diff --git a/includes/math-expr.inc b/includes/math-expr.inc
index 28b2305..acbdfe9 100644
--- a/includes/math-expr.inc
+++ b/includes/math-expr.inc
@@ -13,8 +13,7 @@
  *     ctools_math_expr - safely evaluate math expressions
  *
  * SYNOPSIS
- *    include('ctools_math_expr.class.php');
- *    $m = new ctools_math_expr;
+ *     $m = new ctools_math_expr();
  *     // basic evaluation:
  *     $result = $m->evaluate('2+2');
  *     // supports: order of operation; parentheses; negation; built-in
@@ -98,12 +97,14 @@ class ctools_math_expr {
    * @var bool
    */
   public $suppress_errors = FALSE;
+
   /**
    * The last error message reported.
    *
    * @var string
    */
   public $last_error = NULL;
+
   /**
    * List of all errors reported.
    *
@@ -117,18 +118,21 @@ class ctools_math_expr {
    * @var array
    */
   protected $vars;
+
   /**
    * User defined functions.
    *
    * @var array
    */
   protected $userfuncs;
+
   /**
-   * The names of constants top prevent overwriting.
+   * The names of constants, used to make constants read-only.
    *
    * @var array
    */
   protected $constvars;
+
   /**
    * Built in simple (one arg) functions.
    * Merged into $this->funcs in constructor.
@@ -136,18 +140,26 @@ class ctools_math_expr {
    * @var array
    */
   protected $simplefuncs;
+
   /**
-   * Other built-in functions.
+   * Definitions of all built-in functions.
    *
    * @var array
    */
   protected $funcs;
+
   /**
    * Operators and their precedence.
    *
    * @var array
    */
   protected $ops;
+
+  /**
+   * The set of operators using two arguments.
+   *
+   * @var array
+   */
   protected $binaryops;
 
   /**
@@ -421,8 +433,9 @@ class ctools_math_expr {
     $index = 0;
     $stack = new ctools_math_expr_stack();
     // Postfix form of expression, to be passed to pfx().
-    // @var array
     $output = array();
+
+    // TODO: Because the expr can contain string operands, using strtolower here is a bug.
     $expr = trim(strtolower($expr));
 
     // We use this in syntax-checking the expression and determining when
@@ -533,7 +546,7 @@ class ctools_math_expr {
 
         // Pop the argument expression stuff and push onto the output:
         while (($o2 = $stack->pop()) !== '(') {
-          // Oops, never had a (.
+          // Oops, never had a '('.
           if (is_null($o2)) {
             return $this->trigger("unexpected ',' in $expr $o2");
           }
@@ -809,7 +822,7 @@ class ctools_math_expr {
    *   Message to add to trigger error.
    *
    * @return bool
-   *   can trigger error then return FALSE.
+   *   Can trigger error, then returns FALSE.
    */
   protected function trigger($msg) {
     $this->errors[] = $msg;
@@ -921,7 +934,7 @@ function ctools_math_expr_if($expr, $if, $else = NULL) {
  * Remove any non-digits so that numbers like $4,511.23 still work.
  *
  * It might be good for those using the 12,345.67 format, but is awful for
- * others.
+ * those using other conventions.
  * Use of the php 'intl' module might work here, if the correct locale can be
  * derived, but that seems unlikely to be true in all cases.
  *
@@ -936,7 +949,7 @@ function ctools_math_expr_if($expr, $if, $else = NULL) {
  */
 function ctools_math_expr_number($arg) {
   // TODO: A really bad idea: It might be good for those using the 12,345.67
-  // format, but is awful for others.
+  // format, but is awful for those using other conventions.
   // $arg = preg_replace("/[^0-9\.]/", '', $arg);.
   return $arg;
 }
diff --git a/includes/uuid.inc b/includes/uuid.inc
index 51c15d1..13897f1 100644
--- a/includes/uuid.inc
+++ b/includes/uuid.inc
@@ -10,7 +10,7 @@
  * Pattern for detecting a valid UUID.
  */
 if (!defined('UUID_PATTERN')) {
-  define('UUID_PATTERN', '[0-9a-userfuncs]{8}-([0-9a-userfuncs]{4}-){3}[0-9a-userfuncs]{12}');
+  define('UUID_PATTERN', '[0-9a-f]{8}-([0-9a-f]{4}-){3}[0-9a-f]{12}');
 }
 
 /**