Math.md

Math Notation

By using MathJax, we can display all sorts of notation.

We can do inline math: $E = mc^2$

Or we can do block math:

$$ A \longrightarrow B $$

$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array} $$

And even diagrams via xyjax:

$$ \begin{xy} 0;<1em,0em>: (1,1);p+/v a(18) 5.5em/@{-}, (1,3);p+/v a(18) 5.5em/@2{-}, (1,5);p+/v a(18) 5.5em/@3{-}, (1,9);p+/v a(18) 5.5em/@{.}, (1,11);p+/v a(18) 5.5em/@2{.}, (1,13);p+/v a(18) 5.5em/@3{..}, \end{xy} $$

$$ \begin{xy} \xymatrix { U \ar@/_/[ddr]_y \ar@{.>}[dr]|{\langle x,y \rangle} \ar@/^/[drr]^x \\ & X \times_Z Y \ar[d]^q \ar[r]_p & X \ar[d]_f \\ & Y \ar[r]^g & Z } \end{xy} $$

MathJax $\LaTeX$ vs AsciiMath Syntax

Recently, I learned that MathJax had an alternative syntax, AsciiMath that is simpler for many purposes. Smartdown has enabled this feature, although we are currently using @ as the delimiter instead of ` or $.

$\LaTeX$ Syntax

Currently, Smartdown uses LaTeX-style math syntax, so the following formula:

$$ \sum_{i=1}^{n} i^3=\left(\frac{n(n+1)}{2}\right)^2 $$

is expressed as:

$$
\sum_{i=1}^{n} i^3=\left(\frac{n(n+1)}{2}\right)^2
$$

AsciiMath Syntax

The above formula is expressed in AsciiMath (using @ as delimiters) as:

@sum_(i=1)^n i^3=((n(n+1))/2)^2@

which Smartdown now renders as:

@sum_(i=1)^n i^3=((n(n+1))/2)^2@

Note that AsciiMath via MathJax does not support display-mode equations, but centering can be achieved via Markdown table syntax:

|     |
|:---:|
|@sum_(i=1)^n i^3=((n(n+1))/2)^2@|

which renders as below:

@sum_(i=1)^n i^3=((n(n+1))/2)^2@

More AsciiMath Examples

AsciiMath	Rendered
@[[a,b],[c,d]]@	@[[a,b],[c,d]]@
@sqrt sqrt root3x@	@sqrt sqrt root3x@
@int_0^1 f(x)dx@	@int_0^1 f(x)dx@
@hat(ab) bar(xy) ulA vec v dotx ddot y@	@hat(ab) bar(xy) ulA vec v dotx ddot y@

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Chemistry via mhchem

$$ \ce{Zn^2+ <=>[+ 2OH-][+ 2H+] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$ <=>[+ 2OH-][+ 2H+] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$ } $$

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