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# `Markdown` Editor Demo Features **Markdown** (via `markdown-it`) & (via `marked`) **Math** ($\LaTeX$), **Syntax Highlighting**, **Mermaid Diagrams**, and **Footnotes**[^1]. This demo showcases more of ($\LaTeX$) and Mermaid than markdown. | Feature | Support | Engine(s) | | ------------------- | ------- | ----------------------- | | Basic Markdown | Yes | `markdown-it`, `marked` | | Math (LaTeX) | Yes | `MathJax`, `KaTeX` | | Syntax Highlighting | Yes | `highlight.js` | | Diagrams | Yes | `Mermaid` | | Footnotes | Yes | `markdown-it` | | Custom CSS | Yes | Editor Feature | --- Here are some beautiful and complex physics equations rendered in LaTeX.- (**Generated by Grok 4**) ## 1. Equations ### 1.1 Einstein Field Equations (General Relativity) ```latex $$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$ ``` $$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$ or in full tensor form: ```latex $$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$ ``` $$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$ ### 1.2. Dirac Equation (Relativistic Quantum Mechanics) ```latex $$i \gamma^\mu \partial_\mu \psi - m \psi = 0$$ ``` $$i \gamma^\mu \partial_\mu \psi - m \psi = 0$$ In covariant form with slash notation: ```latex $$(i \not{\partial} - m) \psi = 0$$ ``` $$(i \not{\partial} - m) \psi = 0$$ ### 1.3. Klein-Gordon Equation ```latex $$\left( \frac{\partial^2}{\partial t^2} - \nabla^2 + m^2 \right) \phi = 0$$ ``` $$\left( \frac{\partial^2}{\partial t^2} - \nabla^2 + m^2 \right) \phi = 0$$ or in natural units: ```latex $$(\square + m^2) \phi = 0$$ ``` $$(\square + m^2) \phi = 0$$ ### 1.4. Schrödinger Equation (Time-dependent) ```latex $$i \hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t)$$ ``` $$i \hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t)$$ ### 1.5. Yang-Mills Field Strength Tensor (Quantum Field Theory) ```latex $$F_{\mu\nu}^a = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + g f^{abc} A_\mu^b A_\nu^c$$ ``` $$F_{\mu\nu}^a = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + g f^{abc} A_\mu^b A_\nu^c$$ ### 1.6. Navier-Stokes Equations (Fluid Dynamics) ```latex $$\rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f}$$ ``` $$\rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f}$$ ### 1.7. Lagrangian Density for Quantum Electrodynamics (QED) ```latex $$\mathcal{L} = \bar{\psi}(i \not{D} - m)\psi - \frac{1}{4} F_{\mu\nu} F^{\mu\nu}$$ ``` $$\mathcal{L} = \bar{\psi}(i \not{D} - m)\psi - \frac{1}{4} F_{\mu\nu} F^{\mu\nu}$$ where $$\( D_\mu = \partial_\mu + ie A_\mu \)$$ ### 1.8. Black Hole Entropy (Bekenstein-Hawking) ```latex $$S = \frac{k_B c^3 A}{4 \hbar G}$$ ``` $$S = \frac{k_B c^3 A}{4 \hbar G}$$ ### 1.9. Very Complex One: Einstein-Hilbert Action ```latex $$S = \frac{1}{16\pi G} \int R \sqrt{-g} \, d^4x + S_m$$ ``` $$S = \frac{1}{16\pi G} \int R \sqrt{-g} \, d^4x + S_m$$ ### 1.10. Inline rendering ### Inline: $E=mc^2$ and $\( ax^2 + bx + c = 0\)$ ## 2. Mermaid diagrams ### 2.1 StateDiagram ```mermaid stateDiagram [*] --> Still Still --> [*] Still --> Moving Moving --> Still Moving --> Crash Crash --> [*] ``` ### 2.2 Radar ```mermaid radar-beta title Restaurant Comparison axis food["Food Quality"], service["Service"], price["Price"] axis ambiance["Ambiance"] curve a["Restaurant A"]{4, 3, 2, 4} curve b["Restaurant B"]{3, 4, 3, 3} curve c["Restaurant C"]{2, 3, 4, 2} curve d["Restaurant D"]{2, 2, 4, 3} graticule polygon max 5 ``` ### 2.3 Sankey (Sources and sinks) ```mermaid --- config: sankey: showValues: false --- sankey Agricultural 'waste',Bio-conversion,124.729 Bio-conversion,Liquid,0.597 Bio-conversion,Losses,26.862 Bio-conversion,Solid,280.322 Bio-conversion,Gas,81.144 Biofuel imports,Liquid,35 Biomass imports,Solid,35 Coal imports,Coal,11.606 Coal reserves,Coal,63.965 Coal,Solid,75.571 District heating,Industry,10.639 District heating,Heating and cooling - commercial,22.505 District heating,Heating and cooling - homes,46.184 Electricity grid,Over generation / exports,104.453 Electricity grid,Heating and cooling - homes,113.726 Electricity grid,H2 conversion,27.14 Electricity grid,Industry,342.165 Electricity grid,Road transport,37.797 Electricity grid,Agriculture,4.412 Electricity grid,Heating and cooling - commercial,40.858 Electricity grid,Losses,56.691 Electricity grid,Rail transport,7.863 Electricity grid,Lighting & appliances - commercial,90.008 Electricity grid,Lighting & appliances - homes,93.494 Gas imports,Ngas,40.719 Gas reserves,Ngas,82.233 Gas,Heating and cooling - commercial,0.129 Gas,Losses,1.401 Gas,Thermal generation,151.891 Gas,Agriculture,2.096 Gas,Industry,48.58 Geothermal,Electricity grid,7.013 H2 conversion,H2,20.897 H2 conversion,Losses,6.242 H2,Road transport,20.897 Hydro,Electricity grid,6.995 Liquid,Industry,121.066 Liquid,International shipping,128.69 Liquid,Road transport,135.835 Liquid,Domestic aviation,14.458 Liquid,International aviation,206.267 Liquid,Agriculture,3.64 Liquid,National navigation,33.218 Liquid,Rail transport,4.413 Marine algae,Bio-conversion,4.375 Ngas,Gas,122.952 Nuclear,Thermal generation,839.978 Oil imports,Oil,504.287 Oil reserves,Oil,107.703 Oil,Liquid,611.99 Other waste,Solid,56.587 Other waste,Bio-conversion,77.81 Pumped heat,Heating and cooling - homes,193.026 Pumped heat,Heating and cooling - commercial,70.672 Solar PV,Electricity grid,59.901 Solar Thermal,Heating and cooling - homes,19.263 Solar,Solar Thermal,19.263 Solar,Solar PV,59.901 Solid,Agriculture,0.882 Solid,Thermal generation,400.12 Solid,Industry,46.477 Thermal generation,Electricity grid,525.531 Thermal generation,Losses,787.129 Thermal generation,District heating,79.329 Tidal,Electricity grid,9.452 UK land based bioenergy,Bio-conversion,182.01 Wave,Electricity grid,19.013 Wind,Electricity grid,289.366 ``` --- [^1]: This is a footnote rendered by `markdown-it-footnote`. This text tries to use features that might fail in less robust editors, especially AI-generated content mixing complex math and code blocks.
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