X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=examples.tex;h=cdf2359d4fe22b68738d76ccca052d8b8d719b89;hb=fc7cfa7f3d02715cb09eae2e1c6bc501dc2d8d50;hp=a1605c11bd311340a5212754fe0cc7453220f662;hpb=1b921ba1f02499f5784ddb87fd59c0621255042c;p=mjotex.git

diff --git a/examples.tex b/examples.tex
index a1605c1..cdf2359 100644
--- a/examples.tex
+++ b/examples.tex
@@ -5,6 +5,13 @@
 
 \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.
 
@@ -32,6 +39,11 @@
     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
@@ -104,6 +116,11 @@
     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}
     We can write things like Carathéodory and Güler and $\mathbb{R}$.
   \end{section}
@@ -156,7 +173,7 @@
   \end{section}
 
   \begin{section}{Listing}
-    Here's an interactive sage prompt:
+    Here's an interactive SageMath prompt:
 
     \begin{tcblisting}{listing only,
                        colback=codebg,
@@ -169,6 +186,14 @@
     [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}