Writing LaTeX

Issues and comments are written in LaTeX, much like a short Overleaf document: text-mode LaTeX for structure, and math rendered by MathJax. You can paste a small document — \documentclass, \usepackage and \begin{document} are accepted and ignored. Try things in the playground.

Inline and display math

Let $f\colon X \to Y$ be proper. Then
\[ R^i f_* \mathscr{F} = 0 \quad \text{for } i > \dim X. \]
Double dollars $$\int_0^1 x^n\,dx = \frac{1}{n+1}$$ also work.

Let f\colon X \to Y be proper. Then R^i f_* \mathscr{F} = 0 \quad \text{for } i > \dim X. Double dollars \int_0^1 x^n\,dx = \frac{1}{n+1} also work.

Numbered equations and references

\begin{equation}\label{eq:height}
  h(P + Q) + h(P - Q) = 2h(P) + 2h(Q) + O(1)
\end{equation}
\begin{align}
  \hat h(nP) &= n^2 \hat h(P) \label{eq:quad} \\
  \hat h(P)  &\ge 0 \notag
\end{align}
By \eqref{eq:height} and \eqref{eq:quad}, …

\begin{equation}\label{eq:height} h(P + Q) + h(P - Q) = 2h(P) + 2h(Q) + O(1) \end{equation} \begin{align} \hat h(nP) &= n^2 \hat h(P) \label{eq:quad} \\ \hat h(P) &\ge 0 \notag \end{align} By \eqref{eq:height} and \eqref{eq:quad}, …

Theorems and proofs

theorem, lemma, proposition, corollary, definition, remark, example, claim, conjecture, … are predefined and share one counter.

\begin{lemma}[Hensel]\label{lem:hensel}
If $f(a) \equiv 0 \pmod p$ and $f'(a) \not\equiv 0 \pmod p$, then $a$ lifts uniquely.
\end{lemma}
\begin{proof}
Newton's method; see \cref{lem:hensel}.
\end{proof}

Lemma 1 (Hensel). If f(a) \equiv 0 \pmod p and f'(a) \not\equiv 0 \pmod p, then a lifts uniquely.

Proof. Newton’s method; see Lemma 1.□

Your own macros

Definitions apply only to the post they appear in.

\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\DeclareMathOperator{\Frob}{Frob}
We have $\inner{x}{y} = \inner{y}{x}$ and $\Frob_p$ acts trivially.

We have \inner{x}{y} = \inner{y}{x} and \Frob_p acts trivially.

Lists

\begin{enumerate}
  \item The hypothesis $n \ge 2$ is missing.
  \item In the proof:
  \begin{enumerate}
    \item line 3 should read $a_{n+1}$;
    \item the bound is off by a factor of $2$.
  \end{enumerate}
\end{enumerate}

1.
The hypothesis n \ge 2 is missing.
2.
In the proof:
1. (a)
  line 3 should read a_{n+1};
2. (b)
  the bound is off by a factor of 2.

Text formatting and links

\textbf{Bold}, \emph{emphasis}, \texttt{monospace}, \textsc{Small Caps}.
See \href{https://example.org}{this page}, or \url{https://example.org}.
A footnote.\footnote{Footnotes are listed at the end of the post.}

Bold, emphasis, monospace, Small Caps. See this page, or https://example.org. A footnote.¹

Footnotes are listed at the end of the post. ↩

Commutative diagrams (amscd)

tikz-cd and xymatrix are not supported yet.

\[
\begin{CD}
A @>{f}>> B \\
@V{g}VV @VV{h}V \\
C @>>{k}> D
\end{CD}
\]

\begin{CD} A @>{f}>> B \\ @V{g}VV @VV{h}V \\ C @>>{k}> D \end{CD}

Physics, chemistry and proof trees

$\dv{f}{x}$, $\pdv[2]{u}{t}$, $\abs{\psi}$, $\bra{\phi}H\ket{\psi}$, $\ce{2H2 + O2 -> 2H2O}$
\begin{prooftree}
  \AxiomC{$A$} \AxiomC{$A \to B$} \BinaryInfC{$B$}
\end{prooftree}

