
(/VERSIONCHECK 2) 

(DEFPARAMETER |FiniteAlgebraicExtensionField;CAT| 'NIL) 

(DEFPARAMETER |FiniteAlgebraicExtensionField;AL| 'NIL) 

(DEFUN |FiniteAlgebraicExtensionField| (#1=#:G669)
  (LET (#2=#:G670)
    (COND
     ((SETQ #2#
              (|assoc| #3=(|devaluate| #1#)
                       |FiniteAlgebraicExtensionField;AL|))
      (CDR #2#))
     (T
      (SETQ |FiniteAlgebraicExtensionField;AL|
              (|cons5|
               (CONS #3# (SETQ #2# (|FiniteAlgebraicExtensionField;| #1#)))
               |FiniteAlgebraicExtensionField;AL|))
      #2#)))) 

(DEFUN |FiniteAlgebraicExtensionField;| (|t#1|)
  (PROG (#1=#:G668)
    (RETURN
     (PROG1
         (LETT #1#
               (|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))
                                       . #2=(|FiniteAlgebraicExtensionField|)))))
               . #2#)
       (SETELT #1# 0
               (LIST '|FiniteAlgebraicExtensionField| (|devaluate| |t#1|))))))) 
