
(SDEFUN |FAXF-;represents;VS;1| ((|v| (|Vector| F)) (% (S)))
        (SPROG ((|a| (S)) (#1=#:G19 NIL) (|i| NIL) (|b| (|Vector| S)))
               (SEQ (LETT |a| (|spadConstant| % 8))
                    (LETT |b| (SPADCALL (QREFELT % 10)))
                    (SEQ (LETT |i| 1) (LETT #1# (SPADCALL (QREFELT % 12))) G190
                         (COND ((|greater_SI| |i| #1#) (GO G191)))
                         (SEQ
                          (EXIT
                           (LETT |a|
                                 (SPADCALL |a|
                                           (SPADCALL
                                            (SPADCALL |v| |i| (QREFELT % 15))
                                            (SPADCALL |b| |i| (QREFELT % 17))
                                            (QREFELT % 18))
                                           (QREFELT % 19)))))
                         (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                    (EXIT |a|)))) 

(PUT '|FAXF-;transcendenceDegree;Nni;2| '|SPADreplace| '(XLAM NIL 0)) 

(SDEFUN |FAXF-;transcendenceDegree;Nni;2| ((% (|NonNegativeInteger|))) 0) 

(SDEFUN |FAXF-;extensionDegree;Opc;3|
        ((% (|OnePointCompletion| (|PositiveInteger|))))
        (SPROG ((#1=#:G22 NIL))
               (SPADCALL
                (PROG1 (LETT #1# (QVSIZE (SPADCALL (QREFELT % 10))))
                  (|check_subtype2| (> #1# 0) '(|PositiveInteger|)
                                    '(|NonNegativeInteger|) #1#))
                (QREFELT % 24)))) 

(SDEFUN |FAXF-;degree;SOpc;4|
        ((|a| (S)) (% (|OnePointCompletion| (|PositiveInteger|))))
        (SPADCALL (SPADCALL |a| (QREFELT % 26)) (QREFELT % 24))) 

(SDEFUN |FAXF-;coordinates;VM;5| ((|v| (|Vector| S)) (% (|Matrix| F)))
        (SPROG ((#1=#:G29 NIL) (|i| NIL) (|j| NIL) (|m| (|Matrix| F)))
               (SEQ
                (LETT |m|
                      (MAKE_MATRIX1 (QVSIZE |v|) (SPADCALL (QREFELT % 12))
                                    (|spadConstant| % 28)))
                (SEQ (LETT |j| (PROGN |m| 1))
                     (LETT |i| (SPADCALL |v| (QREFELT % 29)))
                     (LETT #1# (QVSIZE |v|)) G190
                     (COND ((> |i| #1#) (GO G191)))
                     (SEQ
                      (EXIT
                       (SPADCALL |m| |j|
                                 (SPADCALL (QAREF1O |v| |i| 1) (QREFELT % 30))
                                 (QREFELT % 32))))
                     (LETT |i| (PROG1 (+ |i| 1) (LETT |j| (+ |j| 1))))
                     (GO G190) G191 (EXIT NIL))
                (EXIT |m|)))) 

(PUT '|FAXF-;algebraic?;SB;6| '|SPADreplace| '(XLAM (|a|) 'T)) 

(SDEFUN |FAXF-;algebraic?;SB;6| ((|a| (S)) (% (|Boolean|))) 'T) 

(PUT '|FAXF-;transcendent?;SB;7| '|SPADreplace| '(XLAM (|a|) NIL)) 

(SDEFUN |FAXF-;transcendent?;SB;7| ((|a| (S)) (% (|Boolean|))) NIL) 

(SDEFUN |FAXF-;extensionDegree;Pi;8| ((% (|PositiveInteger|)))
        (SPROG ((#1=#:G32 NIL))
               (PROG1 (LETT #1# (QVSIZE (SPADCALL (QREFELT % 10))))
                 (|check_subtype2| (> #1# 0) '(|PositiveInteger|)
                                   '(|NonNegativeInteger|) #1#)))) 

