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‎dev/.documenter/.vitepress/mathjax-plugin.ts‎

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// adapter from https://github.com/orgs/vuepress-theme-hope/discussions/5178#discussioncomment-15642629
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// mathjax-plugin.ts
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// @ts-ignore
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import MathJax from '@mathjax/src'
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import type { Plugin as VitePlugin } from 'vite'
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import type MarkdownIt from 'markdown-it'
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import { tex as mdTex } from '@mdit/plugin-tex'
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const mathjaxStyleModuleID = 'virtual:mathjax-styles.css'
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interface MathJaxOptions {
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font?: string
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}
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async function initializeMathJax(options: MathJaxOptions = {}) {
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const font = options.font || 'mathjax-newcm'
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const config: any = {
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loader: {
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load: [
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'input/tex',
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'output/svg',
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'[tex]/boldsymbol',
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'[tex]/braket',
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'[tex]/mathtools',
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],
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},
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tex: {
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tags: 'ams',
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packages: {
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'[+]': ['boldsymbol', 'braket', 'mathtools'],
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},
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},
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output: {
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font,
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displayOverflow: 'linebreak',
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mtextInheritFont: true,
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},
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svg: {
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fontCache: 'none', // critical: avoids async font loading
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},
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}
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await MathJax.init(config)
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const fontData = MathJax.config.svg?.fontData
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if (fontData?.dynamicFiles) {
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const dynamicFiles = fontData.dynamicFiles
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const dynamicPrefix: string =
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fontData.OPTIONS?.dynamicPrefix || fontData.options?.dynamicPrefix
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if (dynamicPrefix) {
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await Promise.all(
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Object.keys(dynamicFiles).map(async (name) => {
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try {
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await import(/* @vite-ignore */ `${dynamicPrefix}/${name}.js`)
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dynamicFiles[name]?.setup?.(MathJax.startup.output.font)
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} catch {
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// Silently ignore missing dynamic files
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}
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}),
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)
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}
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}
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}
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export function mathjaxPlugin(options: MathJaxOptions = {}) {
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let adaptor: any
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let initialized = false
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async function ensureInitialized() {
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if (!initialized) {
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await initializeMathJax(options)
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adaptor = MathJax.startup.adaptor
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initialized = true
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}
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}
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function renderMath(content: string, displayMode: boolean): string {
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if (!initialized) {
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throw new Error('MathJax not initialized')
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}
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const node = MathJax.tex2svg(content, { display: displayMode })
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// Prevent Vue from touching MathJax output
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adaptor.setAttribute(node, 'v-pre', '')
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let html = adaptor.outerHTML(node)
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// Preserve spaces inside mjx-break (SVG only)
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html = html.replace(
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/<mjx-break(.*?)>(.*?)<\/mjx-break>/g,
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(_: string, attr: string, inner: string) =>
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`<mjx-break${attr}>${inner.replace(/ /g, '&nbsp;')}</mjx-break>`,
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)
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// Wrap only display equations (not inline math)
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html = html.replace(
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/(<mjx-container[^>]*display="true"[^>]*>)([\s\S]*?)(<\/mjx-container>)/,
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'<div class="mjx-scroll-wrapper">$1$2$3</div>'
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)
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return html
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}
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function getMathJaxStyles(): string {
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return initialized
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? adaptor.textContent(MathJax.svgStylesheet()) || ''
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: ''
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}
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function resetMathJax(): void {
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if (!initialized) return
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MathJax.texReset()
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MathJax.typesetClear()
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}
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function viteMathJax(): VitePlugin {
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const virtualModuleID = '\0' + mathjaxStyleModuleID
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return {
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name: 'mathjax-styles',
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resolveId(id) {
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if (id === mathjaxStyleModuleID) {
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return virtualModuleID
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}
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},
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async load(id) {
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if (id === virtualModuleID) {
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await ensureInitialized()
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return getMathJaxStyles()
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}
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},
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}
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}
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function mdMathJax(md: MarkdownIt): void {
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mdTex(md, {
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render: renderMath,
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})
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const orig = md.render
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md.render = function (...args) {
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resetMathJax()
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return orig.apply(this, args)
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}
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}
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const init = ensureInitialized()
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return {
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vitePlugin: viteMathJax(),
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markdownConfig: mdMathJax,
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styleModuleID: mathjaxStyleModuleID,
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init,
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}
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}

