
(/VERSIONCHECK 2) 

(DEFUN |FINAALG-;leftCharacteristicPolynomial;SSup;1| (|a| $)
  (PROG (|n| |ma| |mb| |i| |j|)
    (RETURN
      (SEQ (LETT |n| (SPADCALL (QREFELT $ 9))
                 . #0=(|FINAALG-;leftCharacteristicPolynomial;SSup;1|))
           (LETT |ma|
                 (SPADCALL |a| (SPADCALL (QREFELT $ 11))
                     (QREFELT $ 13)) . #0#)
           (LETT |mb| (SPADCALL |n| |n| (QREFELT $ 16)) . #0#)
           (SEQ (LETT |i| 1 . #0#) G190
                (COND ((QSGREATERP |i| |n|) #1=(GO G191)))
                (SEQ (EXIT (SEQ (LETT |j| 1 . #0#) G190
                                (COND ((QSGREATERP |j| |n|) #1#))
                                (SEQ (EXIT
                                      (SPADCALL |mb| |i| |j|
                                       (COND
                                         ((EQL |i| |j|)
                                          (SPADCALL
                                           (SPADCALL
                                            (SPADCALL |ma| |i| |j|
                                             (QREFELT $ 18))
                                            0 (QREFELT $ 20))
                                           (SPADCALL
                                            (|spadConstant| $ 21) 1
                                            (QREFELT $ 20))
                                           (QREFELT $ 23)))
                                         ('T
                                          (SPADCALL
                                           (SPADCALL |ma| |i| |j|
                                            (QREFELT $ 18))
                                           1 (QREFELT $ 20))))
                                       (QREFELT $ 24))))
                                (LETT |j| (QSADD1 |j|) . #0#)
                                #2=(GO G190) G191 (EXIT NIL))))
                (LETT |i| (QSADD1 |i|) . #0#) #2# G191 (EXIT NIL))
           (EXIT (SPADCALL |mb| (QREFELT $ 25))))))) 

(DEFUN |FINAALG-;rightCharacteristicPolynomial;SSup;2| (|a| $)
  (PROG (|n| |ma| |mb| |i| |j|)
    (RETURN
      (SEQ (LETT |n| (SPADCALL (QREFELT $ 9))
                 . #0=(|FINAALG-;rightCharacteristicPolynomial;SSup;2|))
           (LETT |ma|
                 (SPADCALL |a| (SPADCALL (QREFELT $ 11))
                     (QREFELT $ 27)) . #0#)
           (LETT |mb| (SPADCALL |n| |n| (QREFELT $ 16)) . #0#)
           (SEQ (LETT |i| 1 . #0#) G190
                (COND ((QSGREATERP |i| |n|) #1=(GO G191)))
                (SEQ (EXIT (SEQ (LETT |j| 1 . #0#) G190
                                (COND ((QSGREATERP |j| |n|) #1#))
                                (SEQ (EXIT
                                      (SPADCALL |mb| |i| |j|
                                       (COND
                                         ((EQL |i| |j|)
                                          (SPADCALL
                                           (SPADCALL
                                            (SPADCALL |ma| |i| |j|
                                             (QREFELT $ 18))
                                            0 (QREFELT $ 20))
                                           (SPADCALL
                                            (|spadConstant| $ 21) 1
                                            (QREFELT $ 20))
                                           (QREFELT $ 23)))
                                         ('T
                                          (SPADCALL
                                           (SPADCALL |ma| |i| |j|
                                            (QREFELT $ 18))
                                           1 (QREFELT $ 20))))
                                       (QREFELT $ 24))))
                                (LETT |j| (QSADD1 |j|) . #0#)
                                #2=(GO G190) G191 (EXIT NIL))))
                (LETT |i| (QSADD1 |i|) . #0#) #2# G191 (EXIT NIL))
           (EXIT (SPADCALL |mb| (QREFELT $ 25))))))) 

(DEFUN |FINAALG-;leftTrace;SR;3| (|a| $)
  (PROG (|ma| |i| #0=#:G1849 |t|)
    (RETURN
      (SEQ (LETT |t| (|spadConstant| $ 29)
                 . #1=(|FINAALG-;leftTrace;SR;3|))
           (LETT |ma|
                 (SPADCALL |a| (SPADCALL (QREFELT $ 11))
                     (QREFELT $ 13)) . #1#)
           (SEQ (LETT |i| 1 . #1#)
                (LETT #0# (SPADCALL (QREFELT $ 9)) . #1#) G190
                (COND ((QSGREATERP |i| #0#) (GO G191)))
                (SEQ (EXIT (LETT |t|
                                 (SPADCALL |t|
                                     (SPADCALL |ma| |i| |i|
                                      (QREFELT $ 18))
                                     (QREFELT $ 30)) . #1#)))
                (LETT |i| (QSADD1 |i|) . #1#) (GO G190) G191
                (EXIT NIL))
           (EXIT |t|))))) 

(DEFUN |FINAALG-;rightTrace;SR;4| (|a| $)
  (PROG (|ma| |i| #0=#:G1853 |t|)
    (RETURN
      (SEQ (LETT |t| (|spadConstant| $ 29)
                 . #1=(|FINAALG-;rightTrace;SR;4|))
           (LETT |ma|
                 (SPADCALL |a| (SPADCALL (QREFELT $ 11))
                     (QREFELT $ 27)) . #1#)
           (SEQ (LETT |i| 1 . #1#)
                (LETT #0# (SPADCALL (QREFELT $ 9)) . #1#) G190
                (COND ((QSGREATERP |i| #0#) (GO G191)))
                (SEQ (EXIT (LETT |t|
                                 (SPADCALL |t|
                                     (SPADCALL |ma| |i| |i|
                                      (QREFELT $ 18))
                                     (QREFELT $ 30)) . #1#)))
                (LETT |i| (QSADD1 |i|) . #1#) (GO G190) G191
                (EXIT NIL))
           (EXIT |t|))))) 

(DEFUN |FINAALG-;leftNorm;SR;5| (|a| $)
  (SPADCALL (SPADCALL |a| (SPADCALL (QREFELT $ 11)) (QREFELT $ 13))
      (QREFELT $ 33))) 

(DEFUN |FINAALG-;rightNorm;SR;6| (|a| $)
  (SPADCALL (SPADCALL |a| (SPADCALL (QREFELT $ 11)) (QREFELT $ 27))
      (QREFELT $ 33))) 