(SDEFUN |FAXF-;trace;SF;9| ((|a| (S)) (% (F)))
        (SPROG ((|abs| (F)) (#1=#:G38 NIL) (|i| NIL) (|b| (|Vector| S)))
               (SEQ (LETT |b| (SPADCALL (QREFELT % 10)))
                    (LETT |abs| (|spadConstant| % 28))
                    (SEQ (LETT |i| 1) (LETT #1# (QVSIZE |b|)) G190
                         (COND ((|greater_SI| |i| #1#) (GO G191)))
                         (SEQ
                          (EXIT
                           (LETT |abs|
                                 (SPADCALL |abs|
                                           (SPADCALL
                                            (SPADCALL
                                             (SPADCALL |a|
                                                       (SPADCALL |b| |i|
                                                                 (QREFELT %
                                                                          17))
                                                       (QREFELT % 38))
                                             (QREFELT % 30))
                                            |i| (QREFELT % 15))
                                           (QREFELT % 39)))))
                         (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                    (EXIT |abs|)))) 

(SDEFUN |FAXF-;norm;SF;10| ((|a| (S)) (% (F)))
        (SPROG ((#1=#:G43 NIL) (|i| NIL) (|m| (|Matrix| F)) (|b| (|Vector| S)))
               (SEQ (LETT |b| (SPADCALL (QREFELT % 10)))
                    (LETT |m|
                          (MAKE_MATRIX1 (QVSIZE |b|) (QVSIZE |b|)
                                        (|spadConstant| % 28)))
                    (SEQ (LETT |i| 1) (LETT #1# (QVSIZE |b|)) G190
                         (COND ((|greater_SI| |i| #1#) (GO G191)))
                         (SEQ
                          (EXIT
                           (SPADCALL |m| |i|
                                     (SPADCALL
                                      (SPADCALL |a|
                                                (SPADCALL |b| |i|
                                                          (QREFELT % 17))
                                                (QREFELT % 38))
                                      (QREFELT % 30))
                                     (QREFELT % 32))))
                         (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                    (EXIT (SPADCALL |m| (QREFELT % 41)))))) 

(SDEFUN |FAXF-;linearAssociatedExp;SSupS;11|
        ((|x| (S)) (|f| (|SparseUnivariatePolynomial| F)) (% (S)))
        (SPROG ((|y| (S)) (|erg| (S)) (#1=#:G49 NIL) (|i| NIL))
               (SEQ (LETT |erg| (|spadConstant| % 8)) (LETT |y| |x|)
                    (SEQ (LETT |i| 0) (LETT #1# (SPADCALL |f| (QREFELT % 44)))
                         G190 (COND ((|greater_SI| |i| #1#) (GO G191)))
                         (SEQ
                          (LETT |erg|
                                (SPADCALL |erg|
                                          (SPADCALL
                                           (SPADCALL |f| |i| (QREFELT % 45))
                                           |y| (QREFELT % 18))
                                          (QREFELT % 19)))
                          (EXIT (LETT |y| (SPADCALL |y| (QREFELT % 46)))))
                         (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                    (EXIT |erg|)))) 

