
(/VERSIONCHECK 2) 

(DEFUN |ALGSC;recip;$U;1| (|x| $) (SPADCALL |x| (QREFELT $ 13))) 

(DEFUN |ALGSC;*;Sm2$;2| (|m| |x| $)
  (SPADCALL (SPADCALL |m| (QREFELT $ 17)) |x| (QREFELT $ 18))) 

(DEFUN |ALGSC;coerce;V$;3| (|v| $) (SPADCALL |v| (QREFELT $ 21))) 

(DEFUN |ALGSC;structuralConstants;V;4| ($) (QREFELT $ 9)) 

(DEFUN |ALGSC;coordinates;$V;5| (|x| $)
  (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 27))) 

(DEFUN |ALGSC;coordinates;$VV;6| (|x| |b| $)
  (PROG (#0=#:G1848 |m| |transitionMatrix| |i| |res| #1=#:G1857)
    (RETURN
      (SEQ (LETT |m|
                 (PROG1 (LETT #0# (SPADCALL |b| (QREFELT $ 31))
                              . #2=(|ALGSC;coordinates;$VV;6|))
                   (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|)
                       #0#)) . #2#)
           (LETT |transitionMatrix|
                 (SPADCALL (QREFELT $ 7) |m| (|spadConstant| $ 32)
                     (QREFELT $ 34)) . #2#)
           (SEQ (LETT |i| 1 . #2#) G190
                (COND ((QSGREATERP |i| |m|) (GO G191)))
                (SEQ (EXIT (SPADCALL |transitionMatrix| |i|
                               (SPADCALL
                                   (SPADCALL |b| |i| (QREFELT $ 35))
                                   (QREFELT $ 28))
                               (QREFELT $ 36))))
                (LETT |i| (QSADD1 |i|) . #2#) (GO G190) G191
                (EXIT NIL))
           (LETT |res|
                 (SPADCALL |transitionMatrix|
                     (SPADCALL |x| (QREFELT $ 28)) (QREFELT $ 40)) . #2#)
           (COND
             ((NULL (NULL (QCDR |res|)))
              (|error| "coordinates: warning your 'basis' is linearly dependent")))
           (EXIT (COND
                   ((QEQCAR (QCAR |res|) 1)
                    (|error| "coordinates: first argument is not in linear span of second argument"))
                   ('T
                    (PROG2 (LETT #1# (QCAR |res|) . #2#) (QCDR #1#)
                      (|check-union| (QEQCAR #1# 0)
                          (|Vector| (QREFELT $ 6)) #1#))))))))) 

(DEFUN |ALGSC;basis;V;7| ($)
  (PROG (#0=#:G1864 #1=#:G1865 |i| #2=#:G1866 #3=#:G1861)
    (RETURN
      (SEQ (PRIMVEC2ARR
               (PROGN
                 (LETT #0# (GETREFV #4=(QREFELT $ 7))
                       . #5=(|ALGSC;basis;V;7|))
                 (SEQ (LETT #1# 0 . #5#) (LETT |i| 1 . #5#)
                      (LETT #2# #4# . #5#) G190
                      (COND ((QSGREATERP |i| #2#) (GO G191)))
                      (SEQ (EXIT (SETELT #0# #1#
                                         (SPADCALL
                                          (PROG1 (LETT #3# |i| . #5#)
                                            (|check-subtype| (> #3# 0)
                                             '(|PositiveInteger|) #3#))
                                          (QREFELT $ 45)))))
                      (LETT |i|
                            (PROG1 (QSADD1 |i|)
                              (LETT #1# (QSADD1 #1#) . #5#)) . #5#)
                      (GO G190) G191 (EXIT NIL))
                 #0#)))))) 

(DEFUN |ALGSC;someBasis;V;8| ($) (SPADCALL (QREFELT $ 42))) 

(DEFUN |ALGSC;rank;Pi;9| ($) (QREFELT $ 7)) 

(DEFUN |ALGSC;elt;$IR;10| (|x| |i| $)
  (SPADCALL |x| |i| (QREFELT $ 48))) 

(DEFUN |ALGSC;coerce;$Of;11| (|x| $)
  (PROG (|i| #0=#:G1876 |coef| |le| #1=#:G1870)
    (RETURN
      (SEQ (COND
             ((SPADCALL |x| (QREFELT $ 51))
              (SPADCALL (|spadConstant| $ 32) (QREFELT $ 53)))
             ('T
              (SEQ (LETT |le| NIL . #2=(|ALGSC;coerce;$Of;11|))
                   (SEQ (LETT |i| 1 . #2#)
                        (LETT #0# (QREFELT $ 7) . #2#) G190
                        (COND ((QSGREATERP |i| #0#) (GO G191)))
                        (SEQ (EXIT (SEQ
                                    (LETT |coef|
                                     (SPADCALL |x| |i| (QREFELT $ 49)) . #2#)
                                    (EXIT
                                     (COND
                                       ((NULL
                                         (SPADCALL |coef|
                                          (QREFELT $ 54)))
                                        (PROGN
                                          (LETT #1#
                                           (COND
                                             ((SPADCALL |coef|
                                               (|spadConstant| $ 55)
                                               (QREFELT $ 56))
                                              (LETT |le|
                                               (CONS
                                                (SPADCALL
                                                 (SPADCALL
                                                  (QREFELT $ 8) |i|
                                                  (QREFELT $ 59))
                                                 (QREFELT $ 60))
                                                |le|) . #2#))
                                             ('T
                                              (LETT |le|
                                               (CONS
                                                (SPADCALL
                                                 (SPADCALL |coef|
                                                  (QREFELT $ 53))
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (QREFELT $ 8) |i|
                                                   (QREFELT $ 59))
                                                  (QREFELT $ 60))
                                                 (QREFELT $ 61))
                                                |le|) . #2#))) . #2#)
                                          (GO #1#)))))))
                             #1# (EXIT #1#))
                        (LETT |i| (QSADD1 |i|) . #2#) (GO G190) G191
                        (EXIT NIL))
                   (EXIT (SPADCALL (ELT $ 62) |le| (QREFELT $ 65)))))))))) 

(DEFUN |ALGSC;*;3$;12| (|x| |y| $)
  (PROG (|v| |k| #0=#:G1883 |i| #1=#:G1884 |j| #2=#:G1885 |h|)
    (RETURN
      (SEQ (LETT |v|
                 (SPADCALL (QREFELT $ 7) (|spadConstant| $ 32)
                     (QREFELT $ 67))
                 . #3=(|ALGSC;*;3$;12|))
           (SEQ (LETT |k| 1 . #3#) (LETT #0# (QREFELT $ 7) . #3#) G190
                (COND ((QSGREATERP |k| #0#) #4=(GO G191)))
                (SEQ (LETT |h| (|spadConstant| $ 32) . #3#)
                     (SEQ (LETT |i| 1 . #3#)
                          (LETT #1# (QREFELT $ 7) . #3#) G190
                          (COND ((QSGREATERP |i| #1#) #4#))
                          (SEQ (EXIT (SEQ (LETT |j| 1 . #3#)
                                      (LETT #2# (QREFELT $ 7) . #3#)
                                      G190
                                      (COND
                                        ((QSGREATERP |j| #2#) #4#))
                                      (SEQ
                                       (EXIT
                                        (LETT |h|
                                         (SPADCALL |h|
                                          (SPADCALL
                                           (SPADCALL
                                            (SPADCALL |x| |i|
                                             (QREFELT $ 49))
                                            (SPADCALL |y| |j|
                                             (QREFELT $ 49))
                                            (QREFELT $ 68))
                                           (SPADCALL
                                            (SPADCALL (QREFELT $ 9) |k|
                                             (QREFELT $ 69))
                                            |i| |j| (QREFELT $ 70))
                                           (QREFELT $ 68))
                                          (QREFELT $ 71)) . #3#)))
                                      (LETT |j| (QSADD1 |j|) . #3#)
                                      #5=(GO G190) G191 (EXIT NIL))))
                          (LETT |i| (QSADD1 |i|) . #3#) #5# G191
                          (EXIT NIL))
                     (EXIT (SPADCALL |v| |k| |h| (QREFELT $ 72))))
                (LETT |k| (QSADD1 |k|) . #3#) #5# G191 (EXIT NIL))
           (EXIT (SPADCALL |v| (QREFELT $ 21))))))) 

