
(DECLAIM (NOTINLINE |FiniteFieldExtension;|)) 

(DEFUN |FiniteFieldExtension| (&REST #1=#:G755)
  (SPROG NIL
         (PROG (#2=#:G756)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|FiniteFieldExtension|)
                                               '|domainEqualList|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1 (APPLY (|function| |FiniteFieldExtension;|) #1#)
                    (LETT #2# T))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache| '|FiniteFieldExtension|)))))))))) 

(DEFUN |FiniteFieldExtension;| (|#1| |#2|)
  (SPROG
   ((|pv$| NIL) (#1=#:G754 NIL) ($ NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
   (PROGN
    (LETT DV$1 (|devaluate| |#1|))
    (LETT DV$2 (|devaluate| |#2|))
    (LETT |dv$| (LIST '|FiniteFieldExtension| DV$1 DV$2))
    (LETT $ (GETREFV 50))
    (QSETREFV $ 0 |dv$|)
    (QSETREFV $ 3
              (LETT |pv$|
                    (|buildPredVector| 0 0
                                       (LIST
                                        (|HasCategory| |#1|
                                                       '(|CharacteristicZero|))
                                        (LETT #1#
                                              (|HasCategory| |#1| '(|Finite|)))
                                        (OR
                                         (|HasCategory| |#1|
                                                        '(|CharacteristicNonZero|))
                                         #1#)))))
    (|haddProp| |$ConstructorCache| '|FiniteFieldExtension| (LIST DV$1 DV$2)
                (CONS 1 $))
    (|stuffDomainSlots| $)
    (QSETREFV $ 6 |#1|)
    (QSETREFV $ 7 |#2|)
    (AND #1# (|HasCategory| $ '(|CharacteristicNonZero|))
         (|augmentPredVector| $ 8))
    (SETF |pv$| (QREFELT $ 3))
    $))) 

(MAKEPROP '|FiniteFieldExtension| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL
              (|FiniteFieldExtensionByPolynomial| 6
                                                  (NRTEVAL
                                                   (SPADCALL (QREFELT $ 7)
                                                             (QREFELT $ 11))))
              (|local| |#1|) (|local| |#2|) (|SparseUnivariatePolynomial| 6)
              (|PositiveInteger|) (|FiniteFieldPolynomialPackage| 6)
              (0 . |createIrreduciblePoly|) (|Union| 32 '#1="failed")
              (|Matrix| $) (|OnePointCompletion| 9) (|Union| $ '"failed")
              (|Union| 17 '"failed") (|NonNegativeInteger|) (|List| $)
              (|InputForm|) (|Boolean|) (|Factored| 22)
              (|SparseUnivariatePolynomial| $) (|Union| 24 '#1#) (|List| 22)
              (|Record| (|:| |factor| 28) (|:| |exponent| 17)) (|List| 25)
              (|Table| 9 17) (|Integer|)
              (|Union| '"prime" '"polynomial" '"normal" '"cyclic")
              (|Union| 8 '"failed") (|Matrix| 6) (|Vector| $) (|Vector| 6)
              (|CardinalNumber|) (|Union| 6 '"failed") (|Fraction| 28)
              (|Factored| $) (|Union| 18 '#2="failed")
              (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $))
              (|Record| (|:| |coef1| $) (|:| |coef2| $)) (|Union| 40 '#2#)
              (|Record| (|:| |quotient| $) (|:| |remainder| $))
              (|Record| (|:| |coef| 18) (|:| |generator| $))
              (|Record| (|:| |llcm_res| $) (|:| |coeff1| $) (|:| |coeff2| $))
              (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))
              (|String|) (|SingleInteger|) (|HashState|) (|OutputForm|))
           '#() 'NIL
           (CONS
            (|makeByteWordVec2| 3
                                '(0 0 2 3 0 0 2 0 0 0 0 0 0 0 0 0 0 3 1 2 0 0 0
                                  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                                  0 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 2))
            (CONS
             '#(|FiniteAlgebraicExtensionField&| |ExtensionField&|
                |FiniteFieldCategory&| |FieldOfPrimeCharacteristic&| |Field&|
                |EuclideanDomain&| |PolynomialFactorizationExplicit&| NIL
                |UniqueFactorizationDomain&| |GcdDomain&| NIL |DivisionRing&|
                NIL NIL |Algebra&| |EntireRing&| |Algebra&| NIL NIL
                |DifferentialRing&| NIL |VectorSpace&| |Rng&| NIL |Module&|
                |Module&| |Module&| NIL NIL NIL NIL |NonAssociativeRing&| NIL
                NIL NIL NIL NIL |NonAssociativeRng&| NIL |AbelianGroup&| NIL
                NIL NIL NIL |MagmaWithUnit&| |NonAssociativeSemiRng&|
                |AbelianMonoid&| |Finite&| |Magma&| |AbelianSemiGroup&| NIL NIL
                NIL |SetCategory&| |RetractableTo&| NIL NIL NIL NIL NIL
                |BasicType&| NIL NIL)
             (CONS
              '#((|FiniteAlgebraicExtensionField| 6) (|ExtensionField| 6)
                 (|FiniteFieldCategory|) (|FieldOfPrimeCharacteristic|)
                 (|Field|) (|EuclideanDomain|)
                 (|PolynomialFactorizationExplicit|) (|PrincipalIdealDomain|)
                 (|UniqueFactorizationDomain|) (|GcdDomain|) (|IntegralDomain|)
                 (|DivisionRing|) (|CommutativeRing|) (|LeftOreRing|)
                 (|Algebra| 36) (|EntireRing|) (|Algebra| $$)
                 (|CharacteristicNonZero|) (|CharacteristicZero|)
                 (|DifferentialRing|) (|Ring|) (|VectorSpace| 6) (|Rng|)
                 (|SemiRing|) (|Module| 6) (|Module| 36) (|Module| $$)
                 (|SemiRng|) (|BiModule| 6 6) (|BiModule| 36 36)
                 (|BiModule| $$ $$) (|NonAssociativeRing|) (|RightModule| 6)
                 (|LeftModule| 6) (|RightModule| 36) (|LeftModule| 36)
                 (|LeftModule| $$) (|NonAssociativeRng|) (|RightModule| $$)
                 (|AbelianGroup|) (|Monoid|) (|NonAssociativeSemiRing|)
                 (|CancellationAbelianMonoid|) (|SemiGroup|) (|MagmaWithUnit|)
                 (|NonAssociativeSemiRng|) (|AbelianMonoid|) (|Finite|)
                 (|Magma|) (|AbelianSemiGroup|) (|Comparable|) (|StepThrough|)
                 (|CommutativeStar|) (|SetCategory|) (|RetractableTo| 6)
                 (|canonicalsClosed|) (|canonicalUnitNormal|)
                 (|noZeroDivisors|) (|TwoSidedRecip|) (|unitsKnown|)
                 (|BasicType|) (|CoercibleTo| 49) (|ConvertibleTo| 19))
              (|makeByteWordVec2| 11 '(1 10 8 9 11)))))
           '|lookupIncomplete|)) 
