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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script data-outdated-warner src="../assets/warner.js"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 & 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 "algebras" 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 & 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 "algebras" 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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