(DEFUN |ALGSC;alternative?;B;13| ($)
  (PROG (|i| #0=#:G1913 #1=#:G1914 #2=#:G1915 #3=#:G1916 #4=#:G1917
             #5=#:G1888 |j| #6=#:G1918 #7=#:G1919 #8=#:G1920 #9=#:G1921
             #10=#:G1894 |k| #11=#:G1922 #12=#:G1923 #13=#:G1924
             #14=#:G1899 |r| #15=#:G1925 |l| #16=#:G1926 |res|
             #17=#:G1912 #18=#:G1903)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #19=(|ALGSC;alternative?;B;13|))
                           (LETT #0# (QREFELT $ 7) . #19#) G190
                           (COND ((QSGREATERP |i| #0#) #20=(GO G191)))
                           (SEQ (SEQ (LETT |j| 1 . #19#)
                                     (LETT #1# (- |i| 1) . #19#) G190
                                     (COND
                                       ((QSGREATERP |j| #1#) #20#))
                                     (SEQ
                                      (EXIT
                                       (SEQ (LETT |k| |j| . #19#)
                                        (LETT #2# (QREFELT $ 7) . #19#)
                                        G190 (COND ((> |k| #2#) #20#))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |r| 1 . #19#)
                                           (LETT #3#
                                            (QREFELT $ 7) . #19#)
                                           G190
                                           (COND
                                             ((QSGREATERP |r| #3#)
                                              #20#))
                                           (SEQ
                                            (EXIT
                                             (SEQ
                                              (LETT |res|
                                               (|spadConstant| $ 32) . #19#)
                                              (SEQ (LETT |l| 1 . #19#)
                                               (LETT #4#
                                                (QREFELT $ 7) . #19#)
                                               G190
                                               (COND
                                                 ((QSGREATERP |l| #4#)
                                                  #20#))
                                               (SEQ
                                                (EXIT
                                                 (LETT |res|
                                                  (SPADCALL
                                                   (SPADCALL |res|
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |k| |j|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |r|
                                                       (QREFELT $ 69))
                                                      |i| |l|
                                                      (QREFELT $ 70))
                                                     (QREFELT $ 68))
                                                    (QREFELT $ 74))
                                                   (SPADCALL
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |l|
                                                       (QREFELT $ 69))
                                                      |i| |j|
                                                      (QREFELT $ 70))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |r|
                                                       (QREFELT $ 69))
                                                      |l| |k|
                                                      (QREFELT $ 70))
                                                     (QREFELT $ 68))
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |l|
                                                       (QREFELT $ 69))
                                                      |i| |k|
                                                      (QREFELT $ 70))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |r|
                                                       (QREFELT $ 69))
                                                      |l| |j|
                                                      (QREFELT $ 70))
                                                     (QREFELT $ 68))
                                                    (QREFELT $ 71))
                                                   (QREFELT $ 71)) . #19#)))
                                               (LETT |l|
                                                (QSADD1 |l|) . #19#)
                                               #21=(GO G190) G191
                                               (EXIT NIL))
                                              (EXIT
                                               (COND
                                                 ((NULL
                                                   (SPADCALL |res|
                                                    (QREFELT $ 54)))
                                                  (PROGN
                                                    (LETT #5#
                                                     (SEQ
                                                      (SPADCALL
                                                       "algebra is not right alternative"
                                                       (QREFELT $ 77))
                                                      (EXIT
                                                       (PROGN
                                                         (LETT #17#
                                                          'NIL . #19#)
                                                         (GO #17#)))) . #19#)
                                                    (GO #5#)))))))
                                            #5# (EXIT #5#))
                                           (LETT |r|
                                            (QSADD1 |r|) . #19#)
                                           #21# G191 (EXIT NIL))))
                                        (LETT |k| (+ |k| 1) . #19#)
                                        #21# G191 (EXIT NIL))))
                                     (LETT |j| (QSADD1 |j|) . #19#)
                                     #21# G191 (EXIT NIL))
                                (EXIT (SEQ (LETT |j| |i| . #19#)
                                       (LETT #6# (QREFELT $ 7) . #19#)
                                       G190 (COND ((> |j| #6#) #20#))
                                       (SEQ
                                        (SEQ (LETT |k| 1 . #19#)
                                         (LETT #7# (- |j| 1) . #19#)
                                         G190
                                         (COND
                                           ((QSGREATERP |k| #7#) #20#))
                                         (SEQ
                                          (EXIT
                                           (SEQ (LETT |r| 1 . #19#)
                                            (LETT #8#
                                             (QREFELT $ 7) . #19#)
                                            G190
                                            (COND
                                              ((QSGREATERP |r| #8#)
                                               #20#))
                                            (SEQ
                                             (EXIT
                                              (SEQ
                                               (LETT |res|
                                                (|spadConstant| $ 32) . #19#)
                                               (SEQ (LETT |l| 1 . #19#)
                                                (LETT #9#
                                                 (QREFELT $ 7) . #19#)
                                                G190
                                                (COND
                                                  ((QSGREATERP |l| #9#)
                                                   #20#))
                                                (SEQ
                                                 (EXIT
                                                  (LETT |res|
                                                   (SPADCALL
                                                    (SPADCALL |res|
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |j| |i|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 71))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |l| |k|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71))
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |i| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |i| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |j| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71))
                                                    (QREFELT $ 74)) . #19#)))
                                                (LETT |l|
                                                 (QSADD1 |l|) . #19#)
                                                #21# G191 (EXIT NIL))
                                               (EXIT
                                                (COND
                                                  ((NULL
                                                    (SPADCALL |res|
                                                     (QREFELT $ 54)))
                                                   (PROGN
                                                     (LETT #10#
                                                      (SEQ
                                                       (SPADCALL
                                                        "algebra is not left alternative"
                                                        (QREFELT $ 77))
                                                       (EXIT
                                                        (PROGN
                                                          (LETT #17#
                                                           'NIL . #19#)
                                                          (GO #17#)))) . #19#)
                                                     (GO #10#)))))))
                                             #10# (EXIT #10#))
                                            (LETT |r|
                                             (QSADD1 |r|) . #19#)
                                            #21# G191 (EXIT NIL))))
                                         (LETT |k| (QSADD1 |k|) . #19#)
                                         #21# G191 (EXIT NIL))
                                        (EXIT
                                         (SEQ (LETT |k| |j| . #19#)
                                          (LETT #11#
                                           (QREFELT $ 7) . #19#)
                                          G190
                                          (COND ((> |k| #11#) #20#))
                                          (SEQ
                                           (SEQ (LETT |r| 1 . #19#)
                                            (LETT #12#
                                             (QREFELT $ 7) . #19#)
                                            G190
                                            (COND
                                              ((QSGREATERP |r| #12#)
                                               #20#))
                                            (SEQ
                                             (EXIT
                                              (SEQ
                                               (LETT |res|
                                                (|spadConstant| $ 32) . #19#)
                                               (SEQ (LETT |l| 1 . #19#)
                                                (LETT #13#
                                                 (QREFELT $ 7) . #19#)
                                                G190
                                                (COND
                                                  ((QSGREATERP |l|
                                                    #13#)
                                                   #20#))
                                                (SEQ
                                                 (EXIT
                                                  (LETT |res|
                                                   (SPADCALL
                                                    (SPADCALL |res|
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |j| |i|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 71))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |l| |k|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71))
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |i| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |i| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |j| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71))
                                                    (QREFELT $ 74)) . #19#)))
                                                (LETT |l|
                                                 (QSADD1 |l|) . #19#)
                                                #21# G191 (EXIT NIL))
                                               (EXIT
                                                (COND
                                                  ((NULL
                                                    (SPADCALL |res|
                                                     (QREFELT $ 54)))
                                                   (PROGN
                                                     (LETT #14#
                                                      (SEQ
                                                       (SPADCALL
                                                        "algebra is not left alternative"
                                                        (QREFELT $ 77))
                                                       (EXIT
                                                        (PROGN
                                                          (LETT #17#
                                                           'NIL . #19#)
                                                          (GO #17#)))) . #19#)
                                                     (GO #14#)))))))
                                             #14# (EXIT #14#))
                                            (LETT |r|
                                             (QSADD1 |r|) . #19#)
                                            #21# G191 (EXIT NIL))
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #19#)
                                             (LETT #15#
                                              (QREFELT $ 7) . #19#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #15#)
                                                #20#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #19#)
                                                (SEQ
                                                 (LETT |l| 1 . #19#)
                                                 (LETT #16#
                                                  (QREFELT $ 7) . #19#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #16#)
                                                    #20#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |j| |k|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |k| |j|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |i| |l|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 74))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |k|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |j|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (QREFELT $ 71)) . #19#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #19#)
                                                 #21# G191 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #18#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not right alternative"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #17#
                                                            'NIL . #19#)
                                                           (GO #17#)))) . #19#)
                                                      (GO #18#)))))))
                                              #18# (EXIT #18#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #19#)
                                             #21# G191 (EXIT NIL))))
                                          (LETT |k| (+ |k| 1) . #19#)
                                          #21# G191 (EXIT NIL))))
                                       (LETT |j| (+ |j| 1) . #19#) #21#
                                       G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #19#) #21# G191
                           (EXIT NIL))
                      (SPADCALL
                          "algebra satisfies 2*associator(a,b,b) = 0 = 2*associator(a,a,b) = 0"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #17# (EXIT #17#))))) 