(DEFUN |FINAALG-;antiAssociative?;B;7| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G1862 #1=#:G1858)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;antiAssociative?;B;7|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL |b| |i|
                                                     (QREFELT $ 37))
                                                    (SPADCALL |b| |j|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 38))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 38))
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL
                                                    (SPADCALL |b| |j|
                                                     (QREFELT $ 37))
                                                    (SPADCALL |b| |k|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 38))
                                                   (QREFELT $ 38))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not anti-associative"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is anti-associative"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;jordanAdmissible?;B;8| ($)
  (PROG (|b| |n| |i| |j| |k| |l| #0=#:G1878 #1=#:G1872)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;jordanAdmissible?;B;8|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (EXIT (COND
                              ((QEQCAR (SPADCALL
                                        (SPADCALL 2
                                         (|spadConstant| $ 21)
                                         (QREFELT $ 47))
                                        (QREFELT $ 49))
                                       1)
                               (SEQ (SPADCALL
                                     "this algebra is not Jordan admissible, as 2 is not invertible in the ground ring"
                                     (QREFELT $ 45))
                                    (EXIT 'NIL)))
                              ('T
                               (SEQ (SEQ (LETT |i| 1 . #2#) G190
                                     (COND
                                       ((QSGREATERP |i| |n|)
                                        #3=(GO G191)))
                                     (SEQ
                                      (EXIT
                                       (SEQ (LETT |j| 1 . #2#) G190
                                        (COND
                                          ((QSGREATERP |j| |n|) #3#))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |k| 1 . #2#) G190
                                           (COND
                                             ((QSGREATERP |k| |n|) #3#))
                                           (SEQ
                                            (EXIT
                                             (SEQ (LETT |l| 1 . #2#)
                                              G190
                                              (COND
                                                ((QSGREATERP |l| |n|)
                                                 #3#))
                                              (SEQ
                                               (EXIT
                                                (COND
                                                  ((NULL
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |i|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |j|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 50))
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |l|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |k|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 50))
                                                        (QREFELT $ 50))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |l|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |j|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 50))
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |k|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |i|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 50))
                                                        (QREFELT $ 50))
                                                       (QREFELT $ 39))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL |b|
                                                         |k|
                                                         (QREFELT $ 37))
                                                        (SPADCALL |b|
                                                         |j|
                                                         (QREFELT $ 37))
                                                        (QREFELT $ 50))
                                                       (SPADCALL
                                                        (SPADCALL |b|
                                                         |i|
                                                         (QREFELT $ 37))
                                                        (SPADCALL |b|
                                                         |l|
                                                         (QREFELT $ 37))
                                                        (QREFELT $ 50))
                                                       (QREFELT $ 50))
                                                      (QREFELT $ 39))
                                                     (QREFELT $ 41)))
                                                   (PROGN
                                                     (LETT #1#
                                                      (SEQ
                                                       (SPADCALL
                                                        "this algebra is not Jordan admissible"
                                                        (QREFELT $ 45))
                                                       (EXIT
                                                        (PROGN
                                                          (LETT #0#
                                                           'NIL . #2#)
                                                          (GO #0#)))) . #2#)
                                                     (GO #1#))))))
                                              (LETT |l|
                                               (QSADD1 |l|) . #2#)
                                              #4=(GO G190) G191
                                              (EXIT NIL)))
                                            #1# (EXIT #1#))
                                           (LETT |k|
                                            (QSADD1 |k|) . #2#)
                                           #4# G191 (EXIT NIL))))
                                        (LETT |j| (QSADD1 |j|) . #2#)
                                        #4# G191 (EXIT NIL))))
                                     (LETT |i| (QSADD1 |i|) . #2#) #4#
                                     G191 (EXIT NIL))
                                    (SPADCALL
                                     "this algebra is Jordan admissible"
                                     (QREFELT $ 45))
                                    (EXIT 'T)))))))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;lieAdmissible?;B;9| ($)
  (PROG (|n| |b| |i| |j| |k| #0=#:G1885 #1=#:G1881)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |n| (SPADCALL (QREFELT $ 9))
                            . #2=(|FINAALG-;lieAdmissible?;B;9|))
                      (LETT |b| (SPADCALL (QREFELT $ 11)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL
                                                     (SPADCALL |b| |i|
                                                      (QREFELT $ 37))
                                                     (SPADCALL |b| |j|
                                                      (QREFELT $ 37))
                                                     (QREFELT $ 52))
                                                    (SPADCALL |b| |k|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 52))
                                                   (SPADCALL
                                                    (SPADCALL
                                                     (SPADCALL |b| |j|
                                                      (QREFELT $ 37))
                                                     (SPADCALL |b| |k|
                                                      (QREFELT $ 37))
                                                     (QREFELT $ 52))
                                                    (SPADCALL |b| |i|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 52))
                                                   (QREFELT $ 39))
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL |b| |k|
                                                     (QREFELT $ 37))
                                                    (SPADCALL |b| |i|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 52))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 52))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "this algebra is not Lie admissible"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "this algebra is Lie admissible"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;structuralConstants;VV;10| (|b| $)
  (PROG (#0=#:G1886 |m| #1=#:G1894 #2=#:G1895 |sC| |i| |j| |covec| |k|)
    (RETURN
      (SEQ (LETT |m|
                 (PROG1 (LETT #0# (QVSIZE |b|)
                              . #3=(|FINAALG-;structuralConstants;VV;10|))
                   (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|)
                       #0#)) . #3#)
           (LETT |sC|
                 (PRIMVEC2ARR
                     (PROGN
                       (LETT #1# (GETREFV |m|) . #3#)
                       (SEQ (LETT #2# 0 . #3#) (LETT |k| 1 . #3#) G190
                            (COND ((QSGREATERP |k| |m|) #4=(GO G191)))
                            (SEQ (EXIT (SETELT #1# #2#
                                        (SPADCALL |m| |m|
                                         (|spadConstant| $ 29)
                                         (QREFELT $ 54)))))
                            (LETT |k|
                                  (PROG1 (QSADD1 |k|)
                                    (LETT #2# (QSADD1 #2#) . #3#)) . #3#)
                            #5=(GO G190) G191 (EXIT NIL))
                       #1#)) . #3#)
           (SEQ (LETT |i| 1 . #3#) G190
                (COND ((QSGREATERP |i| |m|) #4#))
                (SEQ (EXIT (SEQ (LETT |j| 1 . #3#) G190
                                (COND ((QSGREATERP |j| |m|) #4#))
                                (SEQ (LETT |covec|
                                      (SPADCALL
                                       (SPADCALL
                                        (SPADCALL |b| |i|
                                         (QREFELT $ 37))
                                        (SPADCALL |b| |j|
                                         (QREFELT $ 37))
                                        (QREFELT $ 38))
                                       |b| (QREFELT $ 56)) . #3#)
                                     (EXIT
                                      (SEQ (LETT |k| 1 . #3#) G190
                                       (COND
                                         ((QSGREATERP |k| |m|) #4#))
                                       (SEQ
                                        (EXIT
                                         (SPADCALL
                                          (SPADCALL |sC| |k|
                                           (QREFELT $ 58))
                                          |i| |j|
                                          (SPADCALL |covec| |k|
                                           (QREFELT $ 59))
                                          (QREFELT $ 60))))
                                       (LETT |k| (QSADD1 |k|) . #3#)
                                       #5# G191 (EXIT NIL))))
                                (LETT |j| (QSADD1 |j|) . #3#) #5# G191
                                (EXIT NIL))))
                (LETT |i| (QSADD1 |i|) . #3#) #5# G191 (EXIT NIL))
           (EXIT |sC|))))) 

