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19 lines
33 KiB
JavaScript
19 lines
33 KiB
JavaScript
import{$ as e,B as t,P as n,_ as r,f as i,g as a,h as o,l as s}from"./runtime-core.esm-bundler-TY2dTQsQ.js";import{t as c}from"./plugin-vue_export-helper-PrwMxFSs.js";var l=JSON.parse(`{"path":"/en/guide/markdown/math/","title":"Mathematical Formulas | Guide","lang":"en-US","frontmatter":{"title":"Mathematical Formulas","icon":"tabler:math","createTime":"2025/11/29 21:36:22","permalink":"/en/guide/markdown/math/","description":"Overview The theme has built-in support for mathematical formulas. This feature is powered by @vuepress/plugin-markdown-math. You can choose to render mathematical formulas in m...","head":[["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Mathematical Formulas\\",\\"image\\":[\\"\\"],\\"dateModified\\":\\"2025-12-01T03:30:33.000Z\\",\\"author\\":[]}"],["meta",{"property":"og:url","content":"https://theme-plume.vuejs.press/en/guide/markdown/math/"}],["meta",{"property":"og:site_name","content":"Plume Theme"}],["meta",{"property":"og:title","content":"Mathematical Formulas"}],["meta",{"property":"og:description","content":"Overview The theme has built-in support for mathematical formulas. This feature is powered by @vuepress/plugin-markdown-math. You can choose to render mathematical formulas in m..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"en-US"}],["meta",{"property":"og:locale:alternate","content":"zh-CN"}],["meta",{"property":"og:updated_time","content":"2025-12-01T03:30:33.000Z"}],["meta",{"property":"article:modified_time","content":"2025-12-01T03:30:33.000Z"}],["link",{"rel":"alternate","hreflang":"zh-cn","href":"https://theme-plume.vuejs.press/guide/markdown/math/"}]]},"readingTime":{"minutes":1.6,"words":479},"git":{"createdTime":1764559833000,"updatedTime":1764559833000,"contributors":[{"name":"pengzhanbo","username":"pengzhanbo","email":"volodymyr@foxmail.com","commits":1,"avatar":"https://avatars.githubusercontent.com/pengzhanbo?v=4","url":"https://github.com/pengzhanbo"}],"changelog":[{"hash":"db8a46eb4cdc6c4bcb15f0e38a5aacfef565975a","time":1764559833000,"email":"volodymyr@foxmail.com","author":"pengzhanbo","message":"docs: optimize and completion docs (#766)"}]},"autoDesc":true,"filePathRelative":"en/guide/markdown/math.md","headers":[],"bulletin":false}`),u={name:`math.md`},d={class:`code-block-title`,"data-title":`.vuepress/config.ts`},f={class:`code-block-title-bar`},p={class:`title`},m={class:`vp-field-group`},h={class:`vp-field-group`},g={class:`vp-field-group`};function _(c,l,u,_,v,y){let b=t(`VPIcon`),x=t(`CodeTabs`),S=t(`VPDemoBasic`),C=t(`VPField`);return n(),i(`div`,null,[l[20]||=o(`<h2 id="overview" tabindex="-1"><a class="header-anchor" href="#overview"><span>Overview</span></a></h2><p>The theme has built-in support for mathematical formulas.</p><p>This feature is powered by <a href="https://ecosystem.vuejs.press/zh/plugins/markdown/markdown-math.html" target="_blank" rel="noopener noreferrer">@vuepress/plugin-markdown-math</a>. You can choose to render mathematical formulas in markdown using the following methods:</p><ul><li><code>katex</code> (default)</li><li><code>mathjax</code></li></ul><h2 id="usage" tabindex="-1"><a class="header-anchor" href="#usage"><span>Usage</span></a></h2>`,5),s(`div`,d,[s(`div`,f,[s(`span`,p,[r(b,{provider:`iconify`,name:`vscode-icons:file-type-typescript`}),l[0]||=a(`.vuepress/config.ts`,-1)])]),l[1]||=o(`<div class="language-ts line-numbers-mode" data-highlighter="shiki" data-ext="ts" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-ts"><span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">export</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> default</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> defineUserConfig</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">({</span></span>