(DEFUN |ALGSC;associative?;B;14| ($)
  (PROG (|i| #0=#:G1936 |j| #1=#:G1937 |k| #2=#:G1938 |r| #3=#:G1939
             |l| #4=#:G1940 |res| #5=#:G1935 #6=#:G1929)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;associative?;B;14|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |i| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 74)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not associative"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (QSADD1 |k|) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is associative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;antiAssociative?;B;15| ($)
  (PROG (|i| #0=#:G1950 |j| #1=#:G1951 |k| #2=#:G1952 |r| #3=#:G1953
             |l| #4=#:G1954 |res| #5=#:G1949 #6=#:G1943)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;antiAssociative?;B;15|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |k|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |i| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not anti-associative"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (QSADD1 |k|) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is anti-associative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;commutative?;B;16| ($)
  (PROG (|i| #0=#:G1962 |j| #1=#:G1963 |k| #2=#:G1964 #3=#:G1961
             #4=#:G1957)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #5=(|ALGSC;commutative?;B;16|))
                           (LETT #0# (QREFELT $ 7) . #5#) G190
                           (COND ((QSGREATERP |i| #0#) #6=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| (+ |i| 1) . #5#)
                                       (LETT #1# (QREFELT $ 7) . #5#)
                                       G190 (COND ((> |j| #1#) #6#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #5#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #5#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #6#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (QREFELT $ 9) |k|
                                                   (QREFELT $ 69))
                                                  |i| |j|
                                                  (QREFELT $ 70))
                                                 (SPADCALL
                                                  (SPADCALL
                                                   (QREFELT $ 9) |k|
                                                   (QREFELT $ 69))
                                                  |j| |i|
                                                  (QREFELT $ 70))
                                                 (QREFELT $ 56)))
                                               (PROGN
                                                 (LETT #4#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not commutative"
                                                    (QREFELT $ 77))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #3#
                                                       'NIL . #5#)
                                                      (GO #3#)))) . #5#)
                                                 (GO #4#))))))
                                          (LETT |k| (QSADD1 |k|) . #5#)
                                          #7=(GO G190) G191 (EXIT NIL)))
                                        #4# (EXIT #4#))
                                       (LETT |j| (+ |j| 1) . #5#) #7#
                                       G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #5#) #7# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is commutative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #3# (EXIT #3#))))) 

(DEFUN |ALGSC;antiCommutative?;B;17| ($)
  (PROG (|i| #0=#:G1972 |j| #1=#:G1973 |k| #2=#:G1974 #3=#:G1971
             #4=#:G1967)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #5=(|ALGSC;antiCommutative?;B;17|))
                           (LETT #0# (QREFELT $ 7) . #5#) G190
                           (COND ((QSGREATERP |i| #0#) #6=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| |i| . #5#)
                                       (LETT #1# (QREFELT $ 7) . #5#)
                                       G190 (COND ((> |j| #1#) #6#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #5#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #5#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #6#))
                                          (SEQ
                                           (EXIT
                                            (COND
                                              ((NULL
                                                (SPADCALL
                                                 (COND
                                                   ((EQL |i| |j|)
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (QREFELT $ 9) |k|
                                                      (QREFELT $ 69))
                                                     |i| |i|
                                                     (QREFELT $ 70)))
                                                   ('T
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |k|
                                                       (QREFELT $ 69))
                                                      |i| |j|
                                                      (QREFELT $ 70))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (QREFELT $ 9)
                                                       |k|
                                                       (QREFELT $ 69))
                                                      |j| |i|
                                                      (QREFELT $ 70))
                                                     (QREFELT $ 71))))
                                                 (QREFELT $ 54)))
                                               (PROGN
                                                 (LETT #4#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not anti-commutative"
                                                    (QREFELT $ 77))
                                                   (EXIT
                                                    (PROGN
                                                      (LETT #3#
                                                       'NIL . #5#)
                                                      (GO #3#)))) . #5#)
                                                 (GO #4#))))))
                                          (LETT |k| (QSADD1 |k|) . #5#)
                                          #7=(GO G190) G191 (EXIT NIL)))
                                        #4# (EXIT #4#))
                                       (LETT |j| (+ |j| 1) . #5#) #7#
                                       G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #5#) #7# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is anti-commutative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #3# (EXIT #3#))))) 

