Julia (programming language)

Dynamic programming language

Julia

Paradigm| Multi-paradigm: multiple dispatch (primary paradigm), functional, array, procedural (imperative), structured, reflective, meta, multistaged[1]
Designed by| Jeff Bezanson, Alan Edelman, Stefan Karpinski, Viral B. Shah
Developer| Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and other contributors[2][3]
First appeared| 2012; 13 years ago (2012)[4]
Stable release|

1.11.4[5] / 10 March 2025; 21 days ago (10 March 2025) and
1.10.9[7] (LTS) / (same-day release)

Preview release|

Being worked on: 1.12.0-beta1[6] and 1.13.0-DEV with daily updates

Typing discipline| Dynamic,[8] inferred, optional, nominative, parametric, strong[8]
Implementation language| Julia, C, C++, LLVM,[9] Scheme (was used the parser; almost exclusively)
Platform| Tier 1: x86-64, IA-32, Apple silicon (ARM64) Macs; Nvidia GPUs/CUDA (on Linux)[10]
Tier 2: FreeBSD, 64-bit Arm on Linux, Apple GPUs; Intel GPUs/OneAPI 6.2+ and Nvidia GPUs (on Windows)
Tier 3: 32-bit Arm, 64-bit RISC-V, and AMD GPUs/ROCm 5.3+.
OS| Linux, macOS, Windows and FreeBSD
License| MIT
Filename extensions| .jl
Website| JuliaLang.org
Influenced by

* Dylan[11]
* Lisp[4][12]
* Lua[13]
* Mathematica[14][15]
* MATLAB[4]
* Perl[13]
* Python[13]
* R[4]
* Ruby[13]
* Fortress

Julia is a high-level, general-purpose[16] dynamic programming language, designed to be fast and productive,[17] for e.g. data science, artificial intelligence, machine learning, modeling and simulation, most commonly used for numerical analysis and computational science.[18][19][20]

Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, a default just-in-time (JIT) compiler[16][21] (with support for ahead-of-time compilation[22][23][24]) and an efficient (multi-threaded) garbage collection implementation.[25] Notably Julia does not support classes with encapsulated methods and instead it relies on structs with generic methods/functions not tied to them.

By default, Julia is run similarly to scripting languages, using its runtime, and allows for interactions,[22] but Julia programs/source code can also optionally be sent to users in one ready-to-install/run file, which can be made quickly, not needing anything preinstalled.[26] Julia programs can also be (separately) compiled to binary executables, even allowing no-source-code distribution, and the executables can get much smaller with Julia 1.12. Such compilation is not needed for speed, though it can decrease constant-factor startup cost, since Julia is also compiled when running interactively, but it can help with hiding source code. Features of the language can be separately compiled, so Julia can be used, for example, with its runtime or without it (which allows for smaller executables and libraries but is limited in capabilities).

Julia programs can reuse libraries from other languages by calling them, e.g. calling C or Rust libraries, and Julia (libraries) can also be called from other languages, e.g. Python and R, and several Julia packages have been made easily available from those languages, in the form of Python and R libraries for corresponding Julia packages. Calling in either direction has been implemented for many languages, not just those and C++.

Julia's Visual Studio Code extension provides a fully-featured integrated development environment with "built-in dynamic autocompletion, inline results, plot pane, integrated REPL, variable view, code navigation, and many other advanced language features"[27] e.g. debugging is possible, linting, and profiling.[28][29][30][31]

## History

[edit]

Work on Julia began in 2009, when Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and Alan Edelman set out to create a free language that was both high-level and fast. On 14 February 2012, the team launched a website with a blog post explaining the language's mission.[4] In an interview with InfoWorld in April 2012, Karpinski said of the name "Julia": "There's no good reason, really. It just seemed like a pretty name."[19] Bezanson said he chose the name on the recommendation of a friend,[32] then years later wrote:

> Maybe julia stands for "Jeff's uncommon lisp is automated"?[33]

Julia's syntax is now considered stable, since version 1.0 in 2018, and Julia has a backward compatibility guarantee for 1.x and also a stability promise for the documented (stable) API, while in the years before in the early development prior to 0.7 the syntax (and semantics) was changed in new versions. All of the (registered package) ecosystem uses the new and improved syntax, and in most cases relies on new APIs that have been added regularly, and in some cases minor additional syntax added in a forward compatible way e.g. in Julia 1.7.

