mirror of https://github.com/thangisme/notes.git
208 lines
4.0 KiB
Markdown
208 lines
4.0 KiB
Markdown
---
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layout: default
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title: Mathjax test
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parent: Mathjax
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mathjax: true
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---
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$$x$$ math at the start of the document
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Nested: $$M = \text{while e^2 $e^2$ do $c^2$ end}$$
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**Numbered equations**
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$$
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\begin{equation}
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\int_0^x \sin(x) dx
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\label{eq:test}
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\end{equation}
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$$
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$$\eqref{eq:test}$$
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**Blockquotes**
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> 1. A block quote
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> 2. With a list inside
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> 3. With $$math$$
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**Math environment Syntax testing**
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Inline Math should work with `$$` $$\frac{x+y}{y}$$
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but not `\(` \(\frac{x+y}{y}\)
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Use `$$` on separate lines:
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$$
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\int_{-\infty}^\infty e^{-x^2} = \sqrt{\pi}
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$$
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Use `$$` on the same line:
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$$ \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$
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Use `$$` on separate lines:
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$$
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a+b
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$$
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Use `$$` on the same line: $$E=mc^2$$
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----
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**Some Tex Functions**
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$$k \times k$$, $$n \times 2$$, $$2 \times n$$, $$\times$$
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$$x \cdot y$$, $$\cdot$$
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$$\sqrt{x^2+y^2+z^2}$$
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$$\alpha \beta \gamma$$
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$$
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\begin{aligned}
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x\ &= y\\
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mc^2\ &= E
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\end{aligned}
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$$
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----
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**Escaped Math environments**
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In the following examples no math environments should render:
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a $5, a $10 and a \$100 Bill.
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All McScrooge sees
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\$$
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and even more:
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\$$
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\\[x+y\]
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\\(x+y\)
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```
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$x
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```
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```
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\$
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```
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`\$`, `\[ \]`, `$x$`
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----
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**Testing `\newcommand`**
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For all $$x$$ and $$y$$ in $$\mathbb{R}^k$$ it is true that
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$$
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\newcommand{sca}[1]{\langle #1 \rangle}
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|\sca{x,y}|^2 \le \sca{x,x} \cdot \sca{y,y},
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$$
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<!-- newcommand not in environment-->
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\newcommand{\scalong}[1]{(#1_1,\dots,#1_k)}
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where $$\sca{\cdot,\cdot}$$ denotes the inner product $$\sca{\scalong{x}, \scalong{x}} = \sum_{i=1}^k x_i y_i$$.
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----
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**Testing several math fonts**
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$$
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p(\mathbf{m}) \sim \mathcal{N}(\mathbf{m}) e^{-\sum_{i} \beta_i m_i}
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$$
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$$
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\langle \vec{m} \rangle =
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\frac{1}{Z(\vec{\beta})}\vec{m}(\mu)
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\sum_{\mu\in\mathcal{G}}
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e^{-\vec{\beta}\cdot\vec{m}(\mu)}
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$$
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----
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Notice below that the `$$`-separated display math doesn't have a blank line before and after (i.e. in an actual $$\LaTeX$$ document it wouldn't be placed in a separate paragraph):
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The _characteristic polynomial_ $$\chi(\lambda)$$ of the
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$$3 \times 3$$ matrix
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$$
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\left( \begin{array}{ccc}
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a & b & c \\
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d & e & f \\
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g & h & i \end{array} \right)
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$$
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is given by the formula
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$$
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\chi(\lambda) = \left| \begin{array}{ccc}
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\lambda - a & -b & -c \\
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-d & \lambda - e & -f \\
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-g & -h & \lambda - i \end{array} \right|.
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$$
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This is a long line: $$\chi(\lambda) = a e i-a e \lambda -a f h-a i \lambda +a \lambda ^2-b d i+b d \lambda +b f g+c d h-c e g+c g \lambda -e i \lambda +e \lambda ^2+f h \lambda +i \lambda ^2-\lambda ^3$$
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----
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**Does it work in different MD elements?**
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# Math $$x^2$$ in heading 1
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## Math $$x^2$$ in heading 2
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### Math $$x^2$$ in heading 3
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#### Math $$x^2$$ in heading 4
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$$x_1, x_2, \dots, x_N$$ should not conflict with `_` _italics_?
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$$(f*g*h)(x)$$ should not conflict with `*` *syn***tax**?
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$$[a+b](c+d)$$ should not conflict link [syntax](#)?
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_math $$x^2$$ in emphasis_
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**math $$x^2$$ in bold**
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[math $$x^2$$ in link](http://www.mathjax.org/)
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`math $$x^2$$ in code`
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~~math $$x^2$$ in strikethrough~~ (doesn't strike through the math)
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**In Tables**
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| Left-Aligned | Center Aligned | Right Aligned |
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| :------------ |:---------------:| -----:|
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| $$a+b$$ | some wordy text | $1600 |
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| $$a+b$$ | some wordy text | $1600 |
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| $$a+b$$ | some wordy text | $1600 |
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The following doesn't work (it only works with Pandoc)
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| Left-Aligned | Center Aligned | Right Aligned |
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| :------------ |:---------------:| -----:|
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| $$a+b$$ | some wordy text | $1600 |
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| | $$
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A=\mathbf{A}=\underline{A}=\begin{pmatrix}
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a_{11} & a_{12} & \cdots & a_{1n}\\
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a_{21} & a_{22} & \cdots & a_{2n}\\
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\vdots & \vdots & & \vdots\\
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a_{m1} & a_{m2} & \cdots & a_{mn}\\
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\end{pmatrix} = (a_{ij})
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$$ | $12 |
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| | | $1 |
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**In Image Captions**
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The `alt` string doesn't work
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