(DEFUN |ALGSC;leftAlternative?;B;18| ($)
  (PROG (|i| #0=#:G1984 |j| #1=#:G1985 |k| #2=#:G1986 |r| #3=#:G1987
             |l| #4=#:G1988 |res| #5=#:G1983 #6=#:G1977)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;leftAlternative?;B;18|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| |i| . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190 (COND ((> |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |i| |j|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |j| |i|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |j| |k|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |i| |l|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |k|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |j| |l|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (QREFELT $ 74)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not left alternative"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (QSADD1 |k|) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (+ |j| 1) . #7#) #9#
                                       G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is left alternative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;rightAlternative?;B;19| ($)
  (PROG (|i| #0=#:G1998 |j| #1=#:G1999 |k| #2=#:G2000 |r| #3=#:G2001
             |l| #4=#:G2002 |res| #5=#:G1997 #6=#:G1991)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;rightAlternative?;B;19|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| |j| . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190 (COND ((> |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |j| |k|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |k| |j|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |i| |l|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 74))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |k|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |j|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (QREFELT $ 71)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not right alternative"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (+ |k| 1) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is right alternative"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;flexible?;B;20| ($)
  (PROG (|i| #0=#:G2012 |j| #1=#:G2013 |k| #2=#:G2014 |r| #3=#:G2015
             |l| #4=#:G2016 |res| #5=#:G2011 #6=#:G2005)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1 . #7=(|ALGSC;flexible?;B;20|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| |i| . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190 (COND ((> |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |l|
                                                           (QREFELT $
                                                            69))
                                                          |i| |j|
                                                          (QREFELT $
                                                           70))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |r|
                                                           (QREFELT $
                                                            69))
                                                          |l| |k|
                                                          (QREFELT $
                                                           70))
                                                         (QREFELT $ 68))
                                                        (QREFELT $ 71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |j| |k|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |r|
                                                          (QREFELT $
                                                           69))
                                                         |i| |l|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 74))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |k| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |i|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |l|
                                                        (QREFELT $ 69))
                                                       |j| |i|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |k| |l|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 74)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not flexible"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (+ |k| 1) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is flexible" (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;lieAdmissible?;B;21| ($)
  (PROG (|i| #0=#:G2026 |j| #1=#:G2027 |k| #2=#:G2028 |r| #3=#:G2029
             |l| #4=#:G2030 |res| #5=#:G2025 #6=#:G2019)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;lieAdmissible?;B;21|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |l| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |l|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL |res|
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |l|
                                                           (QREFELT $
                                                            69))
                                                          |i| |j|
                                                          (QREFELT $
                                                           70))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |l|
                                                           (QREFELT $
                                                            69))
                                                          |j| |i|
                                                          (QREFELT $
                                                           70))
                                                         (QREFELT $ 74))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |r|
                                                           (QREFELT $
                                                            69))
                                                          |l| |k|
                                                          (QREFELT $
                                                           70))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $
                                                            9)
                                                           |r|
                                                           (QREFELT $
                                                            69))
                                                          |k| |l|
                                                          (QREFELT $
                                                           70))
                                                         (QREFELT $ 74))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 71))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |j| |k|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |l|
                                                          (QREFELT $
                                                           69))
                                                         |k| |j|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 74))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |r|
                                                          (QREFELT $
                                                           69))
                                                         |l| |i|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |r|
                                                          (QREFELT $
                                                           69))
                                                         |i| |l|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 74))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |k| |i|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |l|
                                                         (QREFELT $ 69))
                                                        |i| |k|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 74))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |l| |j|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |j| |l|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 74))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71)) . #7#)))
                                                 (LETT |l|
                                                  (QSADD1 |l|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "algebra is not Lie admissible"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (QSADD1 |k|) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "algebra is Lie admissible"
                          (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |ALGSC;jordanAdmissible?;B;22| ($)
  (PROG (|i| #0=#:G2047 |j| #1=#:G2048 |k| #2=#:G2049 |w| #3=#:G2050
             |t| #4=#:G2051 |l| #5=#:G2052 |r| #6=#:G2053 |res|
             #7=#:G2046 #8=#:G2038)
    (RETURN
      (SEQ (EXIT (COND
                   ((QEQCAR (SPADCALL
                                (SPADCALL 2 (|spadConstant| $ 55)
                                    (QREFELT $ 87))
                                (QREFELT $ 88))
                            1)
                    (SEQ (SPADCALL
                             "this algebra is not Jordan admissible, as 2 is not invertible in the ground ring"
                             (QREFELT $ 77))
                         (EXIT 'NIL)))
                   ('T
                    (SEQ (SEQ (LETT |i| 1
                                    . #9=(|ALGSC;jordanAdmissible?;B;22|))
                              (LETT #0# (QREFELT $ 7) . #9#) G190
                              (COND
                                ((QSGREATERP |i| #0#) #10=(GO G191)))
                              (SEQ (EXIT
                                    (SEQ (LETT |j| 1 . #9#)
                                     (LETT #1# (QREFELT $ 7) . #9#)
                                     G190
                                     (COND
                                       ((QSGREATERP |j| #1#) #10#))
                                     (SEQ
                                      (EXIT
                                       (SEQ (LETT |k| 1 . #9#)
                                        (LETT #2# (QREFELT $ 7) . #9#)
                                        G190
                                        (COND
                                          ((QSGREATERP |k| #2#) #10#))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |w| 1 . #9#)
                                           (LETT #3#
                                            (QREFELT $ 7) . #9#)
                                           G190
                                           (COND
                                             ((QSGREATERP |w| #3#)
                                              #10#))
                                           (SEQ
                                            (EXIT
                                             (SEQ (LETT |t| 1 . #9#)
                                              (LETT #4#
                                               (QREFELT $ 7) . #9#)
                                              G190
                                              (COND
                                                ((QSGREATERP |t| #4#)
                                                 #10#))
                                              (SEQ
                                               (EXIT
                                                (SEQ
                                                 (LETT |res|
                                                  (|spadConstant| $ 32) . #9#)
                                                 (SEQ
                                                  (LETT |l| 1 . #9#)
                                                  (LETT #5#
                                                   (QREFELT $ 7) . #9#)
                                                  G190
                                                  (COND
                                                    ((QSGREATERP |l|
                                                      #5#)
                                                     #10#))
                                                  (SEQ
                                                   (EXIT
                                                    (SEQ
                                                     (LETT |r| 1 . #9#)
                                                     (LETT #6#
                                                      (QREFELT $ 7) . #9#)
                                                     G190
                                                     (COND
                                                       ((QSGREATERP |r|
                                                         #6#)
                                                        #10#))
                                                     (SEQ
                                                      (EXIT
                                                       (LETT |res|
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              |res|
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT
                                                                    $
                                                                    9)
                                                                   |l|
                                                                   (QREFELT
                                                                    $
                                                                    69))
                                                                  |i|
                                                                  |j|
                                                                  (QREFELT
                                                                   $
                                                                   70))
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT
                                                                    $
                                                                    9)
                                                                   |l|
                                                                   (QREFELT
                                                                    $
                                                                    69))
                                                                  |j|
                                                                  |i|
                                                                  (QREFELT
                                                                   $
                                                                   70))
                                                                 (QREFELT
                                                                  $ 71))
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT
                                                                    $
                                                                    9)
                                                                   |r|
                                                                   (QREFELT
                                                                    $
                                                                    69))
                                                                  |w|
                                                                  |k|
                                                                  (QREFELT
                                                                   $
                                                                   70))
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT
                                                                    $
                                                                    9)
                                                                   |r|
                                                                   (QREFELT
                                                                    $
                                                                    69))
                                                                  |k|
                                                                  |w|
                                                                  (QREFELT
                                                                   $
                                                                   70))
                                                                 (QREFELT
                                                                  $ 71))
                                                                (QREFELT
                                                                 $ 68))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |t|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |l|
                                                                 |r|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |t|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |r|
                                                                 |l|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (QREFELT
                                                                 $ 71))
                                                               (QREFELT
                                                                $ 68))
                                                              (QREFELT
                                                               $ 71))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |r|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |w|
                                                                 |k|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |r|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |k|
                                                                 |w|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (QREFELT
                                                                 $ 71))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |l|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |j|
                                                                 |r|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |l|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |r|
                                                                 |j|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (QREFELT
                                                                 $ 71))
                                                               (QREFELT
                                                                $ 68))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |t|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |i| |l|
                                                                (QREFELT
                                                                 $ 70))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |t|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |l| |i|
                                                                (QREFELT
                                                                 $ 70))
                                                               (QREFELT
                                                                $ 71))
                                                              (QREFELT
                                                               $ 68))
                                                             (QREFELT $
                                                              74))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |l|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |w| |j|
                                                                (QREFELT
                                                                 $ 70))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |l|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |j| |w|
                                                                (QREFELT
                                                                 $ 70))
                                                               (QREFELT
                                                                $ 71))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |r|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |k| |i|
                                                                (QREFELT
                                                                 $ 70))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |r|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |i| |k|
                                                                (QREFELT
                                                                 $ 70))
                                                               (QREFELT
                                                                $ 71))
                                                              (QREFELT
                                                               $ 68))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |t|
                                                                (QREFELT
                                                                 $ 69))
                                                               |l| |r|
                                                               (QREFELT
                                                                $ 70))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |t|
                                                                (QREFELT
                                                                 $ 69))
                                                               |r| |l|
                                                               (QREFELT
                                                                $ 70))
                                                              (QREFELT
                                                               $ 71))
                                                             (QREFELT $
                                                              68))
                                                            (QREFELT $
                                                             71))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |r|
                                                                (QREFELT
                                                                 $ 69))
                                                               |k| |i|
                                                               (QREFELT
                                                                $ 70))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |r|
                                                                (QREFELT
                                                                 $ 69))
                                                               |k| |i|
                                                               (QREFELT
                                                                $ 70))
                                                              (QREFELT
                                                               $ 71))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |l|
                                                                (QREFELT
                                                                 $ 69))
                                                               |j| |r|
                                                               (QREFELT
                                                                $ 70))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |l|
                                                                (QREFELT
                                                                 $ 69))
                                                               |r| |j|
                                                               (QREFELT
                                                                $ 70))
                                                              (QREFELT
                                                               $ 71))
                                                             (QREFELT $
                                                              68))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |t|
                                                               (QREFELT
                                                                $ 69))
                                                              |w| |l|
                                                              (QREFELT
                                                               $ 70))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |t|
                                                               (QREFELT
                                                                $ 69))
                                                              |l| |w|
                                                              (QREFELT
                                                               $ 70))
                                                             (QREFELT $
                                                              71))
                                                            (QREFELT $
                                                             68))
                                                           (QREFELT $
                                                            74))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |l|
                                                               (QREFELT
                                                                $ 69))
                                                              |k| |j|
                                                              (QREFELT
                                                               $ 70))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |l|
                                                               (QREFELT
                                                                $ 69))
                                                              |j| |k|
                                                              (QREFELT
                                                               $ 70))
                                                             (QREFELT $
                                                              71))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |r|
                                                               (QREFELT
                                                                $ 69))
                                                              |i| |w|
                                                              (QREFELT
                                                               $ 70))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |r|
                                                               (QREFELT
                                                                $ 69))
                                                              |w| |i|
                                                              (QREFELT
                                                               $ 70))
                                                             (QREFELT $
                                                              71))
                                                            (QREFELT $
                                                             68))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |t|
                                                              (QREFELT
                                                               $ 69))
                                                             |l| |r|
                                                             (QREFELT $
                                                              70))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |t|
                                                              (QREFELT
                                                               $ 69))
                                                             |r| |l|
                                                             (QREFELT $
                                                              70))
                                                            (QREFELT $
                                                             71))
                                                           (QREFELT $
                                                            68))
                                                          (QREFELT $
                                                           71))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |r|
                                                              (QREFELT
                                                               $ 69))
                                                             |i| |w|
                                                             (QREFELT $
                                                              70))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |r|
                                                              (QREFELT
                                                               $ 69))
                                                             |w| |i|
                                                             (QREFELT $
                                                              70))
                                                            (QREFELT $
                                                             71))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |l|
                                                              (QREFELT
                                                               $ 69))
                                                             |j| |r|
                                                             (QREFELT $
                                                              70))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |l|
                                                              (QREFELT
                                                               $ 69))
                                                             |r| |j|
                                                             (QREFELT $
                                                              70))
                                                            (QREFELT $
                                                             71))
                                                           (QREFELT $
                                                            68))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (QREFELT $
                                                              9)
                                                             |t|
                                                             (QREFELT $
                                                              69))
                                                            |k| |l|
                                                            (QREFELT $
                                                             70))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (QREFELT $
                                                              9)
                                                             |t|
                                                             (QREFELT $
                                                              69))
                                                            |l| |k|
                                                            (QREFELT $
                                                             70))
                                                           (QREFELT $
                                                            71))
                                                          (QREFELT $
                                                           68))
                                                         (QREFELT $ 74)) . #9#)))
                                                     (LETT |r|
                                                      (QSADD1 |r|) . #9#)
                                                     #11=(GO G190) G191
                                                     (EXIT NIL))))
                                                  (LETT |l|
                                                   (QSADD1 |l|) . #9#)
                                                  #11# G191 (EXIT NIL))
                                                 (EXIT
                                                  (COND
                                                    ((NULL
                                                      (SPADCALL |res|
                                                       (QREFELT $ 54)))
                                                     (PROGN
                                                       (LETT #8#
                                                        (SEQ
                                                         (SPADCALL
                                                          "algebra is not Jordan admissible"
                                                          (QREFELT $
                                                           77))
                                                         (EXIT
                                                          (PROGN
                                                            (LETT #7#
                                                             'NIL . #9#)
                                                            (GO #7#)))) . #9#)
                                                       (GO #8#)))))))
                                               #8# (EXIT #8#))
                                              (LETT |t|
                                               (QSADD1 |t|) . #9#)
                                              #11# G191 (EXIT NIL))))
                                           (LETT |w|
                                            (QSADD1 |w|) . #9#)
                                           #11# G191 (EXIT NIL))))
                                        (LETT |k| (QSADD1 |k|) . #9#)
                                        #11# G191 (EXIT NIL))))
                                     (LETT |j| (QSADD1 |j|) . #9#) #11#
                                     G191 (EXIT NIL))))
                              (LETT |i| (QSADD1 |i|) . #9#) #11# G191
                              (EXIT NIL))
                         (SPADCALL "algebra is Jordan admissible"
                             (QREFELT $ 77))
                         (EXIT 'T)))))
           #7# (EXIT #7#))))) 