(SDEFUN |FAXF-;linearAssociatedLog;2SU;12|
        ((|b| (S)) (|x| (S))
         (% (|Union| (|SparseUnivariatePolynomial| F) "failed")))
        (SPROG
         ((|p| #1=(|SparseUnivariatePolynomial| F)) (#2=#:G61 NIL)
          (#3=#:G60 #1#) (#4=#:G62 #1#) (#5=#:G71 NIL) (|i| NIL)
          (|rown| (|Integer|)) (#6=#:G70 NIL) (|v| (|Vector| F))
          (|m1| (|Matrix| F)) (|l| (|List| (|List| F))) (|a| (S))
          (#7=#:G69 NIL) (|extdeg| (|NonNegativeInteger|)))
         (SEQ
          (COND
           ((SPADCALL |x| (|spadConstant| % 8) (QREFELT % 48))
            (CONS 0 (|spadConstant| % 49)))
           (#8='T
            (SEQ
             (LETT |l|
                   (LIST
                    (SPADCALL (SPADCALL |b| (QREFELT % 30)) (QREFELT % 51))))
             (LETT |a| |b|) (LETT |extdeg| (SPADCALL (QREFELT % 12)))
             (SEQ (LETT |i| 2) (LETT #7# |extdeg|) G190
                  (COND ((|greater_SI| |i| #7#) (GO G191)))
                  (SEQ (LETT |a| (SPADCALL |a| (QREFELT % 46)))
                       (EXIT
                        (LETT |l|
                              (SPADCALL |l|
                                        (SPADCALL (SPADCALL |a| (QREFELT % 30))
                                                  (QREFELT % 51))
                                        (QREFELT % 53)))))
                  (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
             (LETT |l|
                   (SPADCALL |l|
                             (SPADCALL (SPADCALL |x| (QREFELT % 30))
                                       (QREFELT % 51))
                             (QREFELT % 53)))
             (LETT |m1|
                   (SPADCALL
                    (SPADCALL (SPADCALL |l| (QREFELT % 54)) (QREFELT % 55))
                    (QREFELT % 56)))
             (LETT |v| (SPADCALL |extdeg| (QREFELT % 57))) (LETT |rown| 1)
             (SEQ (LETT |i| 1) (LETT #6# |extdeg|) G190
                  (COND ((|greater_SI| |i| #6#) (GO G191)))
                  (SEQ
                   (EXIT
                    (COND
                     ((SPADCALL (QAREF2O |m1| |rown| |i| 1 1)
                                (|spadConstant| % 58) (QREFELT % 59))
                      (SEQ
                       (SPADCALL |v| |i|
                                 (QAREF2O |m1| |rown| (+ |extdeg| 1) 1 1)
                                 (QREFELT % 61))
                       (EXIT (LETT |rown| (+ |rown| 1))))))))
                  (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
             (LETT |p|
                   (PROGN
                    (LETT #2# NIL)
                    (SEQ (LETT |i| 0) (LETT #5# (- (QVSIZE |v|) 1)) G190
                         (COND ((|greater_SI| |i| #5#) (GO G191)))
                         (SEQ
                          (EXIT
                           (PROGN
                            (LETT #4#
                                  (SPADCALL
                                   (SPADCALL |v| (+ |i| 1) (QREFELT % 15)) |i|
                                   (QREFELT % 62)))
                            (COND
                             (#2# (LETT #3# (SPADCALL #3# #4# (QREFELT % 63))))
                             ('T (PROGN (LETT #3# #4#) (LETT #2# 'T)))))))
                         (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                    (COND (#2# #3#) (#8# (|spadConstant| % 49)))))
             (EXIT
              (COND
               ((SPADCALL |p| (|spadConstant| % 49) (QREFELT % 64))
                (SEQ
                 (SPADCALL
                  "linearAssociatedLog: second argument not in                       group generated by first argument"
                  (QREFELT % 68))
                 (EXIT (CONS 1 "failed"))))
               (#8# (CONS 0 |p|)))))))))) 

(SDEFUN |FAXF-;linearAssociatedLog;SSup;13|
        ((|x| (S)) (% (|SparseUnivariatePolynomial| F)))
        (SPROG ((#1=#:G73 NIL))
               (PROG2
                   (LETT #1#
                         (SPADCALL (SPADCALL (QREFELT % 71)) |x|
                                   (QREFELT % 72)))
                   (QCDR #1#)
                 (|check_union2| (QEQCAR #1# 0)
                                 (|SparseUnivariatePolynomial| (QREFELT % 7))
                                 (|Union|
                                  (|SparseUnivariatePolynomial| (QREFELT % 7))
                                  "failed")
                                 #1#)))) 

