modern CAS for a fast and modern language.

ChainRulesCore.jl218ADbackend agnostic system defining custom forward and reverse mode rules. This is the light weight core to allow you to define rules for your functions in your packages, without depending on any particular AD system.

FundamentalsNumericalComputation.jl60Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

GaussianFilters.jl36Julia Package for discretetime linear Gaussian parametric filtering systems, namely KF, EKF, UKF, GMPHD

DynamicalSystems.jl725Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

HighDimPDE.jl60A Julia package that breaks down the curse of dimensionality in solving PDEs.

DiffEqSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

SciMLSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

NonlinearSolve.jl112Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.

OrdinaryDiffEq.jl425High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

DifferentialEquations.jl2503Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.

Transducers.jl381Efficient transducers for Julia

ForwardDiff.jl778Forward Mode Automatic Differentiation for Julia

AlgebraOfGraphics.jl338Combine ingredients for a plot

GaloisFields.jl44Finite fields for Julia

Combinatorics.jl204A combinatorics library for Julia

KrylovKit.jl203Krylov methods for linear problems, eigenvalues, singular values and matrix functions

Roots.jl262Root finding functions for Julia
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