(DEFUN |ALGSC;jordanAlgebra?;B;23| ($)
  (PROG (|i| #0=#:G2072 |j| #1=#:G2073 |k| #2=#:G2074 |l| #3=#:G2075
             |t| #4=#:G2076 |r| #5=#:G2077 |s| #6=#:G2078 |res|
             #7=#:G2071 #8=#:G2059)
    (RETURN
      (SEQ (EXIT (COND
                   ((QEQCAR (SPADCALL
                                (SPADCALL 2 (|spadConstant| $ 55)
                                    (QREFELT $ 87))
                                (QREFELT $ 88))
                            1)
                    (SEQ (SPADCALL
                             "this is not a Jordan algebra, as 2 is not invertible in the ground ring"
                             (QREFELT $ 77))
                         (EXIT 'NIL)))
                   ((SPADCALL (QREFELT $ 81))
                    (SEQ (SEQ (LETT |i| 1
                                    . #9=(|ALGSC;jordanAlgebra?;B;23|))
                              (LETT #0# (QREFELT $ 7) . #9#) G190
                              (COND
                                ((QSGREATERP |i| #0#) #10=(GO G191)))
                              (SEQ (EXIT
                                    (SEQ (LETT |j| 1 . #9#)
                                     (LETT #1# (QREFELT $ 7) . #9#)
                                     G190
                                     (COND
                                       ((QSGREATERP |j| #1#) #10#))
                                     (SEQ
                                      (EXIT
                                       (SEQ (LETT |k| 1 . #9#)
                                        (LETT #2# (QREFELT $ 7) . #9#)
                                        G190
                                        (COND
                                          ((QSGREATERP |k| #2#) #10#))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |l| 1 . #9#)
                                           (LETT #3#
                                            (QREFELT $ 7) . #9#)
                                           G190
                                           (COND
                                             ((QSGREATERP |l| #3#)
                                              #10#))
                                           (SEQ
                                            (EXIT
                                             (SEQ (LETT |t| 1 . #9#)
                                              (LETT #4#
                                               (QREFELT $ 7) . #9#)
                                              G190
                                              (COND
                                                ((QSGREATERP |t| #4#)
                                                 #10#))
                                              (SEQ
                                               (LETT |res|
                                                (|spadConstant| $ 32) . #9#)
                                               (EXIT
                                                (SEQ (LETT |r| 1 . #9#)
                                                 (LETT #5#
                                                  (QREFELT $ 7) . #9#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |r|
                                                     #5#)
                                                    #10#))
                                                 (SEQ
                                                  (EXIT
                                                   (SEQ
                                                    (LETT |s| 1 . #9#)
                                                    (LETT #6#
                                                     (QREFELT $ 7) . #9#)
                                                    G190
                                                    (COND
                                                      ((QSGREATERP |s|
                                                        #6#)
                                                       #10#))
                                                    (SEQ
                                                     (EXIT
                                                      (SEQ
                                                       (LETT |res|
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              |res|
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |r|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |i|
                                                                 |j|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (QREFELT
                                                                   $ 9)
                                                                  |s|
                                                                  (QREFELT
                                                                   $
                                                                   69))
                                                                 |l|
                                                                 |k|
                                                                 (QREFELT
                                                                  $ 70))
                                                                (QREFELT
                                                                 $ 68))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |t|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |r| |s|
                                                                (QREFELT
                                                                 $ 70))
                                                               (QREFELT
                                                                $ 68))
                                                              (QREFELT
                                                               $ 71))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |r|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |l| |k|
                                                                (QREFELT
                                                                 $ 70))
                                                               (SPADCALL
                                                                (SPADCALL
                                                                 (QREFELT
                                                                  $ 9)
                                                                 |s|
                                                                 (QREFELT
                                                                  $ 69))
                                                                |j| |r|
                                                                (QREFELT
                                                                 $ 70))
                                                               (QREFELT
                                                                $ 68))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |t|
                                                                (QREFELT
                                                                 $ 69))
                                                               |i| |s|
                                                               (QREFELT
                                                                $ 70))
                                                              (QREFELT
                                                               $ 68))
                                                             (QREFELT $
                                                              74))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |r|
                                                                (QREFELT
                                                                 $ 69))
                                                               |l| |j|
                                                               (QREFELT
                                                                $ 70))
                                                              (SPADCALL
                                                               (SPADCALL
                                                                (QREFELT
                                                                 $ 9)
                                                                |s|
                                                                (QREFELT
                                                                 $ 69))
                                                               |k| |k|
                                                               (QREFELT
                                                                $ 70))
                                                              (QREFELT
                                                               $ 68))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |t|
                                                               (QREFELT
                                                                $ 69))
                                                              |r| |s|
                                                              (QREFELT
                                                               $ 70))
                                                             (QREFELT $
                                                              68))
                                                            (QREFELT $
                                                             71))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |r|
                                                               (QREFELT
                                                                $ 69))
                                                              |k| |i|
                                                              (QREFELT
                                                               $ 70))
                                                             (SPADCALL
                                                              (SPADCALL
                                                               (QREFELT
                                                                $ 9)
                                                               |s|
                                                               (QREFELT
                                                                $ 69))
                                                              |j| |r|
                                                              (QREFELT
                                                               $ 70))
                                                             (QREFELT $
                                                              68))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |t|
                                                              (QREFELT
                                                               $ 69))
                                                             |l| |s|
                                                             (QREFELT $
                                                              70))
                                                            (QREFELT $
                                                             68))
                                                           (QREFELT $
                                                            74))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |r|
                                                              (QREFELT
                                                               $ 69))
                                                             |k| |j|
                                                             (QREFELT $
                                                              70))
                                                            (SPADCALL
                                                             (SPADCALL
                                                              (QREFELT
                                                               $ 9)
                                                              |s|
                                                              (QREFELT
                                                               $ 69))
                                                             |i| |k|
                                                             (QREFELT $
                                                              70))
                                                            (QREFELT $
                                                             68))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (QREFELT $
                                                              9)
                                                             |t|
                                                             (QREFELT $
                                                              69))
                                                            |r| |s|
                                                            (QREFELT $
                                                             70))
                                                           (QREFELT $
                                                            68))
                                                          (QREFELT $
                                                           71))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (QREFELT $
                                                              9)
                                                             |r|
                                                             (QREFELT $
                                                              69))
                                                            |i| |l|
                                                            (QREFELT $
                                                             70))
                                                           (SPADCALL
                                                            (SPADCALL
                                                             (QREFELT $
                                                              9)
                                                             |s|
                                                             (QREFELT $
                                                              69))
                                                            |j| |r|
                                                            (QREFELT $
                                                             70))
                                                           (QREFELT $
                                                            68))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $
                                                             9)
                                                            |t|
                                                            (QREFELT $
                                                             69))
                                                           |k| |s|
                                                           (QREFELT $
                                                            70))
                                                          (QREFELT $
                                                           68))
                                                         (QREFELT $ 74)) . #9#)
                                                       (EXIT
                                                        (COND
                                                          ((NULL
                                                            (SPADCALL
                                                             |res|
                                                             (QREFELT $
                                                              54)))
                                                           (PROGN
                                                             (LETT #8#
                                                              (SEQ
                                                               (SPADCALL
                                                                "this is not a Jordan algebra"
                                                                (QREFELT
                                                                 $ 77))
                                                               (EXIT
                                                                (PROGN
                                                                  (LETT
                                                                   #7#
                                                                   'NIL . #9#)
                                                                  (GO
                                                                   #7#)))) . #9#)
                                                             (GO #8#)))))))
                                                     #8# (EXIT #8#))
                                                    (LETT |s|
                                                     (QSADD1 |s|) . #9#)
                                                    #11=(GO G190) G191
                                                    (EXIT NIL))))
                                                 (LETT |r|
                                                  (QSADD1 |r|) . #9#)
                                                 #11# G191 (EXIT NIL))))
                                              (LETT |t|
                                               (QSADD1 |t|) . #9#)
                                              #11# G191 (EXIT NIL))))
                                           (LETT |l|
                                            (QSADD1 |l|) . #9#)
                                           #11# G191 (EXIT NIL))))
                                        (LETT |k| (QSADD1 |k|) . #9#)
                                        #11# G191 (EXIT NIL))))
                                     (LETT |j| (QSADD1 |j|) . #9#) #11#
                                     G191 (EXIT NIL))))
                              (LETT |i| (QSADD1 |i|) . #9#) #11# G191
                              (EXIT NIL))
                         (SPADCALL "this is a Jordan algebra"
                             (QREFELT $ 77))
                         (EXIT 'T)))
                   ('T
                    (SEQ (SPADCALL "this is not a Jordan algebra"
                             (QREFELT $ 77))
                         (EXIT 'NIL)))))
           #7# (EXIT #7#))))) 