(SDEFUN |FAXF-;linearAssociatedOrder;SSup;14|
        ((|x| (S)) (% (|SparseUnivariatePolynomial| F)))
        (SPROG
         ((#1=#:G80 NIL) (#2=#:G79 #3=(|SparseUnivariatePolynomial| F))
          (#4=#:G81 #3#) (#5=#:G85 NIL) (|i| NIL) (|v| (|Vector| F))
          (|l| (|List| (|List| F))) (|a| (S)) (#6=#:G84 NIL))
         (SEQ
          (COND
           ((SPADCALL |x| (|spadConstant| % 8) (QREFELT % 48))
            (|spadConstant| % 49))
           (#7='T
            (SEQ
             (LETT |l|
                   (LIST
                    (SPADCALL (SPADCALL |x| (QREFELT % 30)) (QREFELT % 51))))
             (LETT |a| |x|)
             (SEQ (LETT |i| 1) (LETT #6# (SPADCALL (QREFELT % 12))) G190
                  (COND ((|greater_SI| |i| #6#) (GO G191)))
                  (SEQ (LETT |a| (SPADCALL |a| (QREFELT % 46)))
                       (EXIT
                        (LETT |l|
                              (SPADCALL |l|
                                        (SPADCALL (SPADCALL |a| (QREFELT % 30))
                                                  (QREFELT % 51))
                                        (QREFELT % 53)))))
                  (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
             (LETT |v|
                   (|SPADfirst|
                    (SPADCALL
                     (SPADCALL (SPADCALL |l| (QREFELT % 54)) (QREFELT % 55))
                     (QREFELT % 75))))
             (EXIT
              (PROGN
               (LETT #1# NIL)
               (SEQ (LETT |i| 0) (LETT #5# (- (QVSIZE |v|) 1)) G190
                    (COND ((|greater_SI| |i| #5#) (GO G191)))
                    (SEQ
                     (EXIT
                      (PROGN
                       (LETT #4#
                             (SPADCALL (SPADCALL |v| (+ |i| 1) (QREFELT % 15))
                                       |i| (QREFELT % 62)))
                       (COND (#1# (LETT #2# (SPADCALL #2# #4# (QREFELT % 63))))
                             ('T (PROGN (LETT #2# #4#) (LETT #1# 'T)))))))
                    (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
               (COND (#1# #2#) (#7# (|spadConstant| % 49))))))))))) 

(SDEFUN |FAXF-;charthRoot;SU;15| ((|x| (S)) (% (|Union| S "failed")))
        (CONS 0 (SPADCALL |x| (QREFELT % 77)))) 

(SDEFUN |FAXF-;minimalPolynomial;SPiSup;16|
        ((|a| (S)) (|n| (|PositiveInteger|))
         (% (|SparseUnivariatePolynomial| S)))
        (SPROG ((|u| (S)) (|f| (|SparseUnivariatePolynomial| S)))
               (SEQ
                (COND
                 ((SPADCALL (REM (SPADCALL (QREFELT % 12)) |n|) 0
                            (QREFELT % 80))
                  (|error|
                   "minimalPolynomial: 2. argument must divide extension degree"))
                 ('T
                  (SEQ
                   (LETT |f|
                         (SPADCALL
                          (SPADCALL (|spadConstant| % 60) 1 (QREFELT % 82))
                          (SPADCALL |a| 0 (QREFELT % 82)) (QREFELT % 83)))
                   (LETT |u| (SPADCALL |a| |n| (QREFELT % 84)))
                   (SEQ G190
                        (COND
                         ((NULL (NULL (SPADCALL |u| |a| (QREFELT % 48))))
                          (GO G191)))
                        (SEQ
                         (LETT |f|
                               (SPADCALL |f|
                                         (SPADCALL
                                          (SPADCALL (|spadConstant| % 60) 1
                                                    (QREFELT % 82))
                                          (SPADCALL |u| 0 (QREFELT % 82))
                                          (QREFELT % 83))
                                         (QREFELT % 85)))
                         (EXIT (LETT |u| (SPADCALL |u| |n| (QREFELT % 84)))))
                        NIL (GO G190) G191 (EXIT NIL))
                   (EXIT |f|))))))) 