‎dev/.documenter/examples/cumulants_KPO.md‎

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```
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\begin{align}
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\frac{d}{dt} \langle a\rangle &= \left( - U + \Delta \right) \mathit{i} \langle a\rangle -0.5 \langle a\rangle \kappa - U \mathit{i} \langle a\rangle ^{2} \langle a^\dagger\rangle + G \mathit{i} \langle a^\dagger\rangle \\
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\frac{d}{dt} \langle a^\dagger\rangle &= -0.5 \kappa \langle a^\dagger\rangle - G \mathit{i} \langle a\rangle + U \mathit{i} \langle a\rangle \langle a^\dagger\rangle ^{2} + \left( U - \Delta \right) \mathit{i} \langle a^\dagger\rangle
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\frac{d}{dt} \langle a\rangle &= \left( - U + \Delta \right) \mathit{i} \langle a\rangle + G \mathit{i} \langle a^\dagger\rangle -0.5 \langle a\rangle \kappa - U \mathit{i} \langle a\rangle ^{2} \langle a^\dagger\rangle \\
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\frac{d}{dt} \langle a^\dagger\rangle &= - G \mathit{i} \langle a\rangle + U \mathit{i} \langle a\rangle \langle a^\dagger\rangle ^{2} + \left( U - \Delta \right) \mathit{i} \langle a^\dagger\rangle -0.5 \langle a^\dagger\rangle \kappa
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\end{align}
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‎dev/.documenter/examples/forward_transmission.md‎

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```
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\begin{align}
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\frac{d}{dt} \langle m\rangle &= -1 i Vk \langle c\rangle ^{2} -1 i {\Omega}d -1 i \langle m\rangle \Delta -0.5 {\gamma}m \langle m\rangle \\
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\frac{d}{dt} \langle m^\dagger\rangle &= 1 i \langle c^\dagger\rangle ^{2} Vk + 1 i {\Omega}d -0.5 {\gamma}m \langle m^\dagger\rangle + 1 i \Delta \langle m^\dagger\rangle \\
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\frac{d}{dt} \langle c\rangle &= \frac{-1}{2} i \Delta \langle c\rangle -2 i \langle m\rangle \langle c^\dagger\rangle Vk -0.5 {\gamma}k \langle c\rangle \\
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\frac{d}{dt} \langle c^\dagger\rangle &= 2 i Vk \langle m^\dagger\rangle \langle c\rangle + \frac{1}{2} i \langle c^\dagger\rangle \Delta -0.5 \langle c^\dagger\rangle {\gamma}k
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\frac{d}{dt} \langle m\rangle &= -1 i \Delta \langle m\rangle -1 i {\Omega}d -0.5 {\gamma}m \langle m\rangle -1 i \langle c\rangle ^{2} Vk \\
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\frac{d}{dt} \langle m^\dagger\rangle &= 1 i Vk \langle c^\dagger\rangle ^{2} + 1 i {\Omega}d -0.5 {\gamma}m \langle m^\dagger\rangle + 1 i \Delta \langle m^\dagger\rangle \\
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\frac{d}{dt} \langle c\rangle &= -2 i Vk \langle c^\dagger\rangle \langle m\rangle + \frac{-1}{2} i \Delta \langle c\rangle -0.5 {\gamma}k \langle c\rangle \\
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\frac{d}{dt} \langle c^\dagger\rangle &= -0.5 {\gamma}k \langle c^\dagger\rangle + 2 i \langle c\rangle Vk \langle m^\dagger\rangle + \frac{1}{2} i \Delta \langle c^\dagger\rangle
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\end{align}
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‎dev/.documenter/examples/wave_mixing.md‎