(DEFUN |ALGSC;jacobiIdentity?;B;24| ($)
  (PROG (|i| #0=#:G2088 |j| #1=#:G2089 |k| #2=#:G2090 |r| #3=#:G2091
             |s| #4=#:G2092 |res| #5=#:G2087 #6=#:G2081)
    (RETURN
      (SEQ (EXIT (SEQ (SEQ (LETT |i| 1
                                 . #7=(|ALGSC;jacobiIdentity?;B;24|))
                           (LETT #0# (QREFELT $ 7) . #7#) G190
                           (COND ((QSGREATERP |i| #0#) #8=(GO G191)))
                           (SEQ (EXIT (SEQ (LETT |j| 1 . #7#)
                                       (LETT #1# (QREFELT $ 7) . #7#)
                                       G190
                                       (COND
                                         ((QSGREATERP |j| #1#) #8#))
                                       (SEQ
                                        (EXIT
                                         (SEQ (LETT |k| 1 . #7#)
                                          (LETT #2#
                                           (QREFELT $ 7) . #7#)
                                          G190
                                          (COND
                                            ((QSGREATERP |k| #2#) #8#))
                                          (SEQ
                                           (EXIT
                                            (SEQ (LETT |r| 1 . #7#)
                                             (LETT #3#
                                              (QREFELT $ 7) . #7#)
                                             G190
                                             (COND
                                               ((QSGREATERP |r| #3#)
                                                #8#))
                                             (SEQ
                                              (EXIT
                                               (SEQ
                                                (LETT |res|
                                                 (|spadConstant| $ 32) . #7#)
                                                (SEQ (LETT |s| 1 . #7#)
                                                 (LETT #4#
                                                  (QREFELT $ 7) . #7#)
                                                 G190
                                                 (COND
                                                   ((QSGREATERP |s|
                                                     #4#)
                                                    #8#))
                                                 (SEQ
                                                  (EXIT
                                                   (LETT |res|
                                                    (SPADCALL
                                                     (SPADCALL
                                                      (SPADCALL |res|
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |r|
                                                          (QREFELT $
                                                           69))
                                                         |i| |j|
                                                         (QREFELT $ 70))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9)
                                                          |s|
                                                          (QREFELT $
                                                           69))
                                                         |j| |k|
                                                         (QREFELT $ 70))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 71))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |r|
                                                         (QREFELT $ 69))
                                                        |j| |k|
                                                        (QREFELT $ 70))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (QREFELT $ 9)
                                                         |s|
                                                         (QREFELT $ 69))
                                                        |k| |i|
                                                        (QREFELT $ 70))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     (SPADCALL
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |r|
                                                        (QREFELT $ 69))
                                                       |k| |i|
                                                       (QREFELT $ 70))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (QREFELT $ 9)
                                                        |s|
                                                        (QREFELT $ 69))
                                                       |i| |j|
                                                       (QREFELT $ 70))
                                                      (QREFELT $ 68))
                                                     (QREFELT $ 71)) . #7#)))
                                                 (LETT |s|
                                                  (QSADD1 |s|) . #7#)
                                                 #9=(GO G190) G191
                                                 (EXIT NIL))
                                                (EXIT
                                                 (COND
                                                   ((NULL
                                                     (SPADCALL |res|
                                                      (QREFELT $ 54)))
                                                    (PROGN
                                                      (LETT #6#
                                                       (SEQ
                                                        (SPADCALL
                                                         "Jacobi identity does not hold"
                                                         (QREFELT $ 77))
                                                        (EXIT
                                                         (PROGN
                                                           (LETT #5#
                                                            'NIL . #7#)
                                                           (GO #5#)))) . #7#)
                                                      (GO #6#)))))))
                                              #6# (EXIT #6#))
                                             (LETT |r|
                                              (QSADD1 |r|) . #7#)
                                             #9# G191 (EXIT NIL))))
                                          (LETT |k| (QSADD1 |k|) . #7#)
                                          #9# G191 (EXIT NIL))))
                                       (LETT |j| (QSADD1 |j|) . #7#)
                                       #9# G191 (EXIT NIL))))
                           (LETT |i| (QSADD1 |i|) . #7#) #9# G191
                           (EXIT NIL))
                      (SPADCALL "Jacobi identity holds" (QREFELT $ 77))
                      (EXIT 'T)))
           #5# (EXIT #5#))))) 