(SDEFUN |FAXF-;norm;SPiS;17| ((|e| (S)) (|s| (|PositiveInteger|)) (% (S)))
        (SPROG
         ((#1=#:G101 NIL) (|pow| (|Integer|))
          (|qr|
           (|Record| (|:| |quotient| (|NonNegativeInteger|))
                     (|:| |remainder| (|NonNegativeInteger|)))))
         (SEQ (LETT |qr| (DIVIDE2 (SPADCALL (QREFELT % 12)) |s|))
              (EXIT
               (COND
                ((ZEROP (QCDR |qr|))
                 (SEQ
                  (LETT |pow|
                        (QUOTIENT2 (- (SPADCALL (QREFELT % 89)) 1)
                                   (- (EXPT (SPADCALL (QREFELT % 90)) |s|) 1)))
                  (EXIT
                   (SPADCALL |e|
                             (PROG1 (LETT #1# |pow|)
                               (|check_subtype2| (>= #1# 0)
                                                 '(|NonNegativeInteger|)
                                                 '(|Integer|) #1#))
                             (QREFELT % 91)))))
                ('T
                 (|error|
                  "norm: second argument must divide degree of extension"))))))) 

(SDEFUN |FAXF-;trace;SPiS;18| ((|e| (S)) (|s| (|PositiveInteger|)) (% (S)))
        (SPROG
         ((|a| (S)) (#1=#:G111 NIL) (|i| NIL) (|q| (|NonNegativeInteger|))
          (|qr|
           (|Record| (|:| |quotient| (|NonNegativeInteger|))
                     (|:| |remainder| (|NonNegativeInteger|)))))
         (SEQ (LETT |qr| (DIVIDE2 (SPADCALL (QREFELT % 12)) |s|))
              (LETT |q| (SPADCALL (QREFELT % 90)))
              (EXIT
               (COND
                ((ZEROP (QCDR |qr|))
                 (SEQ (LETT |a| (|spadConstant| % 8))
                      (SEQ (LETT |i| 0) (LETT #1# (- (QCAR |qr|) 1)) G190
                           (COND ((|greater_SI| |i| #1#) (GO G191)))
                           (SEQ
                            (EXIT
                             (LETT |a|
                                   (SPADCALL |a|
                                             (SPADCALL |e|
                                                       (EXPT |q| (* |s| |i|))
                                                       (QREFELT % 91))
                                             (QREFELT % 19)))))
                           (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                      (EXIT |a|)))
                ('T
                 (|error|
                  "trace: second argument must divide degree of extension"))))))) 

(SDEFUN |FAXF-;size;Nni;19| ((% (|NonNegativeInteger|)))
        (EXPT (SPADCALL (QREFELT % 90)) (SPADCALL (QREFELT % 12)))) 

(SDEFUN |FAXF-;createNormalElement;S;20| ((% (S)))
        (SPROG
         ((#1=#:G121 NIL) (#2=#:G122 NIL) (|res| (S)) (#3=#:G115 NIL)
          (|i| NIL))
         (SEQ
          (EXIT
           (COND
            ((EQL (SPADCALL (QREFELT % 95)) (SPADCALL (QREFELT % 89)))
             (|spadConstant| % 60))
            ('T
             (SEQ
              (SEQ (LETT |i| 1) G190 NIL
                   (SEQ
                    (EXIT
                     (SEQ
                      (LETT |res|
                            (SPADCALL
                             (PROG1 (LETT #3# |i|)
                               (|check_subtype2| (> #3# 0) '(|PositiveInteger|)
                                                 '(|NonNegativeInteger|) #3#))
                             (QREFELT % 96)))
                      (EXIT
                       (COND
                        ((NULL (SPADCALL |res| (QREFELT % 97)))
                         (PROGN
                          (LETT #1#
                                (COND
                                 ((SPADCALL |res| (QREFELT % 98))
                                  (PROGN
                                   (LETT #1#
                                         (PROGN
                                          (LETT #2# |res|)
                                          (GO #4=#:G120)))
                                   (GO #5=#:G117)))))
                          (GO #5#)))))))
                    #5# (EXIT #1#))
                   (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
              (EXIT |res|)))))
          #4# (EXIT #2#)))) 

