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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · IntervalArithmetic.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://juliaintervals.github.io/IntervalArithmetic.jl/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="assets/intervalarithmetic.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>IntervalArithmetic.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Citation"><span>Citation</span></a></li><li><a class="tocitem" href="#Related-packages"><span>Related packages</span></a></li><li><a class="tocitem" href="#History"><span>History</span></a></li></ul></li><li><a class="tocitem" href="intro/">Overview</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="manual/construction/">Constructing intervals</a></li><li><a class="tocitem" href="manual/usage/">Usage</a></li><li><a class="tocitem" href="manual/decorations/">Decorations</a></li><li><a class="tocitem" href="manual/api/">API</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaIntervals/IntervalArithmetic.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="IntervalArithmetic.jl"><a class="docs-heading-anchor" href="#IntervalArithmetic.jl">IntervalArithmetic.jl</a><a id="IntervalArithmetic.jl-1"></a><a class="docs-heading-anchor-permalink" href="#IntervalArithmetic.jl" title="Permalink"></a></h1><p>IntervalArithmetic.jl is a Julia package for validated numerics in Julia. All calculations are carried out using <a href="https://en.wikipedia.org/wiki/Interval_arithmetic">interval arithmetic</a> where quantities are treated as intervals. The final result is a rigorous enclosure of the true value.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; using Pkg # Julia v1.8 or above</code><code class="nohighlight hljs ansi" style="display:block;"></code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Pkg.add(&quot;IntervalArithmetic&quot;)</code><code class="nohighlight hljs ansi" style="display:block;"></code></pre><h2 id="Citation"><a class="docs-heading-anchor" href="#Citation">Citation</a><a id="Citation-1"></a><a class="docs-heading-anchor-permalink" href="#Citation" title="Permalink"></a></h2><p>If you use the IntervalArithmetic library in your publication, research, teaching, or other activities, please use the BibTeX template <a href="https://github.com/JuliaIntervals/IntervalArithmetic.jl/blob/main/CITATION.bib">CITATION.bib</a>.</p><h2 id="Related-packages"><a class="docs-heading-anchor" href="#Related-packages">Related packages</a><a id="Related-packages-1"></a><a class="docs-heading-anchor-permalink" href="#Related-packages" title="Permalink"></a></h2><ul><li><a href="https://github.com/andrioni/MPFI.jl">MPFI.jl</a>, a Julia wrapper around the <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html">MPFI C library</a>, a multiple-precision interval arithmetic library based on MPFR</li><li><a href="https://github.com/invenia/Intervals.jl">Intervals.jl</a>, an alternative implementation of basic interval functions by Invenia Technical Computing</li></ul><h2 id="History"><a class="docs-heading-anchor" href="#History">History</a><a id="History-1"></a><a class="docs-heading-anchor-permalink" href="#History" title="Permalink"></a></h2><p>This project began in 2014 during a masters&#39; course in the postgraduate programs of Mathematics and Physics at the Universidad Nacional Autónoma de México. It was initially written in Python, then reinitiated in 2015 and rewritten in Julia. We thank the participants of the courses for their contribution, energy and ideas.</p><h3 id="Support"><a class="docs-heading-anchor" href="#Support">Support</a><a id="Support-1"></a><a class="docs-heading-anchor-permalink" href="#Support" title="Permalink"></a></h3><p>Financial support is acknowledged from DGAPA-UNAM PAPIME grants PE-105911 and PE-107114, and DGAPA-UNAM PAPIIT grant IN-117214.</p><p>Luis Benet acknowledges support from <em>Cátedra Marcos Moshinsky</em> (2013).</p><p>David P. Sanders acknowledges a sabbatical fellowship from CONACYT and thanks Alan Edelman and the Julia group at MIT for hosting his sabbatical visit.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="intro/">Overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 5 September 2023 17:41">Tuesday 5 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · IntervalArithmetic.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://juliaintervals.github.io/IntervalArithmetic.jl/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="assets/intervalarithmetic.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>IntervalArithmetic.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Citation"><span>Citation</span></a></li><li><a class="tocitem" href="#Related-packages"><span>Related packages</span></a></li><li><a class="tocitem" href="#History"><span>History</span></a></li></ul></li><li><a class="tocitem" href="intro/">Overview</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="manual/construction/">Constructing intervals</a></li><li><a class="tocitem" href="manual/usage/">Usage</a></li><li><a class="tocitem" href="manual/decorations/">Decorations</a></li><li><a class="tocitem" href="manual/api/">API</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaIntervals/IntervalArithmetic.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="IntervalArithmetic.jl"><a class="docs-heading-anchor" href="#IntervalArithmetic.jl">IntervalArithmetic.jl</a><a id="IntervalArithmetic.jl-1"></a><a class="docs-heading-anchor-permalink" href="#IntervalArithmetic.jl" title="Permalink"></a></h1><p>IntervalArithmetic.jl is a Julia package for validated numerics in Julia. All calculations are carried out using <a href="https://en.wikipedia.org/wiki/Interval_arithmetic">interval arithmetic</a> where quantities are treated as intervals. The final result is a rigorous enclosure of the true value.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; using Pkg # Julia v1.8 or above</code><code class="nohighlight hljs ansi" style="display:block;"></code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Pkg.add(&quot;IntervalArithmetic&quot;)</code><code class="nohighlight hljs ansi" style="display:block;"></code></pre><h2 id="Citation"><a class="docs-heading-anchor" href="#Citation">Citation</a><a id="Citation-1"></a><a class="docs-heading-anchor-permalink" href="#Citation" title="Permalink"></a></h2><p>If you use the IntervalArithmetic library in your publication, research, teaching, or other activities, please use the BibTeX template <a href="https://github.com/JuliaIntervals/IntervalArithmetic.jl/blob/main/CITATION.bib">CITATION.bib</a>.</p><h2 id="Related-packages"><a class="docs-heading-anchor" href="#Related-packages">Related packages</a><a id="Related-packages-1"></a><a class="docs-heading-anchor-permalink" href="#Related-packages" title="Permalink"></a></h2><ul><li><a href="https://github.com/andrioni/MPFI.jl">MPFI.jl</a>, a Julia wrapper around the <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html">MPFI C library</a>, a multiple-precision interval arithmetic library based on MPFR</li><li><a href="https://github.com/invenia/Intervals.jl">Intervals.jl</a>, an alternative implementation of basic interval functions by Invenia Technical Computing</li></ul><h2 id="History"><a class="docs-heading-anchor" href="#History">History</a><a id="History-1"></a><a class="docs-heading-anchor-permalink" href="#History" title="Permalink"></a></h2><p>This project began in 2014 during a masters&#39; course in the postgraduate programs of Mathematics and Physics at the Universidad Nacional Autónoma de México. It was initially written in Python, then reinitiated in 2015 and rewritten in Julia. We thank the participants of the courses for their contribution, energy and ideas.</p><h3 id="Support"><a class="docs-heading-anchor" href="#Support">Support</a><a id="Support-1"></a><a class="docs-heading-anchor-permalink" href="#Support" title="Permalink"></a></h3><p>Financial support is acknowledged from DGAPA-UNAM PAPIME grants PE-105911 and PE-107114, and DGAPA-UNAM PAPIIT grant IN-117214.</p><p>Luis Benet acknowledges support from <em>Cátedra Marcos Moshinsky</em> (2013).</p><p>David P. Sanders acknowledges a sabbatical fellowship from CONACYT and thanks Alan Edelman and the Julia group at MIT for hosting his sabbatical visit.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="intro/">Overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 5 September 2023 17:43">Tuesday 5 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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