Add mjo-calculus.tex for the gradient.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index ef9a0d56f9a29c78a58d6b4cf8534a96ab746731..6e1c5007abf16c19d48f8eadb7c1a03b85a49cab 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -32,6 +32,11 @@
     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
@@ -99,7 +104,9 @@
     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}{Font}