In the 10 years since the 2012 launch of pre-1.0 Julia, the community has grown. The Julia package ecosystem has over 11.8 million lines of code (including docs and tests).[34] The JuliaCon academic conference for Julia users and developers has been held annually since 2014 with JuliaCon2020[35] welcoming over 28,900 unique viewers,[36] and then JuliaCon2021 breaking all previous records (with more than 300 JuliaCon2021 presentations available for free on YouTube, up from 162 the year before), and 43,000 unique viewers during the conference.[37]

Three of the Julia co-creators are the recipients of the 2019 James H. Wilkinson Prize for Numerical Software (awarded every four years) "for the creation of Julia, an innovative environment for the creation of high-performance tools that enable the analysis and solution of computational science problems."[38] Also, Alan Edelman, professor of applied mathematics at MIT, has been selected to receive the 2019 IEEE Computer Society Sidney Fernbach Award "for outstanding breakthroughs in high-performance computing, linear algebra, and computational science and for contributions to the Julia programming language."[39]

Both Julia 0.7[40] and version 1.0 were released on 8 August 2018. Work on Julia 0.7 was a "huge undertaking" (e.g., because of an "entirely new optimizer"), and some changes were made to semantics, e.g. the iteration interface was simplified.[41] Julia 1.6 was the largest release since 1.0, and it was the long-term support (LTS) version for the longest time, faster on many fronts, e.g. introduced parallel precompilation and faster loading of packages, in some cases "50x speedup in load times for large trees of binary artifacts".[42] Since 1.7 Julia development is back to time-based releases.[43] Julia 1.7 was released in November 2021 with many changes, e.g. a new faster random-number generator and Julia 1.7.3 fixed e.g. at least one security issue.[44] Julia 1.8 was released in 2022 and 1.8.5 in January 2023,[45] with 1.8.x improvements for distributing Julia programs without source code, and compiler speedup, in some cases by 25%,[46] and more controllable inlining (i.e. now also allowing applying `@inline` at the call site, not just on the function itself). Julia 1.9 was released on 7 May 2023. It has many improvements, such as the ability to precompile packages to native machine code (older Julia versions also have precompilation for packages, but only partial, never fully to native code, so those earlier versions had a "first use" penalty, slowing down while waiting to fully compile). Precompiled packages, since version 1.9, can be up to hundreds of times faster on first use (e.g. for CSV.jl and DataFrames.jl), and to improve precompilation of packages a new package PrecompileTools.jl has been introduced. Julia 1.10 was released on 25 December 2023 with many new features, e.g. parallel garbage collection, and improved package load times and a new parser, i.e. it rewritten in Julia, with better error messages and improved stacktrace rendering.[47]

Julia 1.11 was released on 7 October 2024 (and 1.11.4 on 10 March 2025), and with it 1.10.5 became the next long-term support (LTS) version (i.e. those are the only two supported versions), since replaced by 1.10.8 released on 10 March, and 1.6 is no longer an LTS version. Julia 1.11 adds e.g. parallel garbage collection and a new `public` keyword to signal safe public API (Julia users are advised to use such API, not internals, of Julia or packages, and package authors advised to use the keyword, generally indirectly, e.g. prefixed with the `@compat` macro, from Compat.jl, to also support older Julia versions, at least the LTS version). Julia 1.11.1 has much improved startup (over 1.11.0 that had a regression), and over 1.10, and this can be important for some benchmarks.

Much smaller binary executables are possible with `juliac` which is available in the upcoming Julia 1.12.

