notes/docs/mathjax/test.md

layout, title, parent, mathjax

layout	title	parent	mathjax
default	Mathjax test	Mathjax	true

x math at the start of the document

Nested: M = \text{while e^2 $e^2$ do $c^2$ end}

Numbered equations

\begin{equation}
\int_0^x \sin(x) dx
\label{eq:test}
\end{equation}

\eqref{eq:test}

Blockquotes

1. A block quote
2. With a list inside
3. With math

Math environment Syntax testing

Inline Math should work with $$ \frac{x+y}{y} but not \( (\frac{x+y}{y})

Use $$ on separate lines:

\int_{-\infty}^\infty e^{-x^2} = \sqrt{\pi}

Use $$ on the same line:

\frac{-b \pm \sqrt{b^2-4ac}}{2a}

Use $$ on separate lines:

a+b

Use $$ on the same line: E=mc^2

---

Some Tex Functions

k \times k, n \times 2, 2 \times n, \times

x \cdot y, \cdot

\sqrt{x^2+y^2+z^2} \alpha \beta \gamma

\begin{aligned}
x\ &= y\\
mc^2\ &= E
\end{aligned}

---

Escaped Math environments

In the following examples no math environments should render:

a $5, a $10 and a $100 Bill.

All McScrooge sees

$$

and even more:

$$

\[x+y] \(x+y)

$x

\$

\$, \[ \], $x$

---

Testing \newcommand

For all x and y in \mathbb{R}^k it is true that

\newcommand{sca}[1]{\langle #1 \rangle}
|\sca{x,y}|^2 \le \sca{x,x} \cdot \sca{y,y},

\newcommand{\scalong}[1]{(#1_1,\dots,#1_k)}

where \sca{\cdot,\cdot} denotes the inner product \sca{\scalong{x}, \scalong{x}} = \sum_{i=1}^k x_i y_i.

---

Testing several math fonts

p(\mathbf{m}) \sim \mathcal{N}(\mathbf{m}) e^{-\sum_{i} \beta_i m_i}

\langle \vec{m} \rangle =
\frac{1}{Z(\vec{\beta})}\vec{m}(\mu)
\sum_{\mu\in\mathcal{G}}
e^{-\vec{\beta}\cdot\vec{m}(\mu)}

---

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):

The characteristic polynomial \chi(\lambda) of the 3 \times 3 matrix
    $$ \left( \begin{array}{ccc} a & b & c \ d & e & f \ g & h & i \end{array} \right)

  
is given by the formula  
    $$
\chi(\lambda) = \left| \begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array} \right|.

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

---

Does it work in different MD elements?

Math x^2 in heading 1

Math x^2 in heading 2

Math x^2 in heading 3

Math x^2 in heading 4

x_1, x_2, \dots, x_N should not conflict with _ italics?

(f*g*h)(x) should not conflict with * syntax?

[a+b](c+d) should not conflict link syntax?

math x^2 in emphasis

math x^2 in bold

math x^2 in link

math $$x^2$$ in code

math x^2 in strikethrough (doesn't strike through the math)

In Tables

Left-Aligned	Center Aligned	Right Aligned
a+b	some wordy text	$1600
a+b	some wordy text	$1600
a+b	some wordy text	$1600

The following doesn't work (it only works with Pandoc)

Left-Aligned	Center Aligned	Right Aligned
a+b	some wordy text	$1600
	$$
A=\mathbf{A}=\underline{A}=\begin{pmatrix}
a_{11} & a_{12} & \cdots & a_{1n}\
a_{21} & a_{22} & \cdots & a_{2n}\
\vdots & \vdots & & \vdots\
a_{m1} & a_{m2} & \cdots & a_{mn}\
\end{pmatrix} = (a_{ij})
$$	$12
		$1

In Image Captions

The alt string doesn't work