(DEFUN |AlgebraGivenByStructuralConstants| (&REST #0=#:G2097)
  (PROG ()
    (RETURN
      (PROG (#1=#:G2098)
        (RETURN
          (COND
            ((LETT #1#
                   (|lassocShiftWithFunction| (|devaluateList| #0#)
                       (HGET |$ConstructorCache|
                             '|AlgebraGivenByStructuralConstants|)
                       '|domainEqualList|)
                   . #2=(|AlgebraGivenByStructuralConstants|))
             (|CDRwithIncrement| #1#))
            ('T
             (UNWIND-PROTECT
               (PROG1 (APPLY (|function|
                                 |AlgebraGivenByStructuralConstants;|)
                             #0#)
                 (LETT #1# T . #2#))
               (COND
                 ((NOT #1#)
                  (HREM |$ConstructorCache|
                        '|AlgebraGivenByStructuralConstants|))))))))))) 

(DEFUN |AlgebraGivenByStructuralConstants;| (|#1| |#2| |#3| |#4|)
  (PROG (DV$1 DV$2 DV$3 DV$4 |dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT DV$1 (|devaluate| |#1|)
              . #0=(|AlgebraGivenByStructuralConstants|))
        (LETT DV$2 (|devaluate| |#2|) . #0#)
        (LETT DV$3 (|devaluate| |#3|) . #0#)
        (LETT DV$4 (|devaluate| |#4|) . #0#)
        (LETT |dv$|
              (LIST '|AlgebraGivenByStructuralConstants| DV$1 DV$2 DV$3
                    DV$4) . #0#)
        (LETT $ (GETREFV 99) . #0#)
        (QSETREFV $ 0 |dv$|)
        (QSETREFV $ 3
            (LETT |pv$|
                  (|buildPredVector| 0 0
                      (LIST (|HasCategory| |#1| '(|IntegralDomain|))
                            (|HasCategory| |#1| '(|Field|)))) . #0#))
        (|haddProp| |$ConstructorCache|
            '|AlgebraGivenByStructuralConstants|
            (LIST DV$1 DV$2 DV$3 DV$4) (CONS 1 $))
        (|stuffDomainSlots| $)
        (QSETREFV $ 6 |#1|)
        (QSETREFV $ 7 |#2|)
        (QSETREFV $ 8 |#3|)
        (QSETREFV $ 9 |#4|)
        (QSETREFV $ 10 (|DirectProduct| |#2| |#1|))
        $)))) 