(SDEFUN |FAXF-;normal?;SB;21| ((|x| (S)) (% (|Boolean|)))
        (SPROG
         ((|f| #1=(|SparseUnivariatePolynomial| S)) (#2=#:G124 NIL)
          (#3=#:G123 #1#) (#4=#:G125 #1#) (#5=#:G128 NIL) (|i| NIL)
          (|p| (|SparseUnivariatePolynomial| S)))
         (SEQ
          (LETT |p|
                (SPADCALL
                 (SPADCALL (|spadConstant| % 60) (SPADCALL (QREFELT % 12))
                           (QREFELT % 82))
                 (SPADCALL (|spadConstant| % 60) 0 (QREFELT % 82))
                 (QREFELT % 83)))
          (LETT |f|
                (PROGN
                 (LETT #2# NIL)
                 (SEQ (LETT |i| 0) (LETT #5# (- (SPADCALL (QREFELT % 12)) 1))
                      G190 (COND ((|greater_SI| |i| #5#) (GO G191)))
                      (SEQ
                       (EXIT
                        (PROGN
                         (LETT #4#
                               (SPADCALL (SPADCALL |x| |i| (QREFELT % 84)) |i|
                                         (QREFELT % 82)))
                         (COND
                          (#2# (LETT #3# (SPADCALL #3# #4# (QREFELT % 100))))
                          ('T (PROGN (LETT #3# #4#) (LETT #2# 'T)))))))
                      (LETT |i| (|inc_SI| |i|)) (GO G190) G191 (EXIT NIL))
                 (COND (#2# #3#) (#6='T (|spadConstant| % 101)))))
          (EXIT
           (COND
            ((SPADCALL (SPADCALL |p| |f| (QREFELT % 102))
                       (|spadConstant| % 103) (QREFELT % 104))
             'T)
            (#6# NIL)))))) 

(SDEFUN |FAXF-;degree;SPi;22| ((|a| (S)) (% (|PositiveInteger|)))
        (SPROG ((|deg| (|PositiveInteger|)) (|y| (S)))
               (SEQ (LETT |y| (SPADCALL |a| (QREFELT % 46))) (LETT |deg| 1)
                    (SEQ G190
                         (COND
                          ((NULL (SPADCALL |y| |a| (QREFELT % 106)))
                           (GO G191)))
                         (SEQ (LETT |y| (SPADCALL |y| (QREFELT % 46)))
                              (EXIT (LETT |deg| (+ |deg| 1))))
                         NIL (GO G190) G191 (EXIT NIL))
                    (EXIT |deg|)))) 

(DECLAIM (NOTINLINE |FiniteAlgebraicExtensionField&;|)) 