### JuliaCon

[edit]

Since 2014,[48] the Julia Community has hosted an annual Julia Conference focused on developers and users. The first JuliaCon took place in Chicago and kickstarted the annual occurrence of the conference. Since 2014, the conference has taken place across a number of locations including MIT[49] and the University of Maryland, Baltimore.[50] The event audience has grown from a few dozen people to over 28,900 unique attendees[51] during JuliaCon 2020, which took place virtually. JuliaCon 2021 also took place virtually[52] with keynote addresses from professors William Kahan, the primary architect of the IEEE 754 floating-point standard (which virtually all CPUs and languages, including Julia, use),[53] Jan Vitek,[54] Xiaoye Sherry Li, and Soumith Chintala, a co-creator of PyTorch.[55] JuliaCon grew to 43,000 unique attendees and more than 300 presentations (still freely accessible, plus for older years). JuliaCon 2022 will also be virtual held between July 27 and July 29, 2022, for the first time in several languages, not just in English.

### Sponsors

[edit]

The Julia language became a NumFOCUS fiscally sponsored project in 2014 in an effort to ensure the project's long-term sustainability.[56] Jeremy Kepner at MIT Lincoln Laboratory was the founding sponsor of the Julia project in its early days. In addition, funds from the Gordon and Betty Moore Foundation, the Alfred P. Sloan Foundation, Intel, and agencies such as NSF, DARPA, NIH, NASA, and FAA have been essential to the development of Julia.[57] Mozilla, the maker of Firefox web browser, with its research grants for H1 2019, sponsored "a member of the official Julia team" for the project "Bringing Julia to the Browser",[58] meaning to Firefox and other web browsers.[59][60][61][62] The Julia language is also supported by individual donors on GitHub.[63]

### The Julia company

[edit]

JuliaHub, Inc. was founded in 2015 as Julia Computing, Inc. by Viral B. Shah, Deepak Vinchhi, Alan Edelman, Jeff Bezanson, Stefan Karpinski and Keno Fischer.[64][65]

In June 2017, Julia Computing raised US$4.6 million in seed funding from General Catalyst and Founder Collective,[66] the same month was "granted $910,000 by the Alfred P. Sloan Foundation to support open-source Julia development, including $160,000 to promote diversity in the Julia community",[67] and in December 2019 the company got $1.1 million funding from the US government to "develop a neural component machine learning tool to reduce the total energy consumption of heating, ventilation, and air conditioning (HVAC) systems in buildings".[68] In July 2021, Julia Computing announced they raised a $24 million Series A round led by Dorilton Ventures,[69] which also owns Formula 1 team Williams Racing, that partnered with Julia Computing. Williams' Commercial Director said: "Investing in companies building best-in-class cloud technology is a strategic focus for Dorilton and Julia's versatile platform, with revolutionary capabilities in simulation and modelling, is hugely relevant to our business. We look forward to embedding Julia Computing in the world's most technologically advanced sport".[70] In June 2023, JuliaHub received (again, now under its new name) a $13 million strategic new investment led by AE Industrial Partners HorizonX ("AEI HorizonX"). AEI HorizonX is a venture capital investment platform formed in partnership with The Boeing Company, which uses Julia.[71] Tim Holy's work (at Washington University in St. Louis's Holy Lab) on Julia 1.9 (improving responsiveness) was funded by the Chan Zuckerberg Initiative.

## Language features

[edit]

Wikibooks has a book on the topic of: Introducing Julia

Julia is a general-purpose programming language,[72] while also originally designed for numerical/technical computing. It is also useful for low-level systems programming,[73] as a specification language,[74] high-level synthesis (HLS) tool (for hardware, e.g. FPGAs),[75] and for web programming[76] at both server[77][78] and client[79][80] side.