(DEFUN |FINAALG-;leftRecip;SU;11| (|x| $)
  (PROG (|lu| |b| |k| |xx| |listOfPowers| |cond| |vectorOfCoef| |invC|
              |invCR| #0=#:G1911 #1=#:G1912 |i| #2=#:G1914 |power|
              #3=#:G1913)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (QREFELT $ 41)) (CONS 1 "failed"))
             ('T
              (SEQ (LETT |lu| (SPADCALL (QREFELT $ 62))
                         . #4=(|FINAALG-;leftRecip;SU;11|))
                   (EXIT (COND
                           ((QEQCAR |lu| 1) (CONS 1 "failed"))
                           ('T
                            (SEQ (LETT |b|
                                       (SPADCALL (QREFELT $ 11)) . #4#)
                                 (LETT |xx| (QCDR |lu|) . #4#)
                                 (LETT |k| 1 . #4#)
                                 (LETT |cond|
                                       (SPADCALL
                                        (SPADCALL |xx| |b|
                                         (QREFELT $ 56))
                                        (QREFELT $ 63)) . #4#)
                                 (LETT |listOfPowers|
                                       (LIST |xx|) . #4#)
                                 (SEQ G190
                                      (COND
                                        ((NULL
                                          (EQL
                                           (SPADCALL |cond|
                                            (QREFELT $ 64))
                                           |k|))
                                         #5=(GO G191)))
                                      (SEQ (LETT |k| (+ |k| 1) . #4#)
                                       (LETT |xx|
                                        (SPADCALL |xx| |x|
                                         (QREFELT $ 38)) . #4#)
                                       (LETT |listOfPowers|
                                        (CONS |xx| |listOfPowers|) . #4#)
                                       (EXIT
                                        (LETT |cond|
                                         (SPADCALL |cond|
                                          (SPADCALL
                                           (SPADCALL |xx| |b|
                                            (QREFELT $ 56))
                                           (QREFELT $ 63))
                                          (QREFELT $ 65)) . #4#)))
                                      NIL #6=(GO G190) G191 (EXIT NIL))
                                 (LETT |vectorOfCoef|
                                       (|SPADfirst|
                                        (SPADCALL |cond|
                                         (QREFELT $ 67))) . #4#)
                                 (LETT |invC|
                                       (SPADCALL
                                        (SPADCALL |vectorOfCoef| 1
                                         (QREFELT $ 59))
                                        (QREFELT $ 49)) . #4#)
                                 (EXIT (COND
                                         ((QEQCAR |invC| 1)
                                          (CONS 1 "failed"))
                                         ('T
                                          (SEQ
                                           (LETT |invCR|
                                            (SPADCALL (QCDR |invC|)
                                             (QREFELT $ 68)) . #4#)
                                           (EXIT
                                            (CONS 0
                                             (SPADCALL (ELT $ 39)
                                              (PRIMVEC2ARR
                                               (PROGN
                                                 (LETT #0#
                                                  (GETREFV
                                                   (MIN
                                                    (QSADD1
                                                     (-
                                                      #7=(QVSIZE
                                                          |vectorOfCoef|)
                                                      2))
                                                    (SIZE
                                                     #8=(REVERSE
                                                         |listOfPowers|)))) . #4#)
                                                 (SEQ
                                                  (LETT #1# 0 . #4#)
                                                  (LETT |i| 2 . #4#)
                                                  (LETT #2# #7# . #4#)
                                                  (LETT |power|
                                                   NIL . #4#)
                                                  (LETT #3# #8# . #4#)
                                                  G190
                                                  (COND
                                                    ((OR (ATOM #3#)
                                                      (PROGN
                                                        (LETT |power|
                                                         (CAR #3#) . #4#)
                                                        NIL)
                                                      (QSGREATERP |i|
                                                       #2#))
                                                     #5#))
                                                  (SEQ
                                                   (EXIT
                                                    (SETELT #0# #1#
                                                     (SPADCALL
                                                      (SPADCALL |invCR|
                                                       (SPADCALL
                                                        |vectorOfCoef|
                                                        |i|
                                                        (QREFELT $ 59))
                                                       (QREFELT $ 69))
                                                      |power|
                                                      (QREFELT $ 70)))))
                                                  (LETT #3#
                                                   (PROG1 (CDR #3#)
                                                     (LETT |i|
                                                      (PROG1
                                                       (QSADD1 |i|)
                                                        (LETT #1#
                                                         (QSADD1 #1#) . #4#)) . #4#)) . #4#)
                                                  #6# G191 (EXIT NIL))
                                                 #0#))
                                              (QREFELT $ 72))))))))))))))))))) 

(DEFUN |FINAALG-;rightRecip;SU;12| (|x| $)
  (PROG (|ru| |b| |k| |xx| |listOfPowers| |cond| |vectorOfCoef| |invC|
              |invCR| #0=#:G1929 #1=#:G1930 |i| #2=#:G1932 |power|
              #3=#:G1931)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (QREFELT $ 41)) (CONS 1 "failed"))
             ('T
              (SEQ (LETT |ru| (SPADCALL (QREFELT $ 74))
                         . #4=(|FINAALG-;rightRecip;SU;12|))
                   (EXIT (COND
                           ((QEQCAR |ru| 1) (CONS 1 "failed"))
                           ('T
                            (SEQ (LETT |b|
                                       (SPADCALL (QREFELT $ 11)) . #4#)
                                 (LETT |xx| (QCDR |ru|) . #4#)
                                 (LETT |k| 1 . #4#)
                                 (LETT |cond|
                                       (SPADCALL
                                        (SPADCALL |xx| |b|
                                         (QREFELT $ 56))
                                        (QREFELT $ 63)) . #4#)
                                 (LETT |listOfPowers|
                                       (LIST |xx|) . #4#)
                                 (SEQ G190
                                      (COND
                                        ((NULL
                                          (EQL
                                           (SPADCALL |cond|
                                            (QREFELT $ 64))
                                           |k|))
                                         #5=(GO G191)))
                                      (SEQ (LETT |k| (+ |k| 1) . #4#)
                                       (LETT |xx|
                                        (SPADCALL |x| |xx|
                                         (QREFELT $ 38)) . #4#)
                                       (LETT |listOfPowers|
                                        (CONS |xx| |listOfPowers|) . #4#)
                                       (EXIT
                                        (LETT |cond|
                                         (SPADCALL |cond|
                                          (SPADCALL
                                           (SPADCALL |xx| |b|
                                            (QREFELT $ 56))
                                           (QREFELT $ 63))
                                          (QREFELT $ 65)) . #4#)))
                                      NIL #6=(GO G190) G191 (EXIT NIL))
                                 (LETT |vectorOfCoef|
                                       (|SPADfirst|
                                        (SPADCALL |cond|
                                         (QREFELT $ 67))) . #4#)
                                 (LETT |invC|
                                       (SPADCALL
                                        (SPADCALL |vectorOfCoef| 1
                                         (QREFELT $ 59))
                                        (QREFELT $ 49)) . #4#)
                                 (EXIT (COND
                                         ((QEQCAR |invC| 1)
                                          (CONS 1 "failed"))
                                         ('T
                                          (SEQ
                                           (LETT |invCR|
                                            (SPADCALL (QCDR |invC|)
                                             (QREFELT $ 68)) . #4#)
                                           (EXIT
                                            (CONS 0
                                             (SPADCALL (ELT $ 39)
                                              (PRIMVEC2ARR
                                               (PROGN
                                                 (LETT #0#
                                                  (GETREFV
                                                   (MIN
                                                    (QSADD1
                                                     (-
                                                      #7=(QVSIZE
                                                          |vectorOfCoef|)
                                                      2))
                                                    (SIZE
                                                     #8=(REVERSE
                                                         |listOfPowers|)))) . #4#)
                                                 (SEQ
                                                  (LETT #1# 0 . #4#)
                                                  (LETT |i| 2 . #4#)
                                                  (LETT #2# #7# . #4#)
                                                  (LETT |power|
                                                   NIL . #4#)
                                                  (LETT #3# #8# . #4#)
                                                  G190
                                                  (COND
                                                    ((OR (ATOM #3#)
                                                      (PROGN
                                                        (LETT |power|
                                                         (CAR #3#) . #4#)
                                                        NIL)
                                                      (QSGREATERP |i|
                                                       #2#))
                                                     #5#))
                                                  (SEQ
                                                   (EXIT
                                                    (SETELT #0# #1#
                                                     (SPADCALL
                                                      (SPADCALL |invCR|
                                                       (SPADCALL
                                                        |vectorOfCoef|
                                                        |i|
                                                        (QREFELT $ 59))
                                                       (QREFELT $ 69))
                                                      |power|
                                                      (QREFELT $ 70)))))
                                                  (LETT #3#
                                                   (PROG1 (CDR #3#)
                                                     (LETT |i|
                                                      (PROG1
                                                       (QSADD1 |i|)
                                                        (LETT #1#
                                                         (QSADD1 #1#) . #4#)) . #4#)) . #4#)
                                                  #6# G191 (EXIT NIL))
                                                 #0#))
                                              (QREFELT $ 72))))))))))))))))))) 

(DEFUN |FINAALG-;recip;SU;13| (|x| $)
  (PROG (|lrx| |rrx|)
    (RETURN
      (SEQ (LETT |lrx| (SPADCALL |x| (QREFELT $ 76))
                 . #0=(|FINAALG-;recip;SU;13|))
           (EXIT (COND
                   ((QEQCAR |lrx| 1) (CONS 1 "failed"))
                   ('T
                    (SEQ (LETT |rrx|
                               (SPADCALL |x| (QREFELT $ 77)) . #0#)
                         (EXIT (COND
                                 ((OR (QEQCAR |rrx| 1)
                                      (NULL
                                       (SPADCALL (QCDR |lrx|)
                                        (QCDR |rrx|) (QREFELT $ 78))))
                                  (CONS 1 "failed"))
                                 ('T (CONS 0 (QCDR |lrx|))))))))))))) 

