katex equation and mermaid in mermaid: forest theme

\[K(a,b) = \int \mathcal{D}x(t) \exp(2\pi i S[x]/\hbar)\]

test latex

$ e = m c^2 $

inline: $f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi$ inline: \(f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi\)

display mode (centered):

\[f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi\] \[f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi\] \[y=\frac{1}{2} \times \sqrt{x^2-1} \\ y=\cfrac{1}{2+\cfrac{1}{2}} \\ y=\int \! (x^2-1) dx \\ y=\int (x^2-1) dx \\ y=\int_{a}^{b=10} (x^2-1) dx \\ y=\sum_{x=1}^ {100} (x^2-1)- 1 \\ BER= erfc(\frac{Q}{\sqrt(2)})\] \[\fbox {this is a demo equation: } \\ BER= erfc(\frac{Q}{\sqrt(2)})\]
graph TD; A-->B; A-->C; B-->D; C-->D;
graph LR; A-->B;
graph LR A(This is A)----->|this is demo text|B[(this is database

demo)] C((This is C))--this is demo text--->B D{This is D}--this is demo text--->B subgraph box A---C----D subgraph newbox C D end end subgraph box2 B end style B fill:#bbf,stroke:#000,stroke-width:4px,color:#f00,stroke-dasharray: 10 2 linkStyle 0 stroke:#f00,stroke-width:4px
sequenceDiagram participant Local participant Remote Local-xRemote: LOS is detected Note right of Remote: LOS will triger RFI Remote->>Local: RFI Local->>Remote: Idle Note left of Local: RFI will stop transmission
and triggers idle Local-->>Remote: LOS clear Note right of Remote: idle is received
after LOS clear Remote->>Local: Data Local->>Remote: Data