\dv{f}{x}, \pdv[2]{u}{t}, \abs{\psi}, \bra{\phi}H\ket{\psi}, \ce{2H2 + O2 -> 2H2O} \begin{prooftree} \AxiomC{$A$} \AxiomC{$A \to B$} \BinaryInfC{$B$} \end{prooftree}

Tables and code

\begin{tabular}{|l|c|}
\hline
Edition & Page \\ \hline
1st & 123 \\
2nd & 131 \\ \hline
\end{tabular}

\begin{verbatim}
for n in range(10): print(n)
\end{verbatim}

Edition	Page
1st	123
2nd	131

for n in range(10): print(n)

Available packages

Always loaded; \usepackage lines for them do nothing.

amsmath — Equations, align, gather, multline, cases, matrices, \DeclareMathOperator
amssymb — Extra symbols (\mathbb, \leqslant, \twoheadrightarrow, …)
amsfonts — \mathbb, \mathfrak
amsthm — Theorem environments and proofs
amscd — Simple commutative diagrams with \begin{CD}
mathtools — \coloneqq, dcases, \xrightarrow, starred matrices, …
mathrsfs — \mathscr
eucal — Euler script letters
bm — \bm (bold math)
physics — \dv, \pdv, \abs, \norm, \qty, \bra, \ket, …
braket — \braket, \Set
cancel — \cancel, \bcancel, \xcancel
cases — numcases
empheq — Boxed / decorated equations
bussproofs — Proof trees (prooftree environment)
mhchem — Chemical formulas with \ce
dsfont — \mathds
bbm — \mathbbm
bbold — Blackboard bold digits
bboldx — Blackboard bold
upgreek — Upright Greek letters (\upalpha, …)
gensymb — \degree, \celsius, …
textcomp — Text symbols
units — \units, \unitfrac
nicefrac — \nicefrac
extpfeil — Extensible arrows
centernot — \centernot
enclose — \enclose
xcolor — \color, \textcolor
color — \color, \textcolor
colortbl — Coloured table cells
hyperref — \href, \url
url — \url
ulem — \uline, \sout
cleveref — \cref, \Cref
enumitem — List options (accepted, options ignored)
enumerate — List labels (accepted, options ignored)
listings — lstlisting code blocks
minted — minted code blocks
verbatim — verbatim environment
booktabs — \toprule, \midrule, \bottomrule
array — Table column types
tabularx — tabularx tables
longtable — longtable tables
graphicx — Accepted, but images are not supported

Not available

tikz — TikZ pictures are not supported yet.
tikz-cd — tikz-cd diagrams are not supported yet — use \begin{CD} … \end{CD} for simple diagrams.
pgfplots — Plots are not supported.
xy — xymatrix diagrams are not supported yet — use \begin{CD} … \end{CD} for simple diagrams.
pstricks — PSTricks is not supported.
Commands that touch files or the system (\input, \include, \write, …) are refused, and so are images.

Predefined macros

Usable in every post (you can redefine them):

\N \Z \Q \R \C \bm \div \divides \ndivides \colim \Spec \Proj \Hom \End \Aut \Isom \Mor \Gal \Pic \Div \Cl \Br \Frac \Sym \Ext \Tor \Ann \Ass \Supp \supp \codim \coker \im \id \rank \sgn \ord \disc \Nm \Res \Ind \Stab \Lie \GL \SL \PGL \PSL \SO \SU \Sp

Keyboard shortcuts

Ctrl/⌘ B bold, Ctrl/⌘ I emphasis, Ctrl/⌘ M inline math, Ctrl/⌘ ⇧ M display math
Ctrl/⌘ Enter submit · Ctrl Space autocomplete · Ctrl/⌘ F search