(DEFUN |FINAALG-;leftMinimalPolynomial;SSup;14| (|x| $)
  (PROG (|b| |k| |xx| |cond| |vectorOfCoef| |i| |res|)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (QREFELT $ 41))
              (SPADCALL (|spadConstant| $ 21) 1 (QREFELT $ 20)))
             ('T
              (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                         . #0=(|FINAALG-;leftMinimalPolynomial;SSup;14|))
                   (LETT |xx| |x| . #0#) (LETT |k| 1 . #0#)
                   (LETT |cond|
                         (SPADCALL (SPADCALL |xx| |b| (QREFELT $ 56))
                             (QREFELT $ 63)) . #0#)
                   (SEQ G190
                        (COND
                          ((NULL (EQL (SPADCALL |cond| (QREFELT $ 64))
                                      |k|))
                           #1=(GO G191)))
                        (SEQ (LETT |k| (+ |k| 1) . #0#)
                             (LETT |xx|
                                   (SPADCALL |x| |xx| (QREFELT $ 38)) . #0#)
                             (EXIT (LETT |cond|
                                    (SPADCALL |cond|
                                     (SPADCALL
                                      (SPADCALL |xx| |b|
                                       (QREFELT $ 56))
                                      (QREFELT $ 63))
                                     (QREFELT $ 65)) . #0#)))
                        NIL #2=(GO G190) G191 (EXIT NIL))
                   (LETT |vectorOfCoef|
                         (|SPADfirst| (SPADCALL |cond| (QREFELT $ 67))) . #0#)
                   (LETT |res| (|spadConstant| $ 80) . #0#)
                   (SEQ (LETT |i| 1 . #0#) G190
                        (COND ((QSGREATERP |i| |k|) #1#))
                        (SEQ (EXIT (LETT |res|
                                    (SPADCALL |res|
                                     (SPADCALL
                                      (SPADCALL |vectorOfCoef| |i|
                                       (QREFELT $ 59))
                                      |i| (QREFELT $ 20))
                                     (QREFELT $ 81)) . #0#)))
                        (LETT |i| (QSADD1 |i|) . #0#) #2# G191
                        (EXIT NIL))
                   (EXIT |res|)))))))) 

(DEFUN |FINAALG-;rightMinimalPolynomial;SSup;15| (|x| $)
  (PROG (|b| |k| |xx| |cond| |vectorOfCoef| |i| |res|)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (QREFELT $ 41))
              (SPADCALL (|spadConstant| $ 21) 1 (QREFELT $ 20)))
             ('T
              (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                         . #0=(|FINAALG-;rightMinimalPolynomial;SSup;15|))
                   (LETT |xx| |x| . #0#) (LETT |k| 1 . #0#)
                   (LETT |cond|
                         (SPADCALL (SPADCALL |xx| |b| (QREFELT $ 56))
                             (QREFELT $ 63)) . #0#)
                   (SEQ G190
                        (COND
                          ((NULL (EQL (SPADCALL |cond| (QREFELT $ 64))
                                      |k|))
                           #1=(GO G191)))
                        (SEQ (LETT |k| (+ |k| 1) . #0#)
                             (LETT |xx|
                                   (SPADCALL |xx| |x| (QREFELT $ 38)) . #0#)
                             (EXIT (LETT |cond|
                                    (SPADCALL |cond|
                                     (SPADCALL
                                      (SPADCALL |xx| |b|
                                       (QREFELT $ 56))
                                      (QREFELT $ 63))
                                     (QREFELT $ 65)) . #0#)))
                        NIL #2=(GO G190) G191 (EXIT NIL))
                   (LETT |vectorOfCoef|
                         (|SPADfirst| (SPADCALL |cond| (QREFELT $ 67))) . #0#)
                   (LETT |res| (|spadConstant| $ 80) . #0#)
                   (SEQ (LETT |i| 1 . #0#) G190
                        (COND ((QSGREATERP |i| |k|) #1#))
                        (SEQ (EXIT (LETT |res|
                                    (SPADCALL |res|
                                     (SPADCALL
                                      (SPADCALL |vectorOfCoef| |i|
                                       (QREFELT $ 59))
                                      |i| (QREFELT $ 20))
                                     (QREFELT $ 81)) . #0#)))
                        (LETT |i| (QSADD1 |i|) . #0#) #2# G191
                        (EXIT NIL))
                   (EXIT |res|)))))))) 

(DEFUN |FINAALG-;associatorDependence;L;16| ($)
  (PROG (|n| |b| |cond| |i| |j| |k| |a123| |a231| |a312| |a132| |a321|
             |a213| |r| |z|)
    (RETURN
      (SEQ (LETT |n| (SPADCALL (QREFELT $ 9))
                 . #0=(|FINAALG-;associatorDependence;L;16|))
           (LETT |b| (SPADCALL (QREFELT $ 11)) . #0#)
           (LETT |cond|
                 (SPADCALL (SPADCALL |n| 4 (QREFELT $ 84)) 6
                     (|spadConstant| $ 29) (QREFELT $ 54)) . #0#)
           (LETT |z| 0 . #0#)
           (SEQ (LETT |i| 1 . #0#) G190
                (COND ((QSGREATERP |i| |n|) #1=(GO G191)))
                (SEQ (EXIT (SEQ (LETT |j| 1 . #0#) G190
                                (COND ((QSGREATERP |j| |n|) #1#))
                                (SEQ (EXIT
                                      (SEQ (LETT |k| 1 . #0#) G190
                                       (COND
                                         ((QSGREATERP |k| |n|) #1#))
                                       (SEQ
                                        (LETT |a123|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (LETT |a231|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (LETT |a312|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (LETT |a132|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (LETT |a321|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (LETT |a213|
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |b| |j|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |i|
                                            (QREFELT $ 37))
                                           (SPADCALL |b| |k|
                                            (QREFELT $ 37))
                                           (QREFELT $ 85))
                                          |b| (QREFELT $ 56)) . #0#)
                                        (EXIT
                                         (SEQ (LETT |r| 1 . #0#) G190
                                          (COND
                                            ((QSGREATERP |r| |n|) #1#))
                                          (SEQ
                                           (LETT |z| (+ |z| 1) . #0#)
                                           (SPADCALL |cond| |z| 1
                                            (SPADCALL |a123| |r|
                                             (QREFELT $ 59))
                                            (QREFELT $ 60))
                                           (SPADCALL |cond| |z| 2
                                            (SPADCALL |a231| |r|
                                             (QREFELT $ 59))
                                            (QREFELT $ 60))
                                           (SPADCALL |cond| |z| 3
                                            (SPADCALL |a312| |r|
                                             (QREFELT $ 59))
                                            (QREFELT $ 60))
                                           (SPADCALL |cond| |z| 4
                                            (SPADCALL |a132| |r|
                                             (QREFELT $ 59))
                                            (QREFELT $ 60))
                                           (SPADCALL |cond| |z| 5
                                            (SPADCALL |a321| |r|
                                             (QREFELT $ 59))
                                            (QREFELT $ 60))
                                           (EXIT
                                            (SPADCALL |cond| |z| 6
                                             (SPADCALL |a213| |r|
                                              (QREFELT $ 59))
                                             (QREFELT $ 60))))
                                          (LETT |r| (QSADD1 |r|) . #0#)
                                          #2=(GO G190) G191 (EXIT NIL))))
                                       (LETT |k| (QSADD1 |k|) . #0#)
                                       #2# G191 (EXIT NIL))))
                                (LETT |j| (QSADD1 |j|) . #0#) #2# G191
                                (EXIT NIL))))
                (LETT |i| (QSADD1 |i|) . #0#) #2# G191 (EXIT NIL))
           (EXIT (SPADCALL |cond| (QREFELT $ 67))))))) 