The main features of the language are:

* Multiple dispatch: providing ability to define function behavior across combinations of argument types
* Dynamic type system: types for documentation, optimization, and dispatch
* Performance approaching that of statically-typed languages like C
* A built-in package manager
* Lisp-like macros and other metaprogramming facilities
* Designed for parallel and distributed computing
* Coroutines: lightweight green threading
* Automatic generation of code for different argument types
* Extensible conversions and promotions for numeric and other types

Multiple dispatch (also termed multimethods in Lisp) is a generalization of single dispatch - the polymorphic mechanism used in common object-oriented programming (OOP) languages, such as Python, C++, Java, JavaScript, and Smalltalk - that uses inheritance. In Julia, all concrete types are subtypes of abstract types, directly or indirectly subtypes of the `Any` type, which is the top of the type hierarchy. Concrete types can not themselves be subtyped the way they can in other languages; composition is used instead (see also inheritance vs subtyping).

By default, the Julia runtime must be pre-installed as user-provided source code is run. Alternatively, Julia (GUI) apps can be quickly bundled up into a single file with AppBundler.jl[26] for "building Julia GUI applications in modern desktop application installer formats. It uses Snap for Linux, MSIX for Windows, and DMG for MacOS as targets. It bundles full Julia within the app".[81] PackageCompiler.jl can build standalone executables that need no Julia source code to run.[22]

In Julia, everything is an object, much like object-oriented languages; however, unlike most object-oriented languages, all functions use multiple dispatch to select methods, rather than single dispatch.

Most programming paradigms can be implemented using Julia's homoiconic macros and packages. Julia's syntactic macros (used for metaprogramming), like Lisp macros, are more powerful than text-substitution macros used in the preprocessor of some other languages such as C, because they work at the level of abstract syntax trees (ASTs). Julia's macro system is hygienic, but also supports deliberate capture when desired (like for anaphoric macros) using the `esc` construct.

Julia draws inspiration from various dialects of Lisp, including Scheme and Common Lisp, and it shares many features with Dylan, also a multiple-dispatch-oriented dynamic language (which features an infix syntax rather than a Lisp-like prefix syntax, while in Julia "everything"[82] is an expression), and with Fortress, another numerical programming language (which features multiple dispatch and a sophisticated parametric type system). While Common Lisp Object System (CLOS) adds multiple dispatch to Common Lisp, not all functions are generic functions.

In Julia, Dylan, and Fortress, extensibility is the default, and the system's built-in functions are all generic and extensible. In Dylan, multiple dispatch is as fundamental as it is in Julia: all user-defined functions and even basic built-in operations like `+` are generic. Dylan's type system, however, does not fully support parametric types, which are more typical of the ML lineage of languages. By default, CLOS does not allow for dispatch on Common Lisp's parametric types; such extended dispatch semantics can only be added as an extension through the CLOS Metaobject Protocol. By convergent design, Fortress also features multiple dispatch on parametric types; unlike Julia, however, Fortress is statically rather than dynamically typed, with separate compiling and executing phases. The language features are summarized in the following table:

Language | Type system | Generic functions | Parametric types

|
|
|

Julia | Dynamic | Default | Yes
Common Lisp | Dynamic | Opt-in | Yes (but no dispatch)
Dylan | Dynamic | Default | Partial (no dispatch)
Fortress | Static | Default | Yes

An example of the extensibility of Julia, the Unitful.jl package adds support for physical units of measurement to the language.

### Interoperability

[edit]

Julia has built-in support for calling C or Fortran language libraries using the `@ccall` macro. Additional libraries allow users to call to or from other languages such as Python,[83] C++,[84][85] Rust, R,[86] Java[87] and to use with SQL.[88][89][90][91]

### Separately-compiled executables option

[edit]

Julia can be compiled to binary executables with PackageCompiler.jl.[22] Smaller executables can also be written using a static subset of the language provided by StaticCompiler.jl that does not support runtime dispatch (nor garbage collection, since excludes the runtime that provides it).[92]

## Interaction

[edit]

The Julia official distribution includes an interactive command-line read–eval–print loop (REPL),[93] with a searchable history, tab completion, and dedicated help and shell modes,[94] which can be used to experiment and test code quickly.[95] The following fragment represents a sample session example where strings are concatenated automatically by println:[96]

julia> p(x) = 2x^2 + 1; f(x, y) = 1 + 2p(x)y
julia> println("Hello world!", " I'm on cloud ", f(0, 4), " as Julia supports recognizable syntax!")
Hello world! I'm on cloud 9 as Julia supports recognizable syntax!