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(2//1)*Differential(T)(v1(T))*ω + Differential(T)(u1(T))*γ + u1(T)*u2(T)*β - u1(T)*(ω^2) + u1(T)*(ω0^2) + v3(T)*v2(T)*β + v2(T)*v1(T)*β + v1(T)*γ*ω + u3(T)*u2(T)*β + (3//4)*(u1(T)^3)*α + (3//4)*(u1(T)^2)*u3(T)*α + (3//2)*u1(T)*(v3(T)^2)*α + (3//2)*u1(T)*v3(T)*v1(T)*α + (3//2)*u1(T)*(v2(T)^2)*α + (3//4)*u1(T)*(v1(T)^2)*α + (3//2)*u1(T)*(u3(T)^2)*α + (3//2)*u1(T)*(u2(T)^2)*α + (3//2)*v3(T)*v2(T)*u2(T)*α - (3//4)*(v2(T)^2)*u3(T)*α - (3//4)*(v1(T)^2)*u3(T)*α + (3//4)*u3(T)*(u2(T)^2)*α ~ F
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Differential(T)(v1(T))*γ - (2//1)*Differential(T)(u1(T))*ω + u1(T)*v2(T)*β - u1(T)*γ*ω + v3(T)*u2(T)*β - v2(T)*u3(T)*β - v1(T)*u2(T)*β - v1(T)*(ω^2) + v1(T)*(ω0^2) + (3//4)*(u1(T)^2)*v3(T)*α + (3//4)*(u1(T)^2)*v1(T)*α - (3//2)*u1(T)*v1(T)*u3(T)*α + (3//2)*(v3(T)^2)*v1(T)*α + (3//4)*v3(T)*(v2(T)^2)*α - (3//4)*v3(T)*(v1(T)^2)*α - (3//4)*v3(T)*(u2(T)^2)*α + (3//2)*(v2(T)^2)*v1(T)*α + (3//2)*v2(T)*u3(T)*u2(T)*α + (3//4)*(v1(T)^3)*α + (3//2)*v1(T)*(u3(T)^2)*α + (3//2)*v1(T)*(u2(T)^2)*α ~ 0
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Differential(T)(v1(T))*γ - (2//1)*Differential(T)(u1(T))*ω + u1(T)*v2(T)*β - u1(T)*γ*ω + v3(T)*u2(T)*β - v2(T)*u3(T)*β - v1(T)*u2(T)*β - v1(T)*(ω^2) + v1(T)*(ω0^2) + (3//4)*(u1(T)^2)*v3(T)*α + (3//4)*(u1(T)^2)*v1(T)*α - (3//2)*u1(T)*v1(T)*u3(T)*α + (3//2)*(v3(T)^2)*v1(T)*α + (3//4)*v3(T)*(v2(T)^2)*α - (3//4)*v3(T)*(v1(T)^2)*α - (3//4)*v3(T)*(u2(T)^2)*α + (3//2)*(v2(T)^2)*v1(T)*α + (3//2)*v2(T)*u3(T)*u2(T)*α + (3//4)*(v1(T)^3)*α + (3//2)*v1(T)*(u3(T)^2)*α + (3//2)*v1(T)*(u2(T)^2)*α ~ 0//1
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Differential(T)(u2(T))*γ + (4//1)*Differential(T)(v2(T))*ω + (1//2)*(u1(T)^2)*β + u1(T)*u3(T)*β + v3(T)*v1(T)*β + (2//1)*v2(T)*γ*ω - (1//2)*(v1(T)^2)*β - (4//1)*u2(T)*(ω^2) + u2(T)*(ω0^2) + (3//2)*(u1(T)^2)*u2(T)*α + (3//2)*u1(T)*v3(T)*v2(T)*α + (3//2)*u1(T)*u3(T)*u2(T)*α + (3//2)*(v3(T)^2)*u2(T)*α - (3//2)*v3(T)*v1(T)*u2(T)*α + (3//4)*(v2(T)^2)*u2(T)*α + (3//2)*v2(T)*v1(T)*u3(T)*α + (3//2)*(v1(T)^2)*u2(T)*α + (3//2)*(u3(T)^2)*u2(T)*α + (3//4)*(u2(T)^3)*α ~ 0//1
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‎dev/.documenter/examples/wflhurk.png‎

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‎dev/.documenter/examples/yalsuip.png‎

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‎dev/.documenter/manual/API.md‎

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@@ -183,7 +183,7 @@ first_order_transform!(diff_eom::DifferentialEquation, time)
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Transforms a higher-order differential equation system into an equivalent first-order system by introducing additional variables. Modifies the system in place. The `time` parameter specifies the independent variable used for differentiation.
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/DifferentialEquation.jl#L1" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/DifferentialEquation.jl#L1" target="_blank" rel="noreferrer">source</a></Badge>
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</details>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/HarmonicEquation.jl#L128-L169" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/HarmonicEquation.jl#L128-L169" target="_blank" rel="noreferrer">source</a></Badge>
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</details>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/krylov-bogoliubov.jl#L4" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/krylov-bogoliubov.jl#L4" target="_blank" rel="noreferrer">source</a></Badge>
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</details>
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Obtain the symbolic Jacobian matrix of `eom`. This is the linearised left-hand side of F(u) = du/dT.
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/Jacobian.jl#L6" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/Jacobian.jl#L6" target="_blank" rel="noreferrer">source</a></Badge>
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Obtain a Jacobian from a `DifferentialEquation` by first converting it into a `HarmonicEquation`.
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/Jacobian.jl#L24" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/Jacobian.jl#L24" target="_blank" rel="noreferrer">source</a></Badge>
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Get the Jacobian of a set of equations `eqs` with respect to the variables `vars`.
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/src/Jacobian.jl#L33" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/src/Jacobian.jl#L33" target="_blank" rel="noreferrer">source</a></Badge>
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</details>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L129" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L128" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L37" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L36" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L83" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L82" target="_blank" rel="noreferrer">source</a></Badge>
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</details>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L202" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L201" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L175" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L174" target="_blank" rel="noreferrer">source</a></Badge>
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‎dev/.documenter/manual/SciMLExt.md‎

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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/616289ce2ad908085b26b56b0d732f6d7bcac0fe/ext/ModelingToolkitExt.jl#L129" target="_blank" rel="noreferrer">source</a></Badge>
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<Badge type="info" class="source-link" text="source"><a href="https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl/blob/eebe3688fe0349e7d4aec6edbb21c4b20addd52e/ext/ModelingToolkitExt.jl#L128" target="_blank" rel="noreferrer">source</a></Badge>
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