(DEFUN |FINAALG-;jacobiIdentity?;B;17| ($)
  (PROG (|n| |b| |i| |j| |k| #0=#:G1965 #1=#:G1961)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |n| (SPADCALL (QREFELT $ 9))
                            . #2=(|FINAALG-;jacobiIdentity?;B;17|))
                      (LETT |b| (SPADCALL (QREFELT $ 11)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL
                                                     (SPADCALL |b| |i|
                                                      (QREFELT $ 37))
                                                     (SPADCALL |b| |j|
                                                      (QREFELT $ 37))
                                                     (QREFELT $ 38))
                                                    (SPADCALL |b| |k|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 38))
                                                   (SPADCALL
                                                    (SPADCALL
                                                     (SPADCALL |b| |j|
                                                      (QREFELT $ 37))
                                                     (SPADCALL |b| |k|
                                                      (QREFELT $ 37))
                                                     (QREFELT $ 38))
                                                    (SPADCALL |b| |i|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 38))
                                                   (QREFELT $ 39))
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL |b| |k|
                                                     (QREFELT $ 37))
                                                    (SPADCALL |b| |i|
                                                     (QREFELT $ 37))
                                                    (QREFELT $ 38))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 38))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "Jacobi identity does not hold"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "Jacobi identity holds" (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;lieAlgebra?;B;18| ($)
  (SEQ (COND
         ((SPADCALL (QREFELT $ 88))
          (COND
            ((SPADCALL (QREFELT $ 89))
             (SEQ (SPADCALL "this is a Lie algebra" (QREFELT $ 45))
                  (EXIT 'T)))
            (#0='T
             (SEQ (SPADCALL "this is not a Lie algebra" (QREFELT $ 45))
                  (EXIT 'NIL)))))
         (#0#
          (SEQ (SPADCALL "this is not a Lie algebra" (QREFELT $ 45))
               (EXIT 'NIL)))))) 

(DEFUN |FINAALG-;jordanAlgebra?;B;19| ($)
  (PROG (|b| |n| |i| |j| |k| |l| #0=#:G1983 #1=#:G1976)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;jordanAlgebra?;B;19|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (EXIT (COND
                              ((QEQCAR (SPADCALL
                                        (SPADCALL 2
                                         (|spadConstant| $ 21)
                                         (QREFELT $ 47))
                                        (QREFELT $ 49))
                                       1)
                               (SEQ (SPADCALL
                                     "this is not a Jordan algebra, as 2 is not invertible in the ground ring"
                                     (QREFELT $ 45))
                                    (EXIT 'NIL)))
                              ((SPADCALL (QREFELT $ 91))
                               (SEQ (SEQ (LETT |i| 1 . #2#) G190
                                     (COND
                                       ((QSGREATERP |i| |n|)
                                        #3=(GO G191)))
                                     (SEQ
                                      (EXIT
                                       (SEQ (LETT |j| 1 . #2#) G190
                                        (COND
                                          ((QSGREATERP |j| |n|) #3#))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |k| 1 . #2#) G190
                                           (COND
                                             ((QSGREATERP |k| |n|) #3#))
                                           (SEQ
                                            (EXIT
                                             (SEQ (LETT |l| 1 . #2#)
                                              G190
                                              (COND
                                                ((QSGREATERP |l| |n|)
                                                 #3#))
                                              (SEQ
                                               (EXIT
                                                (COND
                                                  ((NULL
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL |b|
                                                         |i|
                                                         (QREFELT $ 37))
                                                        (SPADCALL |b|
                                                         |j|
                                                         (QREFELT $ 37))
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |l|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |k|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 38))
                                                        (QREFELT $ 85))
                                                       (SPADCALL
                                                        (SPADCALL |b|
                                                         |l|
                                                         (QREFELT $ 37))
                                                        (SPADCALL |b|
                                                         |j|
                                                         (QREFELT $ 37))
                                                        (SPADCALL
                                                         (SPADCALL |b|
                                                          |k|
                                                          (QREFELT $
                                                           37))
                                                         (SPADCALL |b|
                                                          |i|
                                                          (QREFELT $
                                                           37))
                                                         (QREFELT $ 38))
                                                        (QREFELT $ 85))
                                                       (QREFELT $ 39))
                                                      (SPADCALL
                                                       (SPADCALL |b|
                                                        |k|
                                                        (QREFELT $ 37))
                                                       (SPADCALL |b|
                                                        |j|
                                                        (QREFELT $ 37))
                                                       (SPADCALL
                                                        (SPADCALL |b|
                                                         |i|
                                                         (QREFELT $ 37))
                                                        (SPADCALL |b|
                                                         |l|
                                                         (QREFELT $ 37))
                                                        (QREFELT $ 38))
                                                       (QREFELT $ 85))
                                                      (QREFELT $ 39))
                                                     (QREFELT $ 41)))
                                                   (PROGN
                                                     (LETT #1#
                                                      (SEQ
                                                       (SPADCALL
                                                        "not a Jordan algebra"
                                                        (QREFELT $ 45))
                                                       (EXIT
                                                        (PROGN
                                                          (LETT #0#
                                                           'NIL . #2#)
                                                          (GO #0#)))) . #2#)
                                                     (GO #1#))))))
                                              (LETT |l|
                                               (QSADD1 |l|) . #2#)
                                              #4=(GO G190) G191
                                              (EXIT NIL)))
                                            #1# (EXIT #1#))
                                           (LETT |k|
                                            (QSADD1 |k|) . #2#)
                                           #4# G191 (EXIT NIL))))
                                        (LETT |j| (QSADD1 |j|) . #2#)
                                        #4# G191 (EXIT NIL))))
                                     (LETT |i| (QSADD1 |i|) . #2#) #4#
                                     G191 (EXIT NIL))
                                    (SPADCALL
                                     "this is a Jordan algebra"
                                     (QREFELT $ 45))
                                    (EXIT 'T)))
                              ('T
                               (SEQ (SPADCALL
                                     "this is not a Jordan algebra"
                                     (QREFELT $ 45))
                                    (EXIT 'NIL)))))))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;noncommutativeJordanAlgebra?;B;20| ($)
  (PROG (|b| |n|)
    (RETURN
      (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                 . #0=(|FINAALG-;noncommutativeJordanAlgebra?;B;20|))
           (LETT |n| (SPADCALL (QREFELT $ 9)) . #0#)
           (EXIT (COND
                   ((QEQCAR (SPADCALL
                                (SPADCALL 2 (|spadConstant| $ 21)
                                    (QREFELT $ 47))
                                (QREFELT $ 49))
                            1)
                    (SEQ (SPADCALL
                             "this is not a noncommutative Jordan algebra, as 2 is not invertible in the ground ring"
                             (QREFELT $ 45))
                         (EXIT 'NIL)))
                   ((SPADCALL (QREFELT $ 93))
                    (COND
                      ((SPADCALL (QREFELT $ 94))
                       (SEQ (SPADCALL
                                "this is a noncommutative Jordan algebra"
                                (QREFELT $ 45))
                            (EXIT 'T)))
                      ('T
                       (SEQ (SPADCALL
                                "this is not a noncommutative Jordan algebra, as it is not Jordan admissible"
                                (QREFELT $ 45))
                            (EXIT 'NIL)))))
                   ('T
                    (SEQ (SPADCALL
                             "this is not a noncommutative Jordan algebra, as it is not flexible"
                             (QREFELT $ 45))
                         (EXIT 'NIL))))))))) 

