Mathematics Packages
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DifferentialEquations.jl2841Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
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Symbolics.jl1353Symbolic programming for the next generation of numerical software
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ForwardDiff.jl888Forward Mode Automatic Differentiation for Julia
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DynamicalSystems.jl834Award winning software library for nonlinear dynamics and nonlinear timeseries analysis
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StaticArrays.jl761Statically sized arrays for Julia
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Gridap.jl691Grid-based approximation of partial differential equations in Julia
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LightGraphs.jl671An optimized graphs package for the Julia programming language
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Tullio.jl605⅀
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ApproxFun.jl537Julia package for function approximation
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SymbolicUtils.jl537Symbolic expressions, rewriting and simplification
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OrdinaryDiffEq.jl533High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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Interpolations.jl523Fast, continuous interpolation of discrete datasets in Julia
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Measurements.jl486Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration.
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Grassmann.jl464⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra
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Graphs.jl457An optimized graphs package for the Julia programming language
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TensorOperations.jl450Julia package for tensor contractions and related operations
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ChainRules.jl435Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs
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AlgebraOfGraphics.jl421Combine ingredients for a plot
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IterativeSolvers.jl401Iterative algorithms for solving linear systems, eigensystems, and singular value problems
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Meshes.jl389Computational geometry in Julia
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DSP.jl379Filter design, periodograms, window functions, and other digital signal processing functionality
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Manifolds.jl368Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.
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SpecialFunctions.jl350Special mathematical functions in Julia
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GeometricFlux.jl348Geometric Deep Learning for Flux
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TaylorSeries.jl346Taylor polynomial expansions in one and several independent variables.
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Roots.jl342Root finding functions for Julia
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Ferrite.jl339Finite element toolbox for Julia
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Oscar.jl339A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory.
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Krylov.jl338A Julia Basket of Hand-Picked Krylov Methods
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DiffEqSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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SciMLSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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NLsolve.jl324Julia solvers for systems of nonlinear equations and mixed complementarity problems
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StructArrays.jl319Efficient implementation of struct arrays in Julia
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DiffEqBase.jl309The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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LinearMaps.jl303A Julia package for defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.
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LazyArrays.jl303Lazy arrays and linear algebra in Julia
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Polynomials.jl303Polynomial manipulations in Julia
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BifurcationKit.jl301A Julia package to perform Bifurcation Analysis
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FastGauss.jl298Julia package for Gaussian quadrature
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FastGaussQuadrature.jl298Julia package for Gaussian quadrature
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