
(/VERSIONCHECK 2) 

(DEFPARAMETER |FiniteAlgebraicExtensionField;CAT| 'NIL) 

(DEFPARAMETER |FiniteAlgebraicExtensionField;AL| 'NIL) 

(DEFUN |FiniteAlgebraicExtensionField| (#0=#:G1823)
  (LET (#1=#:G1824)
    (COND
      ((SETQ #1#
             (|assoc| #2=(|devaluate| #0#)
                      |FiniteAlgebraicExtensionField;AL|))
       (CDR #1#))
      (T (SETQ |FiniteAlgebraicExtensionField;AL|
               (|cons5| (CONS #2#
                              (SETQ #1#
                                    (|FiniteAlgebraicExtensionField;|
                                     #0#)))
                        |FiniteAlgebraicExtensionField;AL|))
         #1#)))) 

(DEFUN |FiniteAlgebraicExtensionField;| (|t#1|)
  (PROG (#0=#:G1822)
    (RETURN
      (PROG1 (LETT #0#
                   (|sublisV|
                       (PAIR '(|t#1|) (LIST (|devaluate| |t#1|)))
                       (COND
                         (|FiniteAlgebraicExtensionField;CAT|)
                         ('T
                          (LETT |FiniteAlgebraicExtensionField;CAT|
                                (|Join| (|ExtensionField| '|t#1|)
                                        (|RetractableTo| '|t#1|)
                                        (|mkCategory| '|domain|
                                         '(((|basis| ((|Vector| $))) T)
                                           ((|basis|
                                             ((|Vector| $)
                                              (|PositiveInteger|)))
                                            T)
                                           ((|coordinates|
                                             ((|Vector| |t#1|) $))
                                            T)
                                           ((|coordinates|
                                             ((|Matrix| |t#1|)
                                              (|Vector| $)))
                                            T)
                                           ((|represents|
                                             ($ (|Vector| |t#1|)))
                                            T)
                                           ((|minimalPolynomial|
                                             ((|SparseUnivariatePolynomial|
                                               |t#1|)
                                              $))
                                            T)
                                           ((|definingPolynomial|
                                             ((|SparseUnivariatePolynomial|
                                               |t#1|)))
                                            T)
                                           ((|extensionDegree|
                                             ((|PositiveInteger|)))
                                            T)
                                           ((|degree|
                                             ((|PositiveInteger|) $))
                                            T)
                                           ((|norm| (|t#1| $)) T)
                                           ((|trace| (|t#1| $)) T)
                                           ((|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|))))
                                         '((|SparseUnivariatePolynomial|
                                            |t#1|)
                                           (|Boolean|)
                                           (|PositiveInteger|)
                                           (|SparseUnivariatePolynomial|
                                            $)
                                           (|Vector| |t#1|)
                                           (|Matrix| |t#1|)
                                           (|Vector| $))
                                         NIL))
                                . #1=(|FiniteAlgebraicExtensionField|))))) . #1#)
        (SETELT #0# 0
                (LIST '|FiniteAlgebraicExtensionField|
                      (|devaluate| |t#1|))))))) 