(DEFUN |FINAALG-;antiCommutative?;B;21| ($)
  (PROG (|b| |n| |i| |j| #0=#:G1998 #1=#:G1995)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;antiCommutative?;B;21|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| |i| . #2#) G190
                                       (COND ((> |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (COND
                                           ((NULL
                                             (SPADCALL
                                              (COND
                                                ((EQL |i| |j|)
                                                 (SPADCALL
                                                  (SPADCALL |b| |i|
                                                   (QREFELT $ 37))
                                                  (SPADCALL |b| |i|
                                                   (QREFELT $ 37))
                                                  (QREFELT $ 38)))
                                                ('T
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 38))
                                                  (SPADCALL
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 38))
                                                  (QREFELT $ 39))))
                                              (QREFELT $ 41)))
                                            (PROGN
                                              (LETT #1#
                                               (SEQ
                                                (SPADCALL
                                                 "algebra is not anti-commutative"
                                                 (QREFELT $ 45))
                                                (EXIT
                                                 (PROGN
                                                   (LETT #0#
                                                    'NIL . #2#)
                                                   (GO #0#)))) . #2#)
                                              (GO #1#))))))
                                       (LETT |j| (+ |j| 1) . #2#)
                                       #4=(GO G190) G191 (EXIT NIL)))
                                #1# (EXIT #1#))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is anti-commutative"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;commutative?;B;22| ($)
  (PROG (|b| |n| |i| |j| #0=#:G2004 #1=#:G2001)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;commutative?;B;22|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| (+ |i| 1) . #2#)
                                       G190 (COND ((> |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (COND
                                           ((NULL
                                             (SPADCALL
                                              (SPADCALL
                                               (SPADCALL |b| |i|
                                                (QREFELT $ 37))
                                               (SPADCALL |b| |j|
                                                (QREFELT $ 37))
                                               (QREFELT $ 52))
                                              (QREFELT $ 41)))
                                            (PROGN
                                              (LETT #1#
                                               (SEQ
                                                (SPADCALL
                                                 "algebra is not commutative"
                                                 (QREFELT $ 45))
                                                (EXIT
                                                 (PROGN
                                                   (LETT #0#
                                                    'NIL . #2#)
                                                   (GO #0#)))) . #2#)
                                              (GO #1#))))))
                                       (LETT |j| (+ |j| 1) . #2#)
                                       #4=(GO G190) G191 (EXIT NIL)))
                                #1# (EXIT #1#))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is commutative"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;associative?;B;23| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G2011 #1=#:G2007)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;associative?;B;23|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL |b| |i|
                                                   (QREFELT $ 37))
                                                  (SPADCALL |b| |j|
                                                   (QREFELT $ 37))
                                                  (SPADCALL |b| |k|
                                                   (QREFELT $ 37))
                                                  (QREFELT $ 85))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not associative"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is associative"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;leftAlternative?;B;24| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G2018 #1=#:G2014)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;leftAlternative?;B;24|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (SPADCALL
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not left alternative"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL
                          "algebra satisfies 2*associator(a,a,b) = 0"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;rightAlternative?;B;25| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G2025 #1=#:G2021)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;rightAlternative?;B;25|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not right alternative"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL
                          "algebra satisfies 2*associator(a,b,b) = 0"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;flexible?;B;26| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G2032 #1=#:G2028)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;flexible?;B;26|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (SPADCALL
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not flexible"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#))))))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL)))
                                        #1# (EXIT #1#))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL
                          "algebra satisfies 2*associator(a,b,a) = 0"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;alternative?;B;27| ($)
  (PROG (|b| |n| |i| |j| |k| #0=#:G2041 #1=#:G2036)
    (RETURN
      (SEQ (EXIT (SEQ (LETT |b| (SPADCALL (QREFELT $ 11))
                            . #2=(|FINAALG-;alternative?;B;27|))
                      (LETT |n| (SPADCALL (QREFELT $ 9)) . #2#)
                      (SEQ (LETT |i| 1 . #2#) G190
                           (COND ((QSGREATERP |i| |n|) #3=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #2#) G190
                                       (COND
                                         ((QSGREATERP |j| |n|) #3#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #2#) G190
                                          (COND
                                            ((QSGREATERP |k| |n|) #3#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (SPADCALL
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (SEQ
                                                (SPADCALL
                                                 "algebra is not alternative"
                                                 (QREFELT $ 45))
                                                (EXIT
                                                 (PROGN
                                                   (LETT #0#
                                                    'NIL . #2#)
                                                   (GO #0#)))))
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (SPADCALL
                                                   (SPADCALL |b| |i|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |k|
                                                    (QREFELT $ 37))
                                                   (SPADCALL |b| |j|
                                                    (QREFELT $ 37))
                                                   (QREFELT $ 85))
                                                  (QREFELT $ 39))
                                                 (QREFELT $ 41)))
                                               (PROGN
                                                 (LETT #1#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not alternative"
                                                    (QREFELT $ 45))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #0#
                                                       'NIL . #2#)
                                                      (GO #0#)))) . #2#)
                                                 (GO #1#)))))
                                           #1# (EXIT #1#))
                                          (LETT |k| (QSADD1 |k|) . #2#)
                                          #4=(GO G190) G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #2#)
                                       #4# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #2#) #4# G191
                           (EXIT NIL))
                      (SPADCALL
                          "algebra satisfies 2*associator(a,b,b) = 0 =  2*associator(a,a,b) = 0"
                          (QREFELT $ 45))
                      (EXIT 'T)))
           #0# (EXIT #0#))))) 

(DEFUN |FINAALG-;leftDiscriminant;VR;28| (|v| $)
  (SPADCALL (SPADCALL |v| (QREFELT $ 103)) (QREFELT $ 33))) 

(DEFUN |FINAALG-;rightDiscriminant;VR;29| (|v| $)
  (SPADCALL (SPADCALL |v| (QREFELT $ 105)) (QREFELT $ 33))) 

(DEFUN |FINAALG-;coordinates;2VM;30| (|v| |b| $)
  (PROG (|m| |j| |i| #0=#:G2047)
    (RETURN
      (SEQ (LETT |m|
                 (SPADCALL (QVSIZE |v|) (QVSIZE |b|)
                     (|spadConstant| $ 29) (QREFELT $ 54))
                 . #1=(|FINAALG-;coordinates;2VM;30|))
           (SEQ (LETT |j| (SPADCALL |m| (QREFELT $ 108)) . #1#)
                (LETT |i| (SPADCALL |v| (QREFELT $ 107)) . #1#)
                (LETT #0# (QVSIZE |v|) . #1#) G190
                (COND ((> |i| #0#) (GO G191)))
                (SEQ (EXIT (SPADCALL |m| |j|
                               (SPADCALL
                                   (SPADCALL |v| |i| (QREFELT $ 109))
                                   |b| (QREFELT $ 56))
                               (QREFELT $ 110))))
                (LETT |i|
                      (PROG1 (+ |i| 1) (LETT |j| (+ |j| 1) . #1#)) . #1#)
                (GO G190) G191 (EXIT NIL))
           (EXIT |m|))))) 

(DEFUN |FINAALG-;represents;VVS;31| (|v| |b| $)
  (PROG (|m| #0=#:G2051 #1=#:G2052 |i| #2=#:G2053)
    (RETURN
      (SEQ (LETT |m| (- (SPADCALL |v| (QREFELT $ 112)) 1)
                 . #3=(|FINAALG-;represents;VVS;31|))
           (EXIT (SPADCALL (ELT $ 39)
                     (PRIMVEC2ARR
                         (PROGN
                           (LETT #0# (GETREFV #4=(QVSIZE |b|)) . #3#)
                           (SEQ (LETT #1# 0 . #3#) (LETT |i| 1 . #3#)
                                (LETT #2# #4# . #3#) G190
                                (COND
                                  ((QSGREATERP |i| #2#) (GO G191)))
                                (SEQ (EXIT
                                      (SETELT #0# #1#
                                       (SPADCALL
                                        (SPADCALL |v| (+ |i| |m|)
                                         (QREFELT $ 59))
                                        (SPADCALL |b| (+ |i| |m|)
                                         (QREFELT $ 37))
                                        (QREFELT $ 70)))))
                                (LETT |i|
                                      (PROG1 (QSADD1 |i|)
                                        (LETT #1# (QSADD1 #1#) . #3#)) . #3#)
                                (GO G190) G191 (EXIT NIL))
                           #0#))
                     (QREFELT $ 72))))))) 