(MAKEPROP '|AlgebraGivenByStructuralConstants| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL (|DirectProduct| 7 6) (|local| |#1|)
             (|local| |#2|) (|local| |#3|) (|local| |#4|) '|Rep|
             (|Union| $ '"failed")
             (|FiniteRankNonAssociativeAlgebra&| $$ 6) (0 . |recip|)
             |ALGSC;recip;$U;1| (|Matrix| 6) (|SquareMatrix| 7 6)
             (5 . |coerce|) (10 . |apply|) |ALGSC;*;Sm2$;2|
             (|Vector| 6) (16 . |directProduct|) |ALGSC;coerce;V$;3|
             (|Vector| 15) |ALGSC;structuralConstants;V;4| (|List| 6)
             (21 . |entries|) (26 . |vector|) |ALGSC;coordinates;$V;5|
             (|Integer|) (|Vector| $$) (31 . |maxIndex|) (36 . |Zero|)
             (|NonNegativeInteger|) (40 . |new|) (47 . |elt|)
             (53 . |setColumn!|) (|Union| 20 '"failed")
             (|Record| (|:| |particular| 37) (|:| |basis| 96))
             (|LinearSystemMatrixPackage| 6 20 20 15) (60 . |solve|)
             (|Vector| $) |ALGSC;basis;V;7| |ALGSC;coordinates;$VV;6|
             (|PositiveInteger|) (66 . |unitVector|)
             |ALGSC;someBasis;V;8| |ALGSC;rank;Pi;9| (71 . |elt|)
             |ALGSC;elt;$IR;10| (|Boolean|) (77 . |zero?|)
             (|OutputForm|) (82 . |coerce|) (87 . |zero?|) (92 . |One|)
             (96 . =) (|Symbol|) (|List| 57) (102 . |elt|)
             (108 . |coerce|) (113 . *) (119 . +) (|Mapping| 52 52 52)
             (|List| 52) (125 . |reduce|) |ALGSC;coerce;$Of;11|
             (131 . |new|) (137 . *) (143 . |elt|) (149 . |elt|)
             (156 . +) (162 . |setelt|) |ALGSC;*;3$;12| (169 . -)
             (|Void|) (|String|) (175 . |messagePrint|)
             |ALGSC;alternative?;B;13| |ALGSC;associative?;B;14|
             |ALGSC;antiAssociative?;B;15| |ALGSC;commutative?;B;16|
             |ALGSC;antiCommutative?;B;17|
             |ALGSC;leftAlternative?;B;18|
             |ALGSC;rightAlternative?;B;19| |ALGSC;flexible?;B;20|
             |ALGSC;lieAdmissible?;B;21| (180 . *) (186 . |recip|)
             |ALGSC;jordanAdmissible?;B;22| |ALGSC;jordanAlgebra?;B;23|
             |ALGSC;jacobiIdentity?;B;24|
             (|SparseUnivariatePolynomial| (|Polynomial| 6))
             (|Record| (|:| |particular| $) (|:| |basis| (|List| $)))
             (|Union| 93 '"failed") (|SparseUnivariatePolynomial| 6)
             (|List| 20) (|List| (|Polynomial| 6)) (|SingleInteger|))
          '#(~= 191 |zero?| 197 |unit| 202 |subtractIfCan| 206
             |structuralConstants| 212 |someBasis| 221 |sample| 225
             |rightUnits| 229 |rightUnit| 233 |rightTraceMatrix| 237
             |rightTrace| 246 |rightRegularRepresentation| 251
             |rightRecip| 262 |rightRankPolynomial| 267 |rightPower|
             271 |rightNorm| 277 |rightMinimalPolynomial| 282
             |rightDiscriminant| 287 |rightCharacteristicPolynomial|
             296 |rightAlternative?| 301 |represents| 305 |recip| 316
             |rank| 321 |powerAssociative?| 325 |plenaryPower| 329
             |noncommutativeJordanAlgebra?| 335 |lieAlgebra?| 339
             |lieAdmissible?| 343 |leftUnits| 347 |leftUnit| 351
             |leftTraceMatrix| 355 |leftTrace| 364
             |leftRegularRepresentation| 369 |leftRecip| 380
             |leftRankPolynomial| 385 |leftPower| 389 |leftNorm| 395
             |leftMinimalPolynomial| 400 |leftDiscriminant| 405
             |leftCharacteristicPolynomial| 414 |leftAlternative?| 419
             |latex| 423 |jordanAlgebra?| 428 |jordanAdmissible?| 432
             |jacobiIdentity?| 436 |hash| 440 |flexible?| 445 |elt| 449
             |coordinates| 455 |convert| 477 |conditionsForIdempotents|
             487 |commutator| 496 |commutative?| 502 |coerce| 506
             |basis| 516 |associatorDependence| 520 |associator| 524
             |associative?| 531 |apply| 535 |antiCommutator| 541
             |antiCommutative?| 547 |antiAssociative?| 551
             |alternative?| 555 |Zero| 559 = 563 - 569 + 580 ** 586 *
             592)
          'NIL
          (CONS (|makeByteWordVec2| 1
                    '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1))
                (CONS '#(|FramedNonAssociativeAlgebra&|
                         |FiniteRankNonAssociativeAlgebra&|
                         |NonAssociativeAlgebra&| |Module&| NIL
                         |NonAssociativeRng&| NIL NIL NIL
                         |AbelianGroup&| NIL |AbelianMonoid&|
                         |AbelianSemiGroup&| |Monad&| |SetCategory&|
                         |BasicType&| NIL NIL)
                      (CONS '#((|FramedNonAssociativeAlgebra| 6)
                               (|FiniteRankNonAssociativeAlgebra| 6)
                               (|NonAssociativeAlgebra| 6) (|Module| 6)
                               (|BiModule| 6 6) (|NonAssociativeRng|)
                               (|LeftModule| (|SquareMatrix| 7 6))
                               (|RightModule| 6) (|LeftModule| 6)
                               (|AbelianGroup|)
                               (|CancellationAbelianMonoid|)
                               (|AbelianMonoid|) (|AbelianSemiGroup|)
                               (|Monad|) (|SetCategory|) (|BasicType|)
                               (|CoercibleTo| 52) (|unitsKnown|))
                            (|makeByteWordVec2| 98
                                '(1 12 11 0 13 1 16 15 0 17 2 0 0 15 0
                                  18 1 10 0 20 21 1 10 25 0 26 1 20 0
                                  25 27 1 30 29 0 31 0 6 0 32 3 15 0 33
                                  33 6 34 2 30 2 0 29 35 3 15 0 0 29 20
                                  36 2 39 38 15 20 40 1 10 0 44 45 2 10
                                  6 0 29 48 1 10 50 0 51 1 6 52 0 53 1
                                  6 50 0 54 0 6 0 55 2 6 50 0 0 56 2 58
                                  57 0 29 59 1 57 52 0 60 2 52 0 0 0 61
                                  2 52 0 0 0 62 2 64 52 63 0 65 2 20 0
                                  33 6 67 2 6 0 0 0 68 2 23 15 0 29 69
                                  3 15 6 0 29 29 70 2 6 0 0 0 71 3 20 6
                                  0 29 6 72 2 6 0 0 0 74 1 52 75 76 77
                                  2 6 0 44 0 87 1 6 11 0 88 2 0 50 0 0
                                  1 1 0 50 0 1 0 1 11 1 2 0 11 0 0 1 0
                                  0 23 24 1 0 23 41 1 0 0 41 46 0 0 0 1
                                  0 1 94 1 0 1 11 1 0 0 15 1 1 0 15 41
                                  1 1 0 6 0 1 1 0 15 0 1 2 0 15 0 41 1
                                  1 1 11 0 1 0 2 92 1 2 0 0 0 44 1 1 0
                                  6 0 1 1 1 95 0 1 0 0 6 1 1 0 6 41 1 1
                                  0 95 0 1 0 0 50 84 1 0 0 20 1 2 0 0
                                  20 41 1 1 1 11 0 14 0 0 44 47 0 0 50
                                  1 2 0 0 0 44 1 0 0 50 1 0 0 50 1 0 0
                                  50 86 0 1 94 1 0 1 11 1 0 0 15 1 1 0
                                  15 41 1 1 0 6 0 1 1 0 15 0 1 2 0 15 0
                                  41 1 1 1 11 0 1 0 2 92 1 2 0 0 0 44 1
                                  1 0 6 0 1 1 1 95 0 1 0 0 6 1 1 0 6 41
                                  1 1 0 95 0 1 0 0 50 83 1 0 76 0 1 0 0
                                  50 90 0 0 50 89 0 0 50 91 1 0 98 0 1
                                  0 0 50 85 2 0 6 0 29 49 1 0 20 0 28 1
                                  0 15 41 1 2 0 15 41 41 1 2 0 20 0 41
                                  43 1 0 20 0 1 1 0 0 20 1 0 0 97 1 1 0
                                  97 41 1 2 0 0 0 0 1 0 0 50 81 1 0 0
                                  20 22 1 0 52 0 66 0 0 41 42 0 1 96 1
                                  3 0 0 0 0 0 1 0 0 50 79 2 0 0 15 0 18
                                  2 0 0 0 0 1 0 0 50 82 0 0 50 80 0 0
                                  50 78 0 0 0 1 2 0 50 0 0 1 1 0 0 0 1
                                  2 0 0 0 0 1 2 0 0 0 0 1 2 0 0 0 44 1
                                  2 0 0 16 0 19 2 0 0 6 0 1 2 0 0 0 6 1
                                  2 0 0 0 0 73 2 0 0 29 0 1 2 0 0 33 0
                                  1 2 0 0 44 0 1)))))
          '|lookupComplete|)) 