(DEFUN |FiniteAlgebraicExtensionField&| (|#1| |#2|)
  (SPROG ((|pv$| NIL) (% NIL) (|dv$| NIL) (DV$2 NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|))
          (LETT DV$2 (|devaluate| |#2|))
          (LETT |dv$| (LIST '|FiniteAlgebraicExtensionField&| DV$1 DV$2))
          (LETT % (GETREFV 108))
          (QSETREFV % 0 |dv$|)
          (QSETREFV % 3
                    (LETT |pv$|
                          (|buildPredVector| 0 0
                                             (LIST
                                              (|HasCategory| |#2|
                                                             '(|Finite|))))))
          (|stuffDomainSlots| %)
          (QSETREFV % 6 |#1|)
          (QSETREFV % 7 |#2|)
          (SETF |pv$| (QREFELT % 3))
          (COND
           ((|testBitVector| |pv$| 1)
            (PROGN
             (QSETREFV % 47
                       (CONS
                        (|dispatchFunction|
                         |FAXF-;linearAssociatedExp;SSupS;11|)
                        %))
             (QSETREFV % 70
                       (CONS
                        (|dispatchFunction| |FAXF-;linearAssociatedLog;2SU;12|)
                        %))
             (QSETREFV % 73
                       (CONS
                        (|dispatchFunction|
                         |FAXF-;linearAssociatedLog;SSup;13|)
                        %))
             (QSETREFV % 76
                       (CONS
                        (|dispatchFunction|
                         |FAXF-;linearAssociatedOrder;SSup;14|)
                        %))
             (QSETREFV % 79
                       (CONS (|dispatchFunction| |FAXF-;charthRoot;SU;15|) %))
             (QSETREFV % 87
                       (CONS
                        (|dispatchFunction|
                         |FAXF-;minimalPolynomial;SPiSup;16|)
                        %))
             (QSETREFV % 92 (CONS (|dispatchFunction| |FAXF-;norm;SPiS;17|) %))
             (QSETREFV % 93
                       (CONS (|dispatchFunction| |FAXF-;trace;SPiS;18|) %))
             (QSETREFV % 94 (CONS (|dispatchFunction| |FAXF-;size;Nni;19|) %))
             (QSETREFV % 99
                       (CONS
                        (|dispatchFunction| |FAXF-;createNormalElement;S;20|)
                        %))
             (QSETREFV % 105
                       (CONS (|dispatchFunction| |FAXF-;normal?;SB;21|) %))
             (QSETREFV % 107
                       (CONS (|dispatchFunction| |FAXF-;degree;SPi;22|) %)))))
          %))) 

