X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=examples.tex;h=cb7d28a1f41d3a17c02635b370c3cb0fbe36a54f;hb=37b342a8a6fada8b0fbe828bdf97f346b538f5f4;hp=a1605c11bd311340a5212754fe0cc7453220f662;hpb=1b921ba1f02499f5784ddb87fd59c0621255042c;p=mjotex.git

diff --git a/examples.tex b/examples.tex
index a1605c1..cb7d28a 100644
--- a/examples.tex
+++ b/examples.tex
@@ -1,10 +1,37 @@
 \documentclass{report}
 
+% Setting hypertexnames=false forces hyperref to use a consistent
+% internal counter for proposition/equation references rather than
+% being clever, which doesn't work after we reset those counters.
+\usepackage[hypertexnames=false]{hyperref}
+\hypersetup{
+  colorlinks=true,
+  linkcolor=blue,
+  citecolor=blue
+}
+
+% We have to load this after hyperref, so that links work, but before
+% mjotex so that mjotex knows to define its glossary entries.
+\usepackage[nonumberlist]{glossaries}
+\makenoidxglossaries
+
+% If you want an index, we can do that too. You'll need to define
+% the "INDICES" variable in the GNUmakefile, though.
+\usepackage{makeidx}
+\makeindex
+
 \usepackage{mjotex}
 \usepackage{mathtools}
 
 \begin{document}
 
+  \begin{section}{Algebra}
+    If $R$ is a \index{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.
 
@@ -26,18 +53,46 @@
   \end{section}
 
   \begin{section}{Arrow}
-    The identity operator on $V$ is $\identity{V}$. The composition of
-    $f$ and $g$ is $\compose{f}{g}$. The inverse of $f$ is
+    The constant function that always returns $a$ is $\const{a}$. The
+    identity operator on $V$ is $\identity{V}$. The composition of $f$
+    and $g$ is $\compose{f}{g}$. The inverse of $f$ is
     $\inverse{f}$. If $f$ is a function and $A$ is a subset of its
     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
-    set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. Here's a pair
-    of things $\pair{1}{2}$ or a triple of them $\triple{1}{2}{3}$,
-    and the factorial of the number $10$ is $\factorial{10}$.
+    set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. The tuples go
+    up to seven, for now:
+    %
+    \begin{itemize}
+      \begin{item}
+        Pair: $\pair{1}{2}$,
+      \end{item}
+      \begin{item}
+        Triple: $\triple{1}{2}{3}$,
+      \end{item}
+      \begin{item}
+        Quadruple: $\quadruple{1}{2}{3}{4}$,
+      \end{item}
+      \begin{item}
+        Qintuple: $\quintuple{1}{2}{3}{4}{5}$,
+      \end{item}
+      \begin{item}
+        Sextuple: $\sextuple{1}{2}{3}{4}{5}{6}$,
+      \end{item}
+      \begin{item}
+        Septuple: $\septuple{1}{2}{3}{4}{5}{6}{7}$.
+      \end{item}
+    \end{itemize}
+    %
+    The factorial of the number $10$ is $\factorial{10}$.
 
     The Cartesian product of two sets $A$ and $B$ is
     $\cartprod{A}{B}$; if we take the product with $C$ as well, then
@@ -104,6 +159,11 @@
     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}
@@ -130,6 +190,9 @@
     $\boundedops[W]{V}$. If $W = V$, then we write $\boundedops{V}$
     instead.
 
+    If you want to solve a system of equations, try Cramer's
+    rule~\cite{ehrenborg}.
+
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
     but what if $W = V^{\perp}$? Then we wish to indicate that fact by
     writing $\directsumperp{V}{W}$. That operator should survive a
@@ -156,7 +219,7 @@
   \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 +232,14 @@
     [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}
@@ -295,4 +366,13 @@
     $\closure{X}$ and its boundary is $\boundary{X}$.
   \end{section}
 
+  \setlength{\glslistdottedwidth}{.3\linewidth}
+  \setglossarystyle{listdotted}
+  \glsaddall
+  \printnoidxglossaries
+
+  \bibliographystyle{mjo}
+  \bibliography{local-references}
+
+  \printindex
 \end{document}