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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Glossary · SymbolicGA.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://serenity4.github.io/SymbolicGA.jl/stable/glossary/"/><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><script src="https://plausible.io/js/script.js" data-domain="serenity4.github.io" defer></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">SymbolicGA.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><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Glossary</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../tutorial/getting_started/">Getting started</a></li><li><a class="tocitem" href="../tutorial/euclidean_transformations/">Euclidean transformations</a></li><li><a class="tocitem" href="../tutorial/integration/">Integration with your own types</a></li></ul></li><li><span class="tocitem">Explanation</span><ul><li><a class="tocitem" href="../explanation/geometric_algebra/">Geometric Algebra</a></li><li><a class="tocitem" href="../explanation/design/">Design</a></li></ul></li><li><span class="tocitem">How to</span><ul><li><a class="tocitem" href="../howto/integration/">Use macros with custom types</a></li><li><a class="tocitem" href="../howto/spaces/">Create user-defined geometric spaces</a></li></ul></li><li><span class="tocitem">Reference</span><ul><li><a class="tocitem" href="../reference/symbols/">Symbols &amp; operators</a></li><li><a class="tocitem" href="../reference/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>Glossary</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Glossary</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/serenity4/SymbolicGA.jl/blob/main/docs/src/glossary.md#L" 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="Glossary"><a class="docs-heading-anchor" href="#Glossary">Glossary</a><a id="Glossary-1"></a><a class="docs-heading-anchor-permalink" href="#Glossary" title="Permalink"></a></h1><p><strong>Geometric algebra</strong>: Mathematical framework based around the geometric product, relying on an <a href="https://en.wikipedia.org/wiki/Exterior_algebra">exterior algebra</a> to construct entities of geometric significance.</p><p><strong>Geometric space</strong>: Mathematical space defined with objects and a geometric product satisfying the axioms of geometric algebra, using a metric defined by a custom signature. Usually described as an algebra in most presentations of geometric algebra, e.g. PGA or CGA, even though different &quot;algebras&quot; are still algebraically very similar, as they use the same rules - just a different base space and metric.</p><p><strong>Signature</strong>: Parameter of a geometric space determining the scalar value of the square of its basis vectors under the geometric product.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorial/getting_started/">Getting started »</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 8 August 2023 16:15">Tuesday 8 August 2023</span>. Using Julia version 1.9.2.</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>Glossary · SymbolicGA.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://serenity4.github.io/SymbolicGA.jl/stable/glossary/"/><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><script src="https://plausible.io/js/script.js" data-domain="serenity4.github.io" defer></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">SymbolicGA.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><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Glossary</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../tutorial/getting_started/">Getting started</a></li><li><a class="tocitem" href="../tutorial/euclidean_transformations/">Euclidean transformations</a></li><li><a class="tocitem" href="../tutorial/integration/">Integration with your own types</a></li></ul></li><li><span class="tocitem">Explanation</span><ul><li><a class="tocitem" href="../explanation/geometric_algebra/">Geometric Algebra</a></li><li><a class="tocitem" href="../explanation/design/">Design</a></li></ul></li><li><span class="tocitem">How to</span><ul><li><a class="tocitem" href="../howto/integration/">Use macros with custom types</a></li><li><a class="tocitem" href="../howto/spaces/">Create user-defined geometric spaces</a></li></ul></li><li><span class="tocitem">Reference</span><ul><li><a class="tocitem" href="../reference/symbols/">Symbols &amp; operators</a></li><li><a class="tocitem" href="../reference/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>Glossary</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Glossary</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/serenity4/SymbolicGA.jl/blob/main/docs/src/glossary.md#L" 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="Glossary"><a class="docs-heading-anchor" href="#Glossary">Glossary</a><a id="Glossary-1"></a><a class="docs-heading-anchor-permalink" href="#Glossary" title="Permalink"></a></h1><p><strong>Geometric algebra</strong>: Mathematical framework based around the geometric product, relying on an <a href="https://en.wikipedia.org/wiki/Exterior_algebra">exterior algebra</a> to construct entities of geometric significance.</p><p><strong>Geometric space</strong>: Mathematical space defined with objects and a geometric product satisfying the axioms of geometric algebra, using a metric defined by a custom signature. Usually described as an algebra in most presentations of geometric algebra, e.g. PGA or CGA, even though different &quot;algebras&quot; are still algebraically very similar, as they use the same rules - just a different base space and metric.</p><p><strong>Signature</strong>: Parameter of a geometric space determining the scalar value of the square of its basis vectors under the geometric product.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorial/getting_started/">Getting started »</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="Thursday 14 September 2023 15:05">Thursday 14 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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