Public:Writing LaTeX

\( \newcommand\Ek{\mathbb E_k} \newcommand\Pk{\mathbb P_k} \)

This page serves as an example of how to write LaTeX formulas on this wiki. Go to Edit of this page to see how it's done (especially see the top of the text where I define new macros the same way as we would do in the regular LaTeX). Internally it uses MathJax as its LaTeX engine. See this mathoveflow thread for reference.

Note that there are minor differences with LaTeX on this Wiki. Inline mathematics is typeset with $$...$$, \(...\), and <math> HTML tag. This means that $...$ won't work! And display style maths is written with \[...\], \begin{XXX}...\end{XXX}, where XXX can be, for example, align.

See for example this \(\Ek A\) and \(\Pk A\) and also the following:

\[ \Ek A =\ ... \] and \begin{align} \Pk A = ... \end{align}

Note that the advantage of \(...\) is that it is also valid LaTeX, so it can be then just copy-pasted into papers, when in rush :-).

Commutative diagrams

For commutative diagrams the simplest option is to just use arrays:

\[ \begin{array}{ccc} 0 & \xrightarrow{i} & A & \xrightarrow{f} & B & \xrightarrow{q} & C & \xrightarrow{d} & 0\\ \downarrow & \searrow & \downarrow & \nearrow & \downarrow & \searrow & \downarrow & \nearrow & \downarrow\\ 0 & \xrightarrow{j} & D & \xrightarrow{g} & E & \xrightarrow{r} & F & \xrightarrow{e} & 0 \end{array}\]

or like so \[ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}} \begin{array}{c} 0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\ \da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\ 0 & \ras{h_1} & 0 & \ras{h_2} & E & \ras{h_3} & F & \ras{h_4} & 0 & \ras{h_5} & 0 \\ \end{array} \] Complicated diagrams can be made by just stacking arrays/matrices in layers, e.g. \[ \matrix{ \mathbb C(A) & \xrightarrow{h_t} & B \\ {}_{\epsilon^{\mathbb C}} \downarrow & \matrix{ \nwarrow {}^{\iota_f} & & {}^g \nearrow \\ & \mkern-20mu X \xrightarrow{\quad\phi\quad} Y \mkern-20mu & \\ \swarrow {}_{f} & & {}_{\iota_g} \searrow } & \uparrow {}_{\epsilon^{\mathbb D}} \\ A & \underset{h_b}{\xleftarrow{\quad}} & \mathbb D(B) } \]

Another option is to use CD \(\require{AMScd}\) \begin{CD} \mathbb{Z}/p^n\mathbb{Z} @>{\theta_{n+1,\alpha}}>> U_1/U_{n+1}\\ @VVV @VVV\\ \mathbb{Z}/p^{n-1}\mathbb{Z} @>{\theta_{n,\alpha}}>> U_1/U_n \end{CD} However, CD doesn't support diagnoal arrows [1]. Note that to use CD one has to include <math>\require{AMScd}</math> somewhere in the text. Basic documentation of CD can be found here.