
(DEFPARAMETER |QuaternionCategory;CAT| 'NIL) 

(DECLAIM (NOTINLINE |QuaternionCategory;|)) 

(DEFPARAMETER |QuaternionCategory;AL| 'NIL) 

(DEFUN |QuaternionCategory| (|t#1|)
  (LET (#1=#:G724 (#2=#:G725 (|devaluate| |t#1|)))
    (COND ((SETQ #1# (|assoc| #2# |QuaternionCategory;AL|)) (CDR #1#))
          (T
           (SETQ |QuaternionCategory;AL|
                   (|cons5| (CONS #2# (SETQ #1# (|QuaternionCategory;| #2#)))
                            |QuaternionCategory;AL|))
           #1#)))) 

(DEFUN |QuaternionCategory;| (|t#1|)
  (SPROG ((#1=#:G723 NIL))
         (PROG1
             (LETT #1#
                   (|sublisV| (PAIR '(|t#1|) (LIST |t#1|))
                              (COND (|QuaternionCategory;CAT|)
                                    ('T
                                     (LETT |QuaternionCategory;CAT|
                                           (|Join| (|Algebra| '|t#1|)
                                                   (|FullyRetractableTo|
                                                    '|t#1|)
                                                   (|DifferentialExtension|
                                                    '|t#1|)
                                                   (|FullyEvalableOver| '|t#1|)
                                                   (|FullyLinearlyExplicitOver|
                                                    '|t#1|)
                                                   (|mkCategory|
                                                    '(((|conjugate| ($ $)) T)
                                                      ((|imagI| (|t#1| $)) T)
                                                      ((|imagJ| (|t#1| $)) T)
                                                      ((|imagK| (|t#1| $)) T)
                                                      ((|norm| (|t#1| $)) T)
                                                      ((|quatern|
                                                        ($ |t#1| |t#1| |t#1|
                                                         |t#1|))
                                                       T)
                                                      ((|real| (|t#1| $)) T)
                                                      ((|abs| (|t#1| $))
                                                       (|has| |t#1|
                                                              (|RealNumberSystem|)))
                                                      ((|rational?|
                                                        ((|Boolean|) $))
                                                       (|has| |t#1|
                                                              (|IntegerNumberSystem|)))
                                                      ((|rational|
                                                        ((|Fraction|
                                                          (|Integer|))
                                                         $))
                                                       (|has| |t#1|
                                                              (|IntegerNumberSystem|)))
                                                      ((|rationalIfCan|
                                                        ((|Union|
                                                          (|Fraction|
                                                           (|Integer|))
                                                          "failed")
                                                         $))
                                                       (|has| |t#1|
                                                              (|IntegerNumberSystem|))))
                                                    '(((|EntireRing|)
                                                       (|has| |t#1|
                                                              (|EntireRing|)))
                                                      ((|OrderedSet|)
                                                       (|has| |t#1|
                                                              (|OrderedSet|)))
                                                      ((|DivisionRing|)
                                                       (|has| |t#1| (|Field|)))
                                                      ((|ConvertibleTo|
                                                        (|InputForm|))
                                                       (|has| |t#1|
                                                              (|ConvertibleTo|
                                                               (|InputForm|))))
                                                      ((|CharacteristicZero|)
                                                       (|has| |t#1|
                                                              (|CharacteristicZero|)))
                                                      ((|CharacteristicNonZero|)
                                                       (|has| |t#1|
                                                              (|CharacteristicNonZero|))))
                                                    NIL NIL)))))))
           (SETELT #1# 0 (LIST '|QuaternionCategory| |t#1|))))) 