The REPL gives user access to the system shell and to help mode, by pressing `;` or `?` after the prompt (preceding each command), respectively. It also keeps the history of commands, including between sessions.[97] Code can be tested inside Julia's interactive session or saved into a file with a `.jl` extension and run from the command line by typing:[82]

$ julia <filename>

Julia uses UTF-8 and LaTeX codes, allowing it to support common math symbols for many operators, such as ∈ for the `in` operator, typable with `\in` then pressing `Tab ↹` (i.e. uses LaTeX codes, or also possible by simply copy-pasting, e.g. √ and ∛ possible for sqrt and cbrt functions). Julia has support for Unicode 15.1 (Julia 1.12-DEV supports latest 16.0 release[98] for the languages of the world, even for source code, e.g. variable names (while it's recommended to use English for public code, and e.g. package names).

Julia is supported by Jupyter, an online interactive "notebooks" environment,[99] and Pluto.jl, a "reactive notebook" (where notebooks are saved as pure Julia files), a possible replacement for the former kind.[100] In addition Posit's (formerly RStudio Inc's) Quarto publishing system supports Julia, Python, R and Observable JavaScript (those languages have official support by the company, and can even be weaved together in the same notebook document, more languages are unofficially supported).[101][102]

The REPL can be extended with additional modes, and has been with packages, e.g. with an SQL mode,[103] for database access, and RCall.jl adds an R mode, to work with the R language.[104]

### Use with other languages

[edit]

Julia is in practice interoperable with other languages, in fact the majority of the top 20 languages in popular use. Julia can be used to call shared library functions individually, such as those written in C or Fortran, and packages are available to allow calling other languages (which do not provide C-exported functions directly), e.g. Python (with PythonCall.jl), R,[105] MATLAB, C# (and other .NET languages with DotNET.jl, from them with JdotNET), JavaScript, Java (and other JVM languages, such as Scala with JavaCall.jl). And packages for other languages allow to call to Julia, e.g. from Python, R (to Julia 1.10.x currently possible[106]), Rust, Ruby, or C#. Such as with juliacall (part of PythonCall.jl) to call from Python and a different JuliaCall package for calling, Julia up to 1.10.x, from R. Julia has also been used for hardware, i.e. to compile to VHDL, as a high-level synthesis tool, for example FPGAs.[75]

Julia has packages supporting markup languages such as HTML (and also for HTTP), XML, JSON and BSON, and for databases (such as PostgreSQL,[107] Mongo,[108] Oracle, including for TimesTen,[109] MySQL, SQLite, Microsoft SQL Server,[108] Amazon Redshift, Vertica, ODBC) and web use in general.[110][111]

## Package system

[edit]

Julia has a built-in package manager and includes a default registry system.[112] Packages are most often distributed as source code hosted on GitHub, though alternatives can also be used just as well. Packages can also be installed as binaries, using artifacts.[113] Julia's package manager is used to query and compile packages, as well as managing environments. Federated package registries are supported, allowing registries other than the official to be added locally.[114]

## Implementation

[edit]

Julia's core is implemented in Julia and C, together with C++ for the LLVM dependency. The code parsing, code-lowering, and bootstrapping were implemented in FemtoLisp, a Scheme dialect, up to version 1.10.[115] Since that version the new pure-Julia stdlib package JuliaSyntax.jl is used for the parsing (while the old one can still be chosen)[116] which improves speed and "greatly improves parser error messages in various cases".[117] The LLVM compiler infrastructure project is used as the back end for generating optimized machine code for all commonly-used platforms. With some exceptions, the standard library is implemented in Julia.

