
(DEFPARAMETER |FiniteAlgebraicExtensionField;CAT| 'NIL) 

(DECLAIM (NOTINLINE |FiniteAlgebraicExtensionField;|)) 

(DEFPARAMETER |FiniteAlgebraicExtensionField;AL| 'NIL) 

(DEFUN |FiniteAlgebraicExtensionField| (|t#1|)
  (LET (#1=#:G9 (#2=#:G10 (|devaluate| |t#1|)))
    (COND
     ((SETQ #1# (|assoc| #2# |FiniteAlgebraicExtensionField;AL|)) (CDR #1#))
     (T
      (SETQ |FiniteAlgebraicExtensionField;AL|
              (|cons5|
               (CONS #2# (SETQ #1# (|FiniteAlgebraicExtensionField;| #2#)))
               |FiniteAlgebraicExtensionField;AL|))
      #1#)))) 

(DEFUN |FiniteAlgebraicExtensionField;| (|t#1|)
  (SPROG ((#1=#:G8 NIL))
         (PROG1
             (LETT #1#
                   (|subst_in_cat| '(|t#1|) (LIST |t#1|)
                                   (|subst_in_cat| '(#2=#:G7)
                                                   (LIST
                                                    '(|SparseUnivariatePolynomial|
                                                      |t#1|))
                                                   (COND
                                                    (|FiniteAlgebraicExtensionField;CAT|)
                                                    ('T
                                                     (LETT
                                                      |FiniteAlgebraicExtensionField;CAT|
                                                      (|Join|
                                                       (|ExtensionField|
                                                        '|t#1|)
                                                       (|FramedAlgebra| '|t#1|
                                                                        '#2#)
                                                       (|RetractableTo| '|t#1|)
                                                       (|mkCategory|
                                                        '(((|definingPolynomial|
                                                            ((|SparseUnivariatePolynomial|
                                                              |t#1|)))
                                                           T)
                                                          ((|extensionDegree|
                                                            ((|PositiveInteger|)))
                                                           T)
                                                          ((|degree|
                                                            ((|PositiveInteger|)
                                                             %))
                                                           T)
                                                          ((|basis|
                                                            ((|Vector| %)
                                                             (|PositiveInteger|)))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|minimalPolynomial|
                                                            ((|SparseUnivariatePolynomial|
                                                              %)
                                                             %
                                                             (|PositiveInteger|)))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|norm|
                                                            (% %
                                                             (|PositiveInteger|)))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|trace|
                                                            (% %
                                                             (|PositiveInteger|)))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|createNormalElement|
                                                            (%))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|normalElement|
                                                            (%))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|normal?|
                                                            ((|Boolean|) %))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|generator| (%))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|linearAssociatedExp|
                                                            (% %
                                                             (|SparseUnivariatePolynomial|
                                                              |t#1|)))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|linearAssociatedOrder|
                                                            ((|SparseUnivariatePolynomial|
                                                              |t#1|)
                                                             %))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|linearAssociatedLog|
                                                            ((|SparseUnivariatePolynomial|
                                                              |t#1|)
                                                             %))
                                                           (|has| |t#1|
                                                                  (|Finite|)))
                                                          ((|linearAssociatedLog|
                                                            ((|Union|
                                                              (|SparseUnivariatePolynomial|
                                                               |t#1|)
                                                              "failed")
                                                             % %))
                                                           (|has| |t#1|
                                                                  (|Finite|))))
                                                        '(((|FiniteFieldCategory|)
                                                           (|has| |t#1|
                                                                  (|Finite|))))
                                                        NIL NIL))))))))
           (SETELT #1# 0 (LIST '|FiniteAlgebraicExtensionField| |t#1|))))) 