(MAKEPROP '|FiniteAlgebraicExtensionField&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (0 . |Zero|) (|Vector| %) (4 . |basis|) (|PositiveInteger|)
              (8 . |extensionDegree|) (|Integer|) (|Vector| 7) (12 . |elt|)
              (|Vector| 6) (18 . |elt|) (24 . *) (30 . +)
              |FAXF-;represents;VS;1| (|NonNegativeInteger|)
              |FAXF-;transcendenceDegree;Nni;2| (|OnePointCompletion| 11)
              (36 . |coerce|) |FAXF-;extensionDegree;Opc;3| (41 . |degree|)
              |FAXF-;degree;SOpc;4| (46 . |Zero|) (50 . |minIndex|)
              (55 . |coordinates|) (|Matrix| 7) (60 . |setRow!|)
              |FAXF-;coordinates;VM;5| (|Boolean|) |FAXF-;algebraic?;SB;6|
              |FAXF-;transcendent?;SB;7| |FAXF-;extensionDegree;Pi;8| (67 . *)
              (73 . +) |FAXF-;trace;SF;9| (79 . |determinant|)
              |FAXF-;norm;SF;10| (|SparseUnivariatePolynomial| 7)
              (84 . |degree|) (89 . |coefficient|) (95 . |Frobenius|)
              (100 . |linearAssociatedExp|) (106 . =) (112 . |Zero|) (|List| 7)
              (116 . |entries|) (|List| 50) (121 . |concat|) (127 . |matrix|)
              (132 . |transpose|) (137 . |rowEchelon|) (142 . |zero|)
              (147 . |One|) (151 . =) (157 . |One|) (161 . |setelt!|)
              (168 . |monomial|) (174 . +) (180 . =) (|Void|) (|String|)
              (|OutputForm|) (186 . |messagePrint|) (|Union| 43 '#1="failed")
              (191 . |linearAssociatedLog|) (197 . |normalElement|)
              (201 . |linearAssociatedLog|) (207 . |linearAssociatedLog|)
              (|List| 14) (212 . |nullSpace|) (217 . |linearAssociatedOrder|)
              (222 . |charthRoot|) (|Union| % '"failed") (227 . |charthRoot|)
              (232 . ~=) (|SparseUnivariatePolynomial| 6) (238 . |monomial|)
              (244 . -) (250 . |Frobenius|) (256 . *)
              (|SparseUnivariatePolynomial| %) (262 . |minimalPolynomial|)
              (268 . |extensionDegree|) (272 . |size|) (276 . |size|) (280 . ^)
              (286 . |norm|) (292 . |trace|) (298 . |size|)
              (302 . |characteristic|) (306 . |index|) (311 . |inGroundField?|)
              (316 . |normal?|) (321 . |createNormalElement|) (325 . +)
              (331 . |Zero|) (335 . |gcd|) (341 . |One|) (345 . =)
              (351 . |normal?|) (356 . ~=) (362 . |degree|))
           '#(|transcendent?| 367 |transcendenceDegree| 372 |trace| 376 |size|
              387 |represents| 391 |normal?| 396 |norm| 401 |minimalPolynomial|
              412 |linearAssociatedOrder| 418 |linearAssociatedLog| 423
              |linearAssociatedExp| 434 |extensionDegree| 440 |degree| 448
              |createNormalElement| 458 |coordinates| 462 |charthRoot| 467
              |algebraic?| 472)
           'NIL
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                            (|mkCategory|
                             (LIST
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                                T)
                              '((|charthRoot| (|#1| |#1|)) T)
                              '((|linearAssociatedLog|
                                 ((|Union| (|SparseUnivariatePolynomial| |#2|)
                                           #1#)
                                  |#1| |#1|))
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                              '((|linearAssociatedLog|
                                 ((|SparseUnivariatePolynomial| |#2|) |#1|))
                                T)
                              '((|linearAssociatedOrder|
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                                T)
                              '((|linearAssociatedExp|
                                 (|#1| |#1|
                                  (|SparseUnivariatePolynomial| |#2|)))
                                T)
                              '((|normal?| ((|Boolean|) |#1|)) T)
                              '((|createNormalElement| (|#1|)) T)
                              '((|trace| (|#1| |#1| (|PositiveInteger|))) T)
                              '((|norm| (|#1| |#1| (|PositiveInteger|))) T)
                              '((|minimalPolynomial|
                                 ((|SparseUnivariatePolynomial| |#1|) |#1|
                                  (|PositiveInteger|)))
                                T)
                              '((|degree| ((|PositiveInteger|) |#1|)) T)
                              '((|extensionDegree| ((|PositiveInteger|))) T)
                              '((|trace| (|#2| |#1|)) T)
                              '((|norm| (|#2| |#1|)) T)
                              '((|coordinates|
                                 ((|Vector| |#2|) |#1| (|Vector| |#1|)))
                                T)
                              '((|coordinates|
                                 ((|Matrix| |#2|) (|Vector| |#1|)
                                  (|Vector| |#1|)))
                                T)
                              '((|represents|
                                 (|#1| (|Vector| |#2|) (|Vector| |#1|)))
                                T)
                              '((|minimalPolynomial|
                                 ((|SparseUnivariatePolynomial| |#2|) |#1|))
                                T)
                              '((|size| ((|NonNegativeInteger|))) T)
                              '((|represents| (|#1| (|Vector| |#2|))) T)
                              '((|coordinates|
                                 ((|Matrix| |#2|) (|Vector| |#1|)))
                                T)
                              '((|coordinates| ((|Vector| |#2|) |#1|)) T)
                              '((|transcendenceDegree|
                                 ((|NonNegativeInteger|)))
                                T)
                              '((|extensionDegree|
                                 ((|OnePointCompletion| (|PositiveInteger|))))
                                T)
                              '((|degree|
                                 ((|OnePointCompletion| (|PositiveInteger|))
                                  |#1|))
                                T)
                              '((|transcendent?| ((|Boolean|) |#1|)) T)
                              '((|algebraic?| ((|Boolean|) |#1|)) T))
                             (LIST) NIL NIL)))
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           '|lookupComplete|)) 
