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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 · CliffordNumbers.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://brainandforce.github.io/CliffordNumbers.jl/home.html"/><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></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="home.html">CliffordNumbers.jl</a></span></div><form class="docs-search" action="search.html"><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.html">Home</a><ul class="internal"><li><a class="tocitem" href="#Design-goals"><span>Design goals</span></a></li></ul></li><li><a class="tocitem" href="numeric.html">Clifford number types</a></li><li><a class="tocitem" href="metrics.html">Metric signatures</a></li><li><a class="tocitem" href="indexing.html">Indexing</a></li><li><a class="tocitem" href="operations.html">Operations</a></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="api/clifford.html">CliffordNumbers</a></li><li><a class="tocitem" href="api/indexing.html">Indexing</a></li><li><a class="tocitem" href="api/math.html">Math</a></li><li><a class="tocitem" href="api/metrics.html">Metric signatures</a></li><li><a class="tocitem" href="api/internal.html">Internals</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.html">Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="home.html">Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/brainandforce/CliffordNumbers.jl/blob/main/docs/src/home.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="CliffordNumbers"><a class="docs-heading-anchor" href="#CliffordNumbers">CliffordNumbers</a><a id="CliffordNumbers-1"></a><a class="docs-heading-anchor-permalink" href="#CliffordNumbers" title="Permalink"></a></h1><p><a href="https://github.com/brainandforce/CliffordNumbers.jl">CliffordNumbers.jl</a> is a package that provides fully static multivectors (Clifford numbers) in arbitrary dimensions and metrics. While in many cases, sparse representations of multivectors are more efficient, for spaces of low dimension, dense static representations may provide a performance and convenience advantage.</p><h2 id="Design-goals"><a class="docs-heading-anchor" href="#Design-goals">Design goals</a><a id="Design-goals-1"></a><a class="docs-heading-anchor-permalink" href="#Design-goals" title="Permalink"></a></h2><p>The goal of this package is to provide a multivector implementation that:</p><ul><li>Allows for the construction of multivectors in arbitrary metrics, with coefficients that subtype any instance of Julia&#39;s base numeric types, <code>Real</code> or <code>Complex</code>.</li><li>Provides data structures of fixed sizes that represent multivectors. This allows for instances to be allocated on the stack or stored inline in an <code>Array</code> rather than as pointers to individually allocated instances.</li><li>Provides dense representations of multivectors, as well as convenient sparse representations, which can be constructed from each other, converted in a way that guarantees representability, and allows for promotion between instances.</li><li>Subtypes <code>Number</code>: The term &quot;Clifford number&quot; emphasizes the perspective of multivectors as an extension of the real numbers, in the same way that complex numbers and quaternions extend them. (It should be noted that both complex numbers and quaternions are Clifford algebras themselves!)</li><li>Aggressively optimizes all mathematical operations, utilizing <code>fma</code> operations and SIMD instructions whenever possible.</li><li>Interoperates with automatic differentiation tools and other packages which allow for the implementation of operations from geometric calculus.</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="numeric.html">Clifford number types »</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 0.27.23 on <span class="colophon-date" title="Friday 17 May 2024 00:44">Friday 17 May 2024</span>. Using Julia version 1.10.3.</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 · CliffordNumbers.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://brainandforce.github.io/CliffordNumbers.jl/home.html"/><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></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="home.html">CliffordNumbers.jl</a></span></div><form class="docs-search" action="search.html"><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.html">Home</a><ul class="internal"><li><a class="tocitem" href="#Design-goals"><span>Design goals</span></a></li></ul></li><li><a class="tocitem" href="numeric.html">Clifford number types</a></li><li><a class="tocitem" href="metrics.html">Metric signatures</a></li><li><a class="tocitem" href="indexing.html">Indexing</a></li><li><a class="tocitem" href="operations.html">Operations</a></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="api/clifford.html">CliffordNumbers</a></li><li><a class="tocitem" href="api/indexing.html">Indexing</a></li><li><a class="tocitem" href="api/math.html">Math</a></li><li><a class="tocitem" href="api/metrics.html">Metric signatures</a></li><li><a class="tocitem" href="api/internal.html">Internals</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.html">Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="home.html">Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/brainandforce/CliffordNumbers.jl/blob/main/docs/src/home.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="CliffordNumbers"><a class="docs-heading-anchor" href="#CliffordNumbers">CliffordNumbers</a><a id="CliffordNumbers-1"></a><a class="docs-heading-anchor-permalink" href="#CliffordNumbers" title="Permalink"></a></h1><p><a href="https://github.com/brainandforce/CliffordNumbers.jl">CliffordNumbers.jl</a> is a package that provides fully static multivectors (Clifford numbers) in arbitrary dimensions and metrics. While in many cases, sparse representations of multivectors are more efficient, for spaces of low dimension, dense static representations may provide a performance and convenience advantage.</p><h2 id="Design-goals"><a class="docs-heading-anchor" href="#Design-goals">Design goals</a><a id="Design-goals-1"></a><a class="docs-heading-anchor-permalink" href="#Design-goals" title="Permalink"></a></h2><p>The goal of this package is to provide a multivector implementation that:</p><ul><li>Allows for the construction of multivectors in arbitrary metrics, with coefficients that subtype any instance of Julia&#39;s base numeric types, <code>Real</code> or <code>Complex</code>.</li><li>Provides data structures of fixed sizes that represent multivectors. This allows for instances to be allocated on the stack or stored inline in an <code>Array</code> rather than as pointers to individually allocated instances.</li><li>Provides dense representations of multivectors, as well as convenient sparse representations, which can be constructed from each other, converted in a way that guarantees representability, and allows for promotion between instances.</li><li>Subtypes <code>Number</code>: The term &quot;Clifford number&quot; emphasizes the perspective of multivectors as an extension of the real numbers, in the same way that complex numbers and quaternions extend them. (It should be noted that both complex numbers and quaternions are Clifford algebras themselves!)</li><li>Aggressively optimizes all mathematical operations, utilizing <code>fma</code> operations and SIMD instructions whenever possible.</li><li>Interoperates with automatic differentiation tools and other packages which allow for the implementation of operations from geometric calculus.</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="numeric.html">Clifford number types »</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 0.27.23 on <span class="colophon-date" title="Friday 17 May 2024 05:14">Friday 17 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>