mjo-font: add new \mathpzc (PostScript Zapf Chancery) font face.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index 9e376ccd58757500d96fbf6df2f5395e70b6c39b..e1f375fdc68d219d144010732030850d31cd5869 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -29,7 +29,13 @@
     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 $\Frac{R}$.
+    domain, then its fraction field is $\Frac{R}$. If $x,y,z \in R$,
+    then $\ideal{\set{x,y,z}}$ is the ideal generated by
+    $\set{x,y,z}$, which is defined to be the smallest ideal in $R$
+    containing that set. Likewise, if we are in an algebra
+    $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
+    $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
+    containing the set $\set{x,y,z}$.
   \end{section}
 
   \begin{section}{Algorithm}
@@ -68,9 +74,31 @@
   \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
@@ -143,7 +171,14 @@
   \end{section}
 
   \begin{section}{Font}
-    We can write things like Carathéodory and Güler and $\mathbb{R}$.
+    We can write things like Carathéodory and Güler and
+    $\mathbb{R}$. The PostScript Zapf Chancery font is also available
+    in both upper- and lower-case:
+    %
+    \begin{itemize}
+      \begin{item}$\mathpzc{abcdefghijklmnopqrstuvwxyz}$\end{item}
+      \begin{item}$\mathpzc{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\end{item}
+    \end{itemize}
   \end{section}
 
   \begin{section}{Linear algebra}
@@ -154,7 +189,8 @@
     $L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
     $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
     concept is the Moore-Penrose pseudoinverse of $L$, denoted by
-    $\pseudoinverse{L}$.
+    $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
+    $\rank{L}$.
 
     The span of a set $X$ is $\spanof{X}$, and its codimension is
     $\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The