(DEFUN |FINAALG-;leftTraceMatrix;VM;32| (|v| $)
  (PROG (#0=#:G2057 |i| #1=#:G2058 #2=#:G2059 |j| #3=#:G2060)
    (RETURN
      (SEQ (SPADCALL
               (PROGN
                 (LETT #0# NIL . #4=(|FINAALG-;leftTraceMatrix;VM;32|))
                 (SEQ (LETT |i| (SPADCALL |v| (QREFELT $ 107)) . #4#)
                      (LETT #1# (QVSIZE |v|) . #4#) G190
                      (COND ((> |i| #1#) #5=(GO G191)))
                      (SEQ (EXIT (LETT #0#
                                       (CONS
                                        (PROGN
                                          (LETT #2# NIL . #4#)
                                          (SEQ
                                           (LETT |j|
                                            (SPADCALL |v|
                                             (QREFELT $ 107)) . #4#)
                                           (LETT #3#
                                            (QVSIZE |v|) . #4#)
                                           G190
                                           (COND ((> |j| #3#) #5#))
                                           (SEQ
                                            (EXIT
                                             (LETT #2#
                                              (CONS
                                               (SPADCALL
                                                (SPADCALL
                                                 (SPADCALL |v| |i|
                                                  (QREFELT $ 37))
                                                 (SPADCALL |v| |j|
                                                  (QREFELT $ 37))
                                                 (QREFELT $ 38))
                                                (QREFELT $ 114))
                                               #2#) . #4#)))
                                           (LETT |j| (+ |j| 1) . #4#)
                                           #6=(GO G190) G191
                                           (EXIT (NREVERSE0 #2#))))
                                        #0#) . #4#)))
                      (LETT |i| (+ |i| 1) . #4#) #6# G191
                      (EXIT (NREVERSE0 #0#))))
               (QREFELT $ 116)))))) 

(DEFUN |FINAALG-;rightTraceMatrix;VM;33| (|v| $)
  (PROG (#0=#:G2064 |i| #1=#:G2065 #2=#:G2066 |j| #3=#:G2067)
    (RETURN
      (SEQ (SPADCALL
               (PROGN
                 (LETT #0# NIL
                       . #4=(|FINAALG-;rightTraceMatrix;VM;33|))
                 (SEQ (LETT |i| (SPADCALL |v| (QREFELT $ 107)) . #4#)
                      (LETT #1# (QVSIZE |v|) . #4#) G190
                      (COND ((> |i| #1#) #5=(GO G191)))
                      (SEQ (EXIT (LETT #0#
                                       (CONS
                                        (PROGN
                                          (LETT #2# NIL . #4#)
                                          (SEQ
                                           (LETT |j|
                                            (SPADCALL |v|
                                             (QREFELT $ 107)) . #4#)
                                           (LETT #3#
                                            (QVSIZE |v|) . #4#)
                                           G190
                                           (COND ((> |j| #3#) #5#))
                                           (SEQ
                                            (EXIT
                                             (LETT #2#
                                              (CONS
                                               (SPADCALL
                                                (SPADCALL
                                                 (SPADCALL |v| |i|
                                                  (QREFELT $ 37))
                                                 (SPADCALL |v| |j|
                                                  (QREFELT $ 37))
                                                 (QREFELT $ 38))
                                                (QREFELT $ 118))
                                               #2#) . #4#)))
                                           (LETT |j| (+ |j| 1) . #4#)
                                           #6=(GO G190) G191
                                           (EXIT (NREVERSE0 #2#))))
                                        #0#) . #4#)))
                      (LETT |i| (+ |i| 1) . #4#) #6# G191
                      (EXIT (NREVERSE0 #0#))))
               (QREFELT $ 116)))))) 

(DEFUN |FINAALG-;leftRegularRepresentation;SVM;34| (|x| |b| $)
  (PROG (|m| #0=#:G2071 |i| #1=#:G2072)
    (RETURN
      (SEQ (LETT |m| (- (SPADCALL |b| (QREFELT $ 107)) 1)
                 . #2=(|FINAALG-;leftRegularRepresentation;SVM;34|))
           (EXIT (SPADCALL
                     (PROGN
                       (LETT #0# NIL . #2#)
                       (SEQ (LETT |i| 1 . #2#)
                            (LETT #1# (SPADCALL (QREFELT $ 9)) . #2#)
                            G190
                            (COND ((QSGREATERP |i| #1#) (GO G191)))
                            (SEQ (EXIT (LETT #0#
                                        (CONS
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL |x|
                                            (SPADCALL |b| (+ |i| |m|)
                                             (QREFELT $ 37))
                                            (QREFELT $ 38))
                                           |b| (QREFELT $ 56))
                                          (QREFELT $ 121))
                                         #0#) . #2#)))
                            (LETT |i| (QSADD1 |i|) . #2#) (GO G190)
                            G191 (EXIT (NREVERSE0 #0#))))
                     (QREFELT $ 116))))))) 

(DEFUN |FINAALG-;rightRegularRepresentation;SVM;35| (|x| |b| $)
  (PROG (|m| #0=#:G2076 |i| #1=#:G2077)
    (RETURN
      (SEQ (LETT |m| (- (SPADCALL |b| (QREFELT $ 107)) 1)
                 . #2=(|FINAALG-;rightRegularRepresentation;SVM;35|))
           (EXIT (SPADCALL
                     (PROGN
                       (LETT #0# NIL . #2#)
                       (SEQ (LETT |i| 1 . #2#)
                            (LETT #1# (SPADCALL (QREFELT $ 9)) . #2#)
                            G190
                            (COND ((QSGREATERP |i| #1#) (GO G191)))
                            (SEQ (EXIT (LETT #0#
                                        (CONS
                                         (SPADCALL
                                          (SPADCALL
                                           (SPADCALL
                                            (SPADCALL |b| (+ |i| |m|)
                                             (QREFELT $ 37))
                                            |x| (QREFELT $ 38))
                                           |b| (QREFELT $ 56))
                                          (QREFELT $ 121))
                                         #0#) . #2#)))
                            (LETT |i| (QSADD1 |i|) . #2#) (GO G190)
                            G191 (EXIT (NREVERSE0 #0#))))
                     (QREFELT $ 116))))))) 

(DEFUN |FiniteRankNonAssociativeAlgebra&| (|#1| |#2|)
  (PROG (DV$1 DV$2 |dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT DV$1 (|devaluate| |#1|)
              . #0=(|FiniteRankNonAssociativeAlgebra&|))
        (LETT DV$2 (|devaluate| |#2|) . #0#)
        (LETT |dv$|
              (LIST '|FiniteRankNonAssociativeAlgebra&| DV$1 DV$2) . #0#)
        (LETT $ (GETREFV 124) . #0#)
        (QSETREFV $ 0 |dv$|)
        (QSETREFV $ 3
            (LETT |pv$|
                  (|buildPredVector| 0 0
                      (LIST (|HasCategory| |#2| '(|IntegralDomain|)))) . #0#))
        (|stuffDomainSlots| $)
        (QSETREFV $ 6 |#1|)
        (QSETREFV $ 7 |#2|)
        (COND
          ((|testBitVector| |pv$| 1)
           (PROGN
             (QSETREFV $ 73
                 (CONS (|dispatchFunction| |FINAALG-;leftRecip;SU;11|)
                       $))
             (QSETREFV $ 75
                 (CONS (|dispatchFunction| |FINAALG-;rightRecip;SU;12|)
                       $))
             (QSETREFV $ 79
                 (CONS (|dispatchFunction| |FINAALG-;recip;SU;13|) $))
             (QSETREFV $ 82
                 (CONS (|dispatchFunction|
                           |FINAALG-;leftMinimalPolynomial;SSup;14|)
                       $))
             (QSETREFV $ 83
                 (CONS (|dispatchFunction|
                           |FINAALG-;rightMinimalPolynomial;SSup;15|)
                       $))
             (QSETREFV $ 86
                 (CONS (|dispatchFunction|
                           |FINAALG-;associatorDependence;L;16|)
                       $)))))
        $)))) 