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<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> theme</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">: </span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;">plumeTheme</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">({</span></span>
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<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> markdown</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">: {</span></span>
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<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> math</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">: {</span></span>
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<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> type</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">: </span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">'</span><span style="--shiki-light:#B56959;--shiki-dark:#C98A7D;">katex</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">'</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">, </span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">// 'katex' | 'mathjax'</span></span>
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<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"> // ... Other configuration options</span></span>
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<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;"> }</span></span>
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<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;"> },</span></span>
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<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;"> })</span></span>
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<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">})</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div>`,1)]),l[21]||=s(`p`,null,[a(`When you choose to use `),s(`code`,null,`mathjax`),a(`, you also need to install the dependency by running the following command:`)],-1),r(x,{id:`0`,data:[{id:`pnpm`},{id:`yarn`},{id:`npm`}],"tab-id":`npm-to-pnpm-yarn-npm`},{title0:e(({value:e,isActive:t})=>[r(b,{provider:`iconify`,name:`vscode-icons:file-type-light-pnpm`}),l[2]||=s(`span`,null,`pnpm`,-1)]),title1:e(({value:e,isActive:t})=>[r(b,{provider:`iconify`,name:`vscode-icons:file-type-yarn`}),l[3]||=s(`span`,null,`yarn`,-1)]),title2:e(({value:e,isActive:t})=>[r(b,{provider:`iconify`,name:`logos:npm-icon`}),l[4]||=s(`span`,null,`npm`,-1)]),tab0:e(({value:e,isActive:t})=>[...l[5]||=[s(`div`,{class:`language-sh`,"data-highlighter":`shiki`,"data-ext":`sh`,style:{"--shiki-light":`#393a34`,"--shiki-dark":`#dbd7caee`,"--shiki-light-bg":`#ffffff`,"--shiki-dark-bg":`#121212`}},[s(`pre`,{class:`shiki shiki-themes vitesse-light vitesse-dark vp-code`},[s(`code`,{class:`language-sh`},[s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#59873A`,"--shiki-dark":`#80A665`}},`pnpm`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` add`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` @mathjax/src`)])])])],-1)]]),tab1:e(({value:e,isActive:t})=>[...l[6]||=[s(`div`,{class:`language-sh`,"data-highlighter":`shiki`,"data-ext":`sh`,style:{"--shiki-light":`#393a34`,"--shiki-dark":`#dbd7caee`,"--shiki-light-bg":`#ffffff`,"--shiki-dark-bg":`#121212`}},[s(`pre`,{class:`shiki shiki-themes vitesse-light vitesse-dark vp-code`},[s(`code`,{class:`language-sh`},[s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#59873A`,"--shiki-dark":`#80A665`}},`yarn`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` add`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` @mathjax/src`)])])])],-1)]]),tab2:e(({value:e,isActive:t})=>[...l[7]||=[s(`div`,{class:`language-sh`,"data-highlighter":`shiki`,"data-ext":`sh`,style:{"--shiki-light":`#393a34`,"--shiki-dark":`#dbd7caee`,"--shiki-light-bg":`#ffffff`,"--shiki-dark-bg":`#121212`}},[s(`pre`,{class:`shiki shiki-themes vitesse-light vitesse-dark