\begin{document}
+ \begin{section}{Algebra}
+ If $R$ is a commutative ring, then $\polyring{R}{X,Y,Z}$ is a
+ multivariate polynomial ring with indeterminates $X$, $Y$, and
+ $Z$, and coefficients in $R$. If $R$ is a moreover an integral
+ domain, then its fraction field is $\Frac{R}$.
+ \end{section}
+
\begin{section}{Algorithm}
An example of an algorithm (bogosort) environment.
domain, then the preimage under $f$ of $A$ is $\preimage{f}{A}$.
\end{section}
+ \begin{section}{Calculus}
+ The gradient of $f : \Rn \rightarrow \Rn[1]$ is $\gradient{f} :
+ \Rn \rightarrow \Rn$.
+ \end{section}
+
\begin{section}{Common}
The function $f$ applied to $x$ is $f\of{x}$. We can group terms
like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. Here's a
The conic hull of a set $X$ is $\cone{X}$; its affine hull is
$\aff{X}$, and its convex hull is $\conv{X}$. If $K$ is a cone,
then its lineality space is $\linspace{K}$, its lineality is
- $\lin{K}$, and its extreme directions are $\Ext{K}$.
+ $\lin{K}$, and its extreme directions are $\Ext{K}$. The fact that
+ $F$ is a face of $K$ is denoted by $F \faceof K$; if $F$ is a
+ proper face, then we write $F \properfaceof K$.
+ \end{section}
+
+ \begin{section}{Euclidean Jordan algebras}
+ The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra
+ is $\jp{x}{y}$.
\end{section}
\begin{section}{Font}
\end{section}
\begin{section}{Listing}
- Here's an interactive sage prompt:
+ Here's an interactive SageMath prompt:
\begin{tcblisting}{listing only,
colback=codebg,
[0 0], [0 0], [1 0], [0 1]
]
\end{tcblisting}
+
+ However, the smart way to display a SageMath listing is to load it
+ from an external file (under the ``listings'' subdirectory):
+
+ \sagelisting{example}
+
+ Keeping the listings in separate files makes it easy for the build
+ system to test them.
\end{section}
\begin{section}{Miscellaneous}