(MAKEPROP '|FiniteRankNonAssociativeAlgebra&| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
             (|PositiveInteger|) (0 . |rank|) (|Vector| $)
             (4 . |someBasis|) (|Matrix| 7)
             (8 . |leftRegularRepresentation|) (|NonNegativeInteger|)
             (|Matrix| 19) (14 . |zero|) (|Integer|) (20 . |elt|)
             (|SparseUnivariatePolynomial| 7) (27 . |monomial|)
             (33 . |One|) (37 . |One|) (41 . -) (47 . |setelt|)
             (55 . |determinant|)
             |FINAALG-;leftCharacteristicPolynomial;SSup;1|
             (60 . |rightRegularRepresentation|)
             |FINAALG-;rightCharacteristicPolynomial;SSup;2|
             (66 . |Zero|) (70 . +) |FINAALG-;leftTrace;SR;3|
             |FINAALG-;rightTrace;SR;4| (76 . |determinant|)
             |FINAALG-;leftNorm;SR;5| |FINAALG-;rightNorm;SR;6|
             (|Vector| 6) (81 . |elt|) (87 . *) (93 . +) (|Boolean|)
             (99 . |zero?|) (|Void|) (|String|) (|OutputForm|)
             (104 . |messagePrint|) |FINAALG-;antiAssociative?;B;7|
             (109 . *) (|Union| $ '"failed") (115 . |recip|)
             (120 . |antiCommutator|) |FINAALG-;jordanAdmissible?;B;8|
             (126 . |commutator|) |FINAALG-;lieAdmissible?;B;9|
             (132 . |new|) (|Vector| 7) (139 . |coordinates|)
             (|Vector| 12) (145 . |elt|) (151 . |elt|) (157 . |setelt|)
             |FINAALG-;structuralConstants;VV;10| (165 . |leftUnit|)
             (169 . |coerce|) (174 . |rank|) (179 . |horizConcat|)
             (|List| 55) (185 . |nullSpace|) (190 . -) (195 . *)
             (201 . *) (|Mapping| 6 6 6) (207 . |reduce|)
             (213 . |leftRecip|) (218 . |rightUnit|)
             (222 . |rightRecip|) (227 . |leftRecip|)
             (232 . |rightRecip|) (237 . =) (243 . |recip|)
             (248 . |Zero|) (252 . +) (258 . |leftMinimalPolynomial|)
             (263 . |rightMinimalPolynomial|) (268 . **)
             (274 . |associator|) (281 . |associatorDependence|)
             |FINAALG-;jacobiIdentity?;B;17| (285 . |antiCommutative?|)
             (289 . |jacobiIdentity?|) |FINAALG-;lieAlgebra?;B;18|
             (293 . |commutative?|) |FINAALG-;jordanAlgebra?;B;19|
             (297 . |flexible?|) (301 . |jordanAdmissible?|)
             |FINAALG-;noncommutativeJordanAlgebra?;B;20|
             |FINAALG-;antiCommutative?;B;21|
             |FINAALG-;commutative?;B;22| |FINAALG-;associative?;B;23|
             |FINAALG-;leftAlternative?;B;24|
             |FINAALG-;rightAlternative?;B;25|
             |FINAALG-;flexible?;B;26| |FINAALG-;alternative?;B;27|
             (305 . |leftTraceMatrix|)
             |FINAALG-;leftDiscriminant;VR;28|
             (310 . |rightTraceMatrix|)
             |FINAALG-;rightDiscriminant;VR;29| (315 . |minIndex|)
             (320 . |minRowIndex|) (325 . |qelt|) (331 . |setRow!|)
             |FINAALG-;coordinates;2VM;30| (338 . |minIndex|)
             |FINAALG-;represents;VVS;31| (343 . |leftTrace|)
             (|List| 120) (348 . |matrix|)
             |FINAALG-;leftTraceMatrix;VM;32| (353 . |rightTrace|)
             |FINAALG-;rightTraceMatrix;VM;33| (|List| 7)
             (358 . |parts|)
             |FINAALG-;leftRegularRepresentation;SVM;34|
             |FINAALG-;rightRegularRepresentation;SVM;35|)
          '#(|structuralConstants| 363 |rightTraceMatrix| 368
             |rightTrace| 373 |rightRegularRepresentation| 378
             |rightRecip| 384 |rightNorm| 389 |rightMinimalPolynomial|
             394 |rightDiscriminant| 399
             |rightCharacteristicPolynomial| 404 |rightAlternative?|
             409 |represents| 413 |recip| 419
             |noncommutativeJordanAlgebra?| 424 |lieAlgebra?| 428
             |lieAdmissible?| 432 |leftTraceMatrix| 436 |leftTrace| 441
             |leftRegularRepresentation| 446 |leftRecip| 452 |leftNorm|
             457 |leftMinimalPolynomial| 462 |leftDiscriminant| 467
             |leftCharacteristicPolynomial| 472 |leftAlternative?| 477
             |jordanAlgebra?| 481 |jordanAdmissible?| 485
             |jacobiIdentity?| 489 |flexible?| 493 |coordinates| 497
             |commutative?| 503 |associatorDependence| 507
             |associative?| 511 |antiCommutative?| 515
             |antiAssociative?| 519 |alternative?| 523)
          'NIL
          (CONS (|makeByteWordVec2| 1 'NIL)
                (CONS '#()
                      (CONS '#()
                            (|makeByteWordVec2| 123
                                '(0 6 8 9 0 6 10 11 2 6 12 0 10 13 2 15
                                  0 14 14 16 3 12 7 0 17 17 18 2 19 0 7
                                  14 20 0 7 0 21 0 19 0 22 2 19 0 0 0
                                  23 4 15 19 0 17 17 19 24 1 15 19 0 25
                                  2 6 12 0 10 27 0 7 0 29 2 7 0 0 0 30
                                  1 12 7 0 33 2 36 6 0 17 37 2 6 0 0 0
                                  38 2 6 0 0 0 39 1 6 40 0 41 1 44 42
                                  43 45 2 7 0 8 0 47 1 7 48 0 49 2 6 0
                                  0 0 50 2 6 0 0 0 52 3 12 0 14 14 7 54
                                  2 6 55 0 10 56 2 57 12 0 17 58 2 55 7
                                  0 17 59 4 12 7 0 17 17 7 60 0 6 48 62
                                  1 12 0 55 63 1 12 14 0 64 2 12 0 0 0
                                  65 1 12 66 0 67 1 7 0 0 68 2 7 0 0 0
                                  69 2 6 0 7 0 70 2 36 6 71 0 72 1 0 48
                                  0 73 0 6 48 74 1 0 48 0 75 1 6 48 0
                                  76 1 6 48 0 77 2 6 40 0 0 78 1 0 48 0
                                  79 0 19 0 80 2 19 0 0 0 81 1 0 19 0
                                  82 1 0 19 0 83 2 8 0 0 8 84 3 6 0 0 0
                                  0 85 0 0 66 86 0 6 40 88 0 6 40 89 0
                                  6 40 91 0 6 40 93 0 6 40 94 1 6 12 10
                                  103 1 6 12 10 105 1 36 17 0 107 1 12
                                  17 0 108 2 36 6 0 17 109 3 12 0 0 17
                                  55 110 1 55 17 0 112 1 6 7 0 114 1 12
                                  0 115 116 1 6 7 0 118 1 55 120 0 121
                                  1 0 57 10 61 1 0 12 10 119 1 0 7 0 32
                                  2 0 12 0 10 123 1 0 48 0 75 1 0 7 0
                                  35 1 0 19 0 83 1 0 7 10 106 1 0 19 0
                                  28 0 0 40 100 2 0 0 55 10 113 1 0 48
                                  0 79 0 0 40 95 0 0 40 90 0 0 40 53 1
                                  0 12 10 117 1 0 7 0 31 2 0 12 0 10
                                  122 1 0 48 0 73 1 0 7 0 34 1 0 19 0
                                  82 1 0 7 10 104 1 0 19 0 26 0 0 40 99
                                  0 0 40 92 0 0 40 51 0 0 40 87 0 0 40
                                  101 2 0 12 10 10 111 0 0 40 97 0 0 66
                                  86 0 0 40 98 0 0 40 96 0 0 40 46 0 0
                                  40 102)))))
          '|lookupComplete|)) 