vp-code`},[s(`code`,{class:`language-sh`},[s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#59873A`,"--shiki-dark":`#80A665`}},`npm`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` i`),s(`span`,{style:{"--shiki-light":`#B56959`,"--shiki-dark":`#C98A7D`}},` @mathjax/src`)])])])],-1)]]),_:1}),l[22]||=s(`h2`,{id:`syntax`,tabindex:`-1`},[s(`a`,{class:`header-anchor`,href:`#syntax`},[s(`span`,null,`Syntax`)])],-1),l[23]||=s(`h3`,{id:`inline-syntax`,tabindex:`-1`},[s(`a`,{class:`header-anchor`,href:`#inline-syntax`},[s(`span`,null,`Inline Syntax`)])],-1),l[24]||=s(`p`,null,[a(`Use `),s(`code`,null,`$`),a(` to wrap mathematical formulas `),s(`em`,null,[a(`(i.e., write the mathematical formula between two `),s(`code`,null,`$`),a(` symbols)`)])],-1),r(S,{type:`markdown`,title:`Inline Mode`,expanded:``},{code:e(()=>[...l[8]||=[s(`div`,{class:`language-md`,"data-highlighter":`shiki`,"data-ext":`md`,style:{"--shiki-light":`#393a34`,"--shiki-dark":`#dbd7caee`,"--shiki-light-bg":`#ffffff`,"--shiki-dark-bg":`#121212`}},[s(`pre`,{class:`shiki shiki-themes vitesse-light vitesse-dark vp-code`},[s(`code`,{class:`language-md`},[s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`Euler's identity $e^{i\\pi}+1=0$ is a beautiful formula in $\\mathbb{R}^2$.`)])])])],-1)]]),default:e(()=>[l[9]||=s(`p`,null,[a(`Euler's identity 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mtight`,style:{"margin-right":`0.0359em`}},`iπ`)])])])])])])])]),s(`span`,{class:`mspace`,style:{"margin-right":`0.2222em`}}),s(`span`,{class:`mbin`},`+`),s(`span`,{class:`mspace`,style:{"margin-right":`0.2222em`}})]),s(`span`,{class:`base`},[s(`span`,{class:`strut`,style:{height:`0.6444em`}}),s(`span`,{class:`mord`},`1`),s(`span`,{class:`mspace`,style:{"margin-right":`0.2778em`}}),s(`span`,{class:`mrel`},`=`),s(`span`,{class:`mspace`,style:{"margin-right":`0.2778em`}})]),s(`span`,{class:`base`},[s(`span`,{class:`strut`,style:{height:`0.6444em`}}),s(`span`,{class:`mord`},`0`)])])]),a(` is a beautiful formula in `),s(`span`,{class:`katex`},[s(`span`,{class:`katex-mathml`},[s(`math`,{xmlns:`http://www.w3.org/1998/Math/MathML`},[s(`semantics`,null,[s(`mrow`,null,[s(`msup`,null,[s(`mi`,{mathvariant:`double-struck`},`R`),s(`mn`,null,`2`)])]),s(`annotation`,{encoding:`application/x-tex`},`\\mathbb{R}^2`)])])]),s(`span`,{class:`katex-html`,"aria-hidden":`true`},[s(`span`,{class:`base`},[s(`span`,{class:`strut`,style:{height:`0.8141em`}}),s(`span`,{class:`mord`},[s(`span`,{class:`mord mathbb`},`R`),s(`span`,{class:`msupsub`},[s(`span`,{class:`vlist-t`},[s(`span`,{class:`vlist-r`},[s(`span`,{class:`vlist`,style:{height:`0.8141em`}},[s(`span`,{style:{top:`-3.063em`,"margin-right":`0.05em`}},[s(`span`,{class:`pstrut`,style:{height:`2.7em`}}),s(`span`,{class:`sizing reset-size6 size3 mtight`},[s(`span`,{class:`mord mtight`},`2`)])])])])])])])])])]),a(`.`)],-1)]),_:1}),l[25]||=o(`<h3 id="block-syntax" tabindex="-1"><a class="header-anchor" href="#block-syntax"><span>Block Syntax</span></a></h3><p>Use <code>$$</code> to wrap mathematical formulas <em>(i.e., write the mathematical formula between two <code>$$</code> symbols)</em></p><div class="language-md" data-highlighter="shiki" data-ext="md" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-md"><span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"><!-- Write the mathematical formula between two \`</span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;" class="highlighted-word">$$</span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">\` symbols, rendered in a separate block --></span></span>
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<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;" class="highlighted-word">$$</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">xxx</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;" class="highlighted-word">$$</span></span>
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<span class="line"></span>
