Add examples and clean up some stuff

parse.lisp

@@ -1,5 +1,7 @@
+;;;; Parse back the states printed by pprint.lisp
 (defpackage :cl-quantum/parse
-  (:use :cl :cl-quantum/state)
+  (:documentation "Parse back the states printed by pprint.lisp.")
+  (:use :cl :cl-quantum/math :cl-quantum/state)
   (:export #:parse-real
            #:parse-complex
            #:parse-state
@@ -44,7 +46,7 @@ stopped. That is, the index of the first un-parsed character."
         (list 0 0)
         (error "Malformed number: ~s" (subseq string start end))))))
 
-(define-constatnt +parse-complex-regexp+
+(define-constant +parse-complex-regexp+
     (ppcre:create-scanner
      "^\\s*([-+])?\\s*([-+]?)([0-9/.]+(?:[eE][-+]?[0-9]+)?)?(i)?"
      :extended-mode t)