### Current and future platforms

[edit]

Julia has tier 1 macOS support, for 64-bit Apple Silicon Macs, natively (previously such Apple M1-based Macs were only supported by running in Rosetta 2 emulation[118][119]), and also fully supports Intel-based Macs. Windows on ARM has no official support yet. Julia has "initial support of OpenBSD in julia." but more is coming to make it actually work: https://github.com/JuliaLang/julia/issues/53632 \-->

Julia has four support tiers.[120] All IA-32 processors completely implementing the i686 subarchitecture are supported and all 64-bit x86-64 (aka amd64), i.e. all less than about a decade old are supported. Armv8 (AArch64) processors are supported on first tier (for macOS); otherwise second tier on Linux, and ARMv7 (AArch32) on third tier.[121] Hundreds of packages are GPU-accelerated:[122] Nvidia GPUs have support with CUDA.jl (tier 1 on 64-bit Linux and tier 2 on 64-bit Windows, the package implementing PTX, for compute capability 3.5 (Kepler) or higher; both require CUDA 11+, older package versions work down to CUDA 9). There are also additionally packages supporting other accelerators, such as Google's TPUs,[123] and some Intel (integrated) GPUs, through oneAPI.jl,[124] and AMD's GPUs have support with e.g. OpenCL; and experimental support for the AMD ROCm stack.[125]

On some platforms, Julia may need to be compiled from source code (e.g., the original Raspberry Pi), with specific build options, which has been done and unofficial pre-built binaries (and build instructions) are available.[126][127] Julia has been built for several ARM platforms, from small Raspberry Pis to the world's fastest (at one point, until recently) supercomputer Fugaku's ARM-based A64FX.[128] PowerPC LE (64-bit) has tier 3 support, meaning it "may or may not build", and its tier will lower to 4 for 1.12, i.e. then no longer builds/works.[129] Julia is now supported in Raspbian[130] while support is better for newer Pis, e.g., those with Armv7 or newer; the Julia support is promoted by the Raspberry Pi Foundation.[131] Julia has also been built for 64-bit RISC-V,[132][133] that has some supporting code in core Julia.

While Julia requires an operating system by default, and has no official support to run without or on embedded system platforms such as Arduino, Julia code has still been run on it, with some limitations, i.e. on a baremetal 16 MHz 8-bit (ATmega328P) AVR-microcontroller Arduino with 2 KB RAM (plus 32 KB of flash memory).[134][135]

## Adoption

[edit]

Julia has been adopted at many universities including MIT, Stanford, UC Berkeley, Ferdowsi University of Mashhad and the University of Cape Town. Large private firms across many sectors have adopted the language including Amazon, IBM, JP Morgan AI Research,[136] and ASML. Julia has also been used by government agencies including NASA and the FAA, as well as every US national energy laboratory.[17][137]

### Scientific computing and engineering

[edit]

* Amazon, for quantum computing[138] and machine learning through Amazon SageMaker[139]
* ASML, for hard real-time programming with their machines[140]
* The Climate Modeling Alliance[141] for climate change modeling[142]
* CERN, to analyze data from the Large Hadron Collider (LHCb experiment)[143][144][145][146][147][148]
* NASA and the Jet Propulsion Laboratory use Julia to model spacecraft separation dynamics,[149][150][151] analyze TRAPPIST exoplanet datasets,[152][153] and analyze cosmic microwave background data from the Big Bang[154]
* The Brazilian INPE, for space missions and satellite simulations[155]
* Julia has also flown in space, on a small satellite,[156] used for a GPS module. And Julia has also been used to design satellites constallations.[157]
* Embedded hardware to plan and execute flight of autonomous U.S. Air Force Research Laboratory VTOL drones[158]

#### Pharmaceuticals and drug development

[edit]