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<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"><!-- The two \`</span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;" class="highlighted-word">$$</span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">\` symbols can each occupy a separate line, with the mathematical formula between them --></span></span>
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<span class="line highlighted-word"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">$$</span></span>
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<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">xxx</span></span>
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<span class="line highlighted-word"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">$$</span></span></code></pre></div>`,3),r(S,{type:`markdown`,title:`Block Mode`,expanded:``},{code:e(()=>[...l[10]||=[s(`div`,{class:`language-md`,"data-highlighter":`shiki`,"data-ext":`md`,style:{"--shiki-light":`#393a34`,"--shiki-dark":`#dbd7caee`,"--shiki-light-bg":`#ffffff`,"--shiki-dark-bg":`#121212`}},[s(`pre`,{class:`shiki shiki-themes vitesse-light vitesse-dark vp-code`},[s(`code`,{class:`language-md`},[s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`$$`)]),a(`
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`),s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`\\frac {\\partial^r} {\\partial \\omega^r} \\left(\\frac {y^{\\omega}} {\\omega}\\right)`)]),a(`
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`),s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`= \\left(\\frac {y^{\\omega}} {\\omega}\\right) \\left`),s(`span`,{style:{"--shiki-light":`#A65E2B`,"--shiki-dark":`#C99076`}},`\\{`),s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`(\\log y)^r + \\sum_{i=1}^r \\frac {(-1)^ Ir \\cdots (r-i+1) (\\log y)^{ri}} {\\omega^i} \\right`),s(`span`,{style:{"--shiki-light":`#A65E2B`,"--shiki-dark":`#C99076`}},`\\}`)]),a(`
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`),s(`span`,{class:`line`},[s(`span`,{style:{"--shiki-light":`#393A34`,"--shiki-dark":`#DBD7CAEE`}},`$$`)])])])],-1)]]),default:e(()=>[l[11]||=s(`p`,{class:`katex-block`},[s(`span`,{class:`katex-display`},[s(`span`,{class:`katex`},[s(`span`,{class:`katex-mathml`},[s(`math`,{xmlns:`http://www.w3.org/1998/Math/MathML`,display:`block`},[s(`semantics`,null,[s(`mrow`,null,[s(`mfrac`,null,[s(`msup`,null,[s(`mi`,{mathvariant:`normal`},`∂`),s(`mi`,null,`r`)]),s(`mrow`,null,[s(`mi`,{mathvariant:`normal`},`∂`),s(`msup`,null,[s(`mi`,null,`ω`),s(`mi`,null,`r`)])])]),s(`mrow`,null,[s(`mo`,{fence:`true`},`(`),s(`mfrac`,null,[s(`msup`,null,[s(`mi`,null,`y`),s(`mi`,null,`ω`)]),s(`mi`,null,`ω`)]),s(`mo`,{fence:`true`},`)`)]),s(`mo`,null,`=`),s(`mrow`,null,[s(`mo`,{fence:`true`},`(`),s(`mfrac`,null,[s(`msup`,null,[s(`mi`,null,`y`),s(`mi`,null,`ω`)]),s(`mi`,null,`ω`)]),s(`mo`,{fence:`true`},`)`)]),s(`mrow`,null,[s(`mo`,{fence:`true`},`{`),s(`mo`,{stretchy:`false`},`(`),s(`mi`,null,`log`),s(`mo`,null,``),s(`mi`,null,`y`),s(`msup`,null,[s(`mo`,{stretchy:`false`},`)`),s(`mi`,null,`r`)]),s(`mo`,null,`+`),s(`munderover`,null,[s(`mo`,null,`∑`),s(`mrow`,null,[s(`mi`,null,`i`),s(`mo`,null,`=`),s(`mn`,null,`1`)]),s(`mi`,null,`r`)]),s(`mfrac`,null,[s(`mrow`,null,[s(`mo`,{stretchy:`false`},`(`),s(`mo`,null,`−`),s(`mn`,null,`1`),s(`msup`,null,[s(`mo`,{stretchy:`false`},`)`),s(`mi`,null,`I`)]),s(`mi`,null,`r`),s(`mo`,null,`⋯`),s(`mo`,{stretchy:`false`},`(`),s(`mi`,null,`r`),s(`mo`,null,`−`),s(`mi`,null,`i`),s(`mo`,null,`+`),s(`mn`,null,`1`),s(`mo`,{stretchy:`false`},`)`),s(`mo`,{stretchy:`false`},`(`),s(`mi`,null,`log`),s(`mo`,null,``),s(`mi`,null,`y`),s(`msup`,null,[s(`mo`,{stretchy:`false`},`)`),s(`mrow`,null,[s(`mi`,null,`r`),s(`mi`,null,`i`)])])]),s(`msup`,null,[s(`mi`,null,`ω`),s(`mi`,null,`i`)])]),s(`mo`,{fence:`true`},`}`)])]),s(`annotation`,{encoding:`application/x-tex`},`\\frac 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