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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>About Nemo · Nemo.jl</title><meta name="title" content="About Nemo · Nemo.jl"/><meta property="og:title" content="About Nemo · Nemo.jl"/><meta property="twitter:title" content="About Nemo · Nemo.jl"/><meta name="description" content="Documentation for Nemo.jl."/><meta property="og:description" content="Documentation for Nemo.jl."/><meta property="twitter:description" content="Documentation for Nemo.jl."/><script data-outdated-warner src="../assets/warner.js"></script><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/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="../search_index.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></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Nemo.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Getting Started</a></li><li class="is-active"><a class="tocitem" href>About Nemo</a><ul class="internal"><li><a class="tocitem" href="#Why-Julia?"><span>Why Julia?</span></a></li></ul></li><li><a class="tocitem" href="../types/">Types in Nemo</a></li><li><a class="tocitem" href="../constructors/">Constructing mathematical objects in Nemo</a></li><li><span class="tocitem">Rings</span><ul><li><a class="tocitem" href="../integer/">Integers</a></li><li><a class="tocitem" href="../polynomial/">Univariate polynomials</a></li><li><a class="tocitem" href="../mpolynomial/">Multivariate polynomials</a></li><li><a class="tocitem" href="../series/">Power series and Laurent series</a></li><li><a class="tocitem" href="../puiseux/">Puiseux series</a></li><li><a class="tocitem" href="../residue/">Residue rings</a></li></ul></li><li><span class="tocitem">Fields</span><ul><li><a class="tocitem" href="../fraction/">Fraction fields</a></li><li><a class="tocitem" href="../rational/">Rationals</a></li><li><a class="tocitem" href="../algebraic/">Algebraic numbers</a></li><li><a class="tocitem" href="../exact/">Exact real and complex numbers</a></li><li><a class="tocitem" href="../complex/">Arbitrary precision complex balls</a></li><li><a class="tocitem" href="../real/">Arbitrary precision real balls</a></li><li><a class="tocitem" href="../arb/">Fixed precision real balls</a></li><li><a class="tocitem" href="../acb/">Fixed precisioncomplex balls</a></li><li><a class="tocitem" href="../gfp/">Galois fields</a></li><li><a class="tocitem" href="../finitefield/">Finite fields</a></li><li><a class="tocitem" href="../ff_embedding/">Finite field embeddings</a></li><li><a class="tocitem" href="../numberfield/">Number field arithmetic</a></li><li><a class="tocitem" href="../padic/">Padics</a></li><li><a class="tocitem" href="../qadic/">Qadics</a></li></ul></li><li><a class="tocitem" href="../matrix/">Matrices</a></li><li><a class="tocitem" href="../factor/">Factorisation</a></li><li><a class="tocitem" href="../misc/">Miscellaneous</a></li><li><span class="tocitem">Developer</span><ul><li><a class="tocitem" href="../developer/introduction/">Introduction to Nemo development</a></li><li><a class="tocitem" href="../developer/conventions/">Conventions</a></li><li><a class="tocitem" href="../developer/typesystem/">The type system</a></li><li><a class="tocitem" href="../developer/parents/">Parent objects</a></li><li><a class="tocitem" href="../developer/interfaces/">Interfaces</a></li><li><a class="tocitem" href="../developer/topics/">Specific topics</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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>About Nemo</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>About Nemo</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Nemocas/Nemo.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Nemocas/Nemo.jl/blob/master/docs/src/about.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="About-Nemo"><a class="docs-heading-anchor" href="#About-Nemo">About Nemo</a><a id="About-Nemo-1"></a><a class="docs-heading-anchor-permalink" href="#About-Nemo" title="Permalink"></a></h1><p>Nemo is a library for fast basic arithmetic in various commonly used rings, for the Julia programming language. Our aim is to provide a highly performant package covering</p><ul><li>Commutative Algebra</li><li>Number Theory</li><li>Group Theory</li></ul><p>Nemo consists of wrappers of specialised C/C++ libraries:</p><ul><li>Flint    <a href="http://flintlib.org/">http://flintlib.org/</a></li><li>Arb      <a href="https://arblib.org/">https://arblib.org/</a></li><li>Antic    <a href="https://github.com/wbhart/antic/">https://github.com/wbhart/antic/</a></li><li>Calcium  <a href="https://fredrikj.net/calcium/">https://fredrikj.net/calcium/</a></li></ul><p>Nemo also uses AbstractAlgebra.jl to provide generic constructions over the basic rings provided by the above packages.</p><h2 id="Why-Julia?"><a class="docs-heading-anchor" href="#Why-Julia?">Why Julia?</a><a id="Why-Julia?-1"></a><a class="docs-heading-anchor-permalink" href="#Why-Julia?" title="Permalink"></a></h2><p>Julia is a sophisticated, modern programming language which is designed to be both performant and flexible. It was written by mathematicians, for mathematicians.</p><p>The benefits of Julia include</p><ul><li>Familiar imperative syntax</li><li>JIT compilation (provides near native performance, even for highly generic code)</li><li>REPL console (cuts down on development time)</li><li>Parametric types (allows for fast generic constructions over other data types)</li><li>Powerful metaprogramming facilities</li><li>Operator overloading</li><li>Multiple dispatch (dispatch on every argument of a function)</li><li>Efficient native C interface (little or no wrapper overhead)</li><li>Experimental C++ interface</li><li>Dynamic type inference</li><li>Built-in bignums</li><li>Able to be embedded in C programs</li><li>High performance collection types (dictionaries, iterators, arrays, etc.)</li><li>Jupyter support (for web based notebooks)</li></ul><p>The main benefits for Nemo are the parametric type system and JIT compilation. The former allows us to model many mathematical types, e.g. generic polynomial rings over an arbitrary base ring. The latter speeds up the runtime performance, even of highly generic mathematical procedures.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Getting Started</a><a class="docs-footer-nextpage" href="../types/">Types in Nemo »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 10 February 2024 08:09">Saturday 10 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>