Test Markdown Neovim UltiSnips

Since I was not able to figure out how to implement macros/own commands in \(\KaTeX\) with jekyll-katex and want to use the macros/commands of the \usepackage{physics}-latex-package, I am going to implement markdown snippets as an alternative.

Let’s begin with sets.

\[\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}.\]

Then, Euler’s identity (for \mathrm{e} and \mathrm{i}).

\[\mathrm{e}^{\mathrm{i}x} = \cos(x) + \mathrm{i} \sin(x).\]

Vector operations on \(\mathbb{R}^{3}\)

Vectorbold (macro: \boldsymbol{v}):

\[\boldsymbol{v}\]

Unit vector (macro: \hat{\boldsymbol{e}}):

\[\hat{\boldsymbol{e}}\]

Scalarproduct (macro: \boldsymbol{x} \boldsymbol{\cdot} \boldsymbol{y}):

\[\boldsymbol{x} \boldsymbol{\cdot} \boldsymbol{y}\]

Vectorproduct (macro: \boldsymbol{x} \boldsymbol{\times} \boldsymbol{y}):

\[\boldsymbol{x} \boldsymbol{\times} \boldsymbol{y}\]

Gradient (macro: \boldsymbol{\nabla} \phi):

\[\boldsymbol{\nabla} \phi\]

Divergence (macro: \boldsymbol{\nabla \cdot A}):

\[\boldsymbol{\nabla \cdot A}\]

Curl (macro: \boldsymbol{\nabla \times A}):

\[\boldsymbol{\nabla \times A}\]

Laplacian (macro: \boldsymbol{\nabla}^{2} \phi):

\[\boldsymbol{\nabla}^{2} \phi\]

D’Alembertian (macro: \Box A):

\[\Box A\]

Differentiation

Differential (macro: \operatorname{d}\!x\, f(x)):

\[\operatorname{d}\!x\, f(x)\]

Fractional derivative (macro: \frac{\operatorname{d}\!f(x)}{\operatorname{d}\!x} ):

\[\frac{\operatorname{d}\!f(x)}{\operatorname{d}\!x}\]

Powered fractional derivative (macro: \frac{\operatorname{d}^{n}\!f(x)}{\operatorname{d}\!x^{n}}):

\[\frac{\operatorname{d}^{n}\!f(x)}{\operatorname{d}\!x^{n}}\]

Fractional partial derivative (macro: \frac{\partial f(x)}{\partial x}):

\[\frac{\partial f(x)}{\partial x}\]

Powered partial derivative (macro: \frac{\partial^{n} f(x)}{\partial x^{n}}):

\[\frac{\partial^{n} f(x)}{\partial x^{n}}\]

Integrals

One dimensional integral (macro: \int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\, f(x)):

\[\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\, f(x)\]

Two dimensional integral (macro: \int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!y\, f(x,y)):

\[\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!y\, f(x,y)\]

Two dimensional integral in polar coordinates (macro: \int\limits_{0}^{2\pi}\!\!\operatorname{d}\!phi\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r f(r,\phi)):

\[\int\limits_{0}^{2\pi}\!\!\operatorname{d}\!\phi\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r f(r,\phi)\]

Three dimentional integral (macro: \int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!y\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!z\, f(x,y,z)):

\[\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!x\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!y\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!z\, f(x,y,z)\]

Three dimensional integral in cylindrical coordinates (macro: \int\limits_{0}^{2\pi}\!\!\operatorname{d}\!\phi\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!z\, f(r,\phi,z)):

\[\int\limits_{0}^{2\pi}\!\!\operatorname{d}\!\phi\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r\!\!\int\limits_{-\infty}^{\infty}\!\!\operatorname{d}\!z\, f(x,y,z)\]

Three dimensional integral in spherical coordinates (macro: \int\limits_{0}^{2\pi}\!\!\operatorname{d}\!\phi\,\!\!\int\limits_{0}^{\pi}\!\!\operatorname{d}\!\theta\,\sin(\theta)\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r^2 f(r,\theta,\phi)):

\[\int\limits_{0}^{2\pi}\!\!\operatorname{d}\!\phi\,\!\!\int\limits_{0}^{\pi}\!\!\operatorname{d}\!\theta\,\sin(\theta)\!\!\int\limits_{0}^{\infty}\!\!\operatorname{d}\!r\,r^2 f(r,\theta,\phi)\]

\(n\)-dimensional integral (macro: \int\limits_{\R^{n}}\!\!\operatorname{d}^{n}\!\, f(\boldsymbol{r})):

\[\int\limits_{\R^n}\!\!\operatorname{d}^{n}\!r\, f(\boldsymbol{r})\]

The Wave Equation

\[\Box \psi(\boldsymbol{r},t) := -\frac{1}{c^{2}} \frac{\partial^{2} }{\partial t^{2}} \psi(\boldsymbol{r},t) + \boldsymbol{\nabla}^{2} \psi(\boldsymbol{r},t) = 0\]

The Maxwell Equations

And, last but not least, again, the Maxwell equations:

\[\begin{aligned} \boldsymbol{\nabla \cdot E} &= 4 \pi \rho \\ \boldsymbol{\nabla \cdot B} &= 0 \\ \boldsymbol{\nabla \times E} &= - \frac{1}{c} \frac{\partial }{\partial t} \boldsymbol{B} \\ \boldsymbol{\nabla \times B} &= \frac{1}{c} \biggl(4 \pi \boldsymbol{j} + \frac{\partial }{\partial t} \boldsymbol{E} \biggr) \end{aligned}\]