Julia is widely used for drug development in the pharmaceutical industry, having been adopted by Moderna, Pfizer, AstraZeneca, Procter & Gamble, and United Therapeutics.[159][160]

### Economics, finance, and political science

[edit]

* The Federal Reserve Bank of New York, for macroeconomic modeling in Julia since 2015, including estimates of COVID-19 shocks in 2021[161]
* Also the Bank of Canada, central bank, for macroeconomic modeling[162]
* BlackRock, the world's largest asset manager, for financial time-series analysis[163]
* Aviva, the UK's largest general insurer, for actuarial calculations[163]
* Mitre Corporation, for verification of published election results[164]
* Nobel laureate Thomas J. Sargent, for macroeconometric modeling[165]

## See also

[edit]

* Comparison of numerical-analysis software
* Comparison of statistical packages
* Differentiable programming
* JuMP – an algebraic modeling language for mathematical optimization embedded in Julia
* Python
* Nim
* Ring
* Mojo

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[edit]

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## Further reading

[edit]

* Nagar, Sandeep (2017). Beginning Julia Programming: For Engineers and Scientists. Springer. ISBN 978-1-4842-3171-5.
* Bezanson, J; Edelman, A; Karpinski, S; Shah, V. B (2017). "Julia: A fresh approach to numerical computing". SIAM Review. 59 (1): 65–98\. arXiv:1411.1607. CiteSeerX 10.1.1.760.8894. doi:10.1137/141000671. S2CID 13026838.65-98&rft.date=2017&rft_id=info:arxiv/1411.1607&rft_id=https://api.semanticscholar.org/CorpusID:13026838#id-name=S2CID&rft_id=https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.8894#id-name=CiteSeerX&rft_id=info:doi/10.1137/141000671&rft.aulast=Bezanson&rft.aufirst=J&rft.au=Edelman,+A&rft.au=Karpinski,+S&rft.au=Shah,+V.+B&rfr_id=info:sid/en.wikipedia.org:Julia+(programming+language)" class="Z3988">
* Joshi, Anshul (2016). Julia for Data Science － Explore the world of data science from scratch with Julia by your side. Packt. ISBN 978-1-78355-386-0.
* Tobin A Driscoll and Richard J. Braun (Aug. 2022). "Fundamentals of Numerical Computation: Julia Edition". SIAM. ISBN 978-1-611977-00-4.
* C. T. Kelley (2022). "Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia", SIAM. ISBN 978-1-611977-26-4.
* Kalicharan, Noel (2021). Julia - Bit by Bit. Undergraduate Topics in Computer Science. Springer. doi:10.1007/978-3-030-73936-2. ISBN 978-3-030-73936-2. S2CID 235917112.
* Clemens Heitzinger (2022): "Algorithms with Julia", Springer, ISBN 978-3-031-16559-7.

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* AMPL
* APMonitor
* ECLiPSe-CLP
* Gekko
* GAMS
* GNU MathProg
* JuMP
* LINDO
* OPL
* Mathematica
* MiniZinc
* OptimJ
* PuLP
* Pyomo
* TOMLAB
* Xpress Mosel
* ZIMPL

Solvers|

| LP, MILP∗|

* APOPT∗
* ANTIGONE∗
* Artelys Knitro∗
* BCP∗
* CLP
* CBC∗
* CPLEX∗
* FortMP∗
* GCG∗
* GLOP∗
* GLPK/GLPSOL∗
* Gurobi Optimizer∗
* HiGHS∗
* LINDO∗
* Lp_solve
* LOQO
* Mathematica
* MINOS
* MINTO∗
* MOSEK∗
* NAG
* SCIP∗
* SoPlex
* Octeract Engine∗
* SYMPHONY∗
* Xpress Optimizer∗

|

QP, MIQP∗|

* APOPT∗
* ANTIGONE∗
* Artelys Knitro∗
* CBC∗
* CLP
* CPLEX∗
* FortMP∗
* HiGHS
* Gurobi Optimizer∗
* IPOPT
* LINDO∗
* Mathematica
* MINOS
* MOSEK∗
* NAG
* Octeract Engine∗
* SCIP∗
* Xpress Optimizer∗

