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}

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.

If one prefers to use TikZ diagrams or XY, it's possible to prepare the diagram in presheaf.com and then just add a link to the generated image. For example, this one

or (preferably) also include a link to the source (so that it can be easily eddited if needed):

The problem with this approach is that it's not as reliable (we had a couple of images disappearing in time). Please always include the source of the diagram from presheaf.com also in the HTML comment on the page in between <!-- and -->.