QCP, MIQCP∗|

* APOPT∗
* ANTIGONE∗
* Artelys Knitro∗
* CPLEX∗
* Gurobi Optimizer∗
* IPOPT
* LINDO∗
* Mathematica
* MINOS
* MOSEK∗
* NAG
* SCIP∗
* Octeract Engine∗
* Xpress Optimizer∗
* Xpress NonLinear∗

SOCP, MISOCP∗|

* Artelys Knitro∗
* CPLEX∗
* Gurobi Optimizer∗
* LINDO∗
* LOQO
* Mathematica
* MOSEK∗
* NAG
* SCIP∗
* Xpress Optimizer∗

SDP, MISDP∗|

* Mathematica
* MOSEK
* NAG

NLP, MINLP∗|

* AOA∗
* APOPT∗
* ANTIGONE∗
* Artelys Knitro∗
* BARON∗
* Couenne∗
* Galahad library
* Gurobi Optimizer∗
* IPOPT
* LINDO∗
* LOQO
* MIDACO∗
* MINOS
* NAG
* NLPQLP
* NPSOL
* SCIP∗
* SNOPT∗
* Octeract Engine∗
* WORHP
* Xpress NonLinear∗

GO|

* ANTIGONE∗
* BARON
* Couenne∗
* Xpress Global
* Mathematica
* LINDO
* SCIP
* Octeract Engine

CP|

* Artelys Kalis
* Comet
* CPLEX CP Optimizer
* Gecode
* Mathematica
* JaCoP
* Xpress Kalis

* List of optimization software
* Comparison of optimization software

* v
* t
* e

Statistical software

Public domain|

* Dataplot
* Epi Info
* CSPro
* X-12-ARIMA

Open-source|

* ADMB
* DAP
* gretl
* jamovi
* JASP
* JAGS
* JMulTi
* Julia
* Jupyter (Julia, Python, R)
* GNU Octave
* OpenBUGS
* Orange
* PSPP
* Python (statsmodels, PyMC3, IPython, IDLE)
* R (RStudio)
* SageMath
* SimFiT
* SOFA Statistics
* Stan
* XLispStat

Freeware|

* BV4.1
* CumFreq
* SegReg
* XploRe
* WinBUGS

Commercial|

| Cross-platform|

* Data Desk
* GAUSS
* GraphPad InStat
* GraphPad Prism
* IBM SPSS Statistics
* IBM SPSS Modeler
* JMP
* Maple
* Mathcad
* Mathematica
* MATLAB
* OxMetrics
* RATS
* Revolution Analytics
* SAS
* SmartPLS
* Stata
* StatView
* SUDAAN
* S-PLUS
* TSP
* World Programming System (WPS)

|

Windows only|

* BMDP
* EViews
* GenStat
* LIMDEP
* LISREL
* MedCalc
* Microfit
* Minitab
* MLwiN
* NCSS
* Shazam
* SigmaStat
* Statistica
* StatsDirect
* StatXact
* SYSTAT
* The Unscrambler
* Unistat

Excel add-ons|

* Analyse-it
* Unistat for Excel
* XLfit
* RExcel

Comparison • Category

* v
* t
* e

Differentiable computing

General|

* Differentiable programming
* Information geometry
* Statistical manifold
* Automatic differentiation
* Neuromorphic computing
* Pattern recognition
* Ricci calculus
* Computational learning theory
* Inductive bias

Hardware|

* IPU
* TPU
* VPU
* Memristor
* SpiNNaker

Software libraries|

* TensorFlow
* PyTorch
* Keras
* scikit-learn
* Theano
* JAX
* Flux.jl
* MindSpore

* Portals
* Computer programming
* Technology

Authority control databases

International|

* FAST

National|

* United States
* France
* BnF data
* Israel

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