
(SDEFUN |ALGSC;recip;$U;1| ((|x| $) ($ |Union| $ "failed"))
        (SPADCALL |x| (QREFELT $ 13))) 

(SDEFUN |ALGSC;*;Sm2$;2| ((|m| |SquareMatrix| |n| R) (|x| $) ($ $))
        (SPADCALL (SPADCALL |m| (QREFELT $ 17)) |x| (QREFELT $ 18))) 

(SDEFUN |ALGSC;coerce;V$;3| ((|v| |Vector| R) ($ $))
        (SPADCALL |v| (QREFELT $ 21))) 

(SDEFUN |ALGSC;structuralConstants;V;4| (($ |Vector| (|Matrix| R)))
        (QREFELT $ 9)) 

(SDEFUN |ALGSC;coordinates;$V;5| ((|x| $) ($ |Vector| R))
        (SPADCALL (SPADCALL |x| (QREFELT $ 26)) (QREFELT $ 27))) 

(SDEFUN |ALGSC;coordinates;$VV;6| ((|x| $) (|b| |Vector| $) ($ |Vector| R))
        (SPROG
         ((#1=#:G667 NIL)
          (|res|
           (|Record| (|:| |particular| (|Union| (|Vector| R) "failed"))
                     (|:| |basis| (|List| (|Vector| R)))))
          (|i| NIL) (|transitionMatrix| (|Matrix| R))
          (|m| (|NonNegativeInteger|)) (#2=#:G655 NIL))
         (SEQ
          (LETT |m|
                (PROG1
                    (LETT #2# (SPADCALL |b| (QREFELT $ 31))
                          . #3=(|ALGSC;coordinates;$VV;6|))
                  (|check_subtype| (>= #2# 0) '(|NonNegativeInteger|) #2#))
                . #3#)
          (LETT |transitionMatrix|
                (MAKE_MATRIX1 (QREFELT $ 7) |m| (|spadConstant| $ 32)) . #3#)
          (SEQ (LETT |i| 1 . #3#) G190
               (COND ((|greater_SI| |i| |m|) (GO G191)))
               (SEQ
                (EXIT
                 (SPADCALL |transitionMatrix| |i|
                           (SPADCALL (SPADCALL |b| |i| (QREFELT $ 33))
                                     (QREFELT $ 28))
                           (QREFELT $ 34))))
               (LETT |i| (|inc_SI| |i|) . #3#) (GO G190) G191 (EXIT NIL))
          (LETT |res|
                (SPADCALL |transitionMatrix| (SPADCALL |x| (QREFELT $ 28))
                          (QREFELT $ 38))
                . #3#)
          (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|) . #3#)
                 (QCDR #1#)
               (|check_union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 6))
                              #1#)))))))) 

(SDEFUN |ALGSC;basis;V;7| (($ |Vector| $))
        (SPROG
         ((#1=#:G672 NIL) (#2=#:G675 NIL) (#3=#:G677 NIL) (|i| NIL)
          (#4=#:G676 NIL))
         (SEQ
          (PROGN
           (LETT #4# (GETREFV #5=(QREFELT $ 7)) . #6=(|ALGSC;basis;V;7|))
           (SEQ (LETT |i| 1 . #6#) (LETT #3# #5# . #6#) (LETT #2# 0 . #6#) G190
                (COND ((|greater_SI| |i| #3#) (GO G191)))
                (SEQ
                 (EXIT
                  (SETELT #4# #2#
                          (SPADCALL
                           (PROG1 (LETT #1# |i| . #6#)
                             (|check_subtype| (> #1# 0) '(|PositiveInteger|)
                                              #1#))
                           (QREFELT $ 43)))))
                (LETT #2#
                      (PROG1 (|inc_SI| #2#) (LETT |i| (|inc_SI| |i|) . #6#))
                      . #6#)
                (GO G190) G191 (EXIT NIL))
           #4#)))) 

(SDEFUN |ALGSC;someBasis;V;8| (($ |Vector| $)) (SPADCALL (QREFELT $ 40))) 

(SDEFUN |ALGSC;rank;Pi;9| (($ |PositiveInteger|)) (QREFELT $ 7)) 

(SDEFUN |ALGSC;elt;$IR;10| ((|x| $) (|i| |Integer|) ($ R))
        (SPADCALL |x| |i| (QREFELT $ 46))) 

(SDEFUN |ALGSC;coerce;$Of;11| ((|x| $) ($ |OutputForm|))
        (SPROG
         ((#1=#:G702 NIL) (|le| (|List| (|OutputForm|))) (|coef| (R))
          (#2=#:G703 NIL) (|i| NIL))
         (SEQ
          (COND
           ((SPADCALL |x| (QREFELT $ 49))
            (SPADCALL (|spadConstant| $ 32) (QREFELT $ 51)))
           ('T
            (SEQ (LETT |le| NIL . #3=(|ALGSC;coerce;$Of;11|))
                 (SEQ (LETT |i| 1 . #3#) (LETT #2# (QREFELT $ 7) . #3#) G190
                      (COND ((|greater_SI| |i| #2#) (GO G191)))
                      (SEQ
                       (EXIT
                        (SEQ
                         (LETT |coef| (SPADCALL |x| |i| (QREFELT $ 47)) . #3#)
                         (EXIT
                          (COND
                           ((NULL (SPADCALL |coef| (QREFELT $ 52)))
                            (PROGN
                             (LETT #1#
                                   (COND
                                    ((SPADCALL |coef| (|spadConstant| $ 53)
                                               (QREFELT $ 54))
                                     (LETT |le|
                                           (CONS
                                            (SPADCALL
                                             (SPADCALL (QREFELT $ 8) |i|
                                                       (QREFELT $ 57))
                                             (QREFELT $ 58))
                                            |le|)
                                           . #3#))
                                    ('T
                                     (LETT |le|
                                           (CONS
                                            (SPADCALL
                                             (SPADCALL |coef| (QREFELT $ 51))
                                             (SPADCALL
                                              (SPADCALL (QREFELT $ 8) |i|
                                                        (QREFELT $ 57))
                                              (QREFELT $ 58))
                                             (QREFELT $ 59))
                                            |le|)
                                           . #3#)))
                                   . #3#)
                             (GO #4=#:G695)))))))
                       #4# (EXIT #1#))
                      (LETT |i| (|inc_SI| |i|) . #3#) (GO G190) G191
                      (EXIT NIL))
                 (EXIT (SPADCALL (ELT $ 60) |le| (QREFELT $ 63))))))))) 

(SDEFUN |ALGSC;*;3$;12| ((|x| $) (|y| $) ($ $))
        (SPROG
         ((|h| (R)) (#1=#:G712 NIL) (|j| NIL) (#2=#:G711 NIL) (|i| NIL)
          (#3=#:G710 NIL) (|k| NIL) (|v| (|Vector| R)))
         (SEQ
          (LETT |v| (MAKEARR1 (QREFELT $ 7) (|spadConstant| $ 32))
                . #4=(|ALGSC;*;3$;12|))
          (SEQ (LETT |k| 1 . #4#) (LETT #3# (QREFELT $ 7) . #4#) G190
               (COND ((|greater_SI| |k| #3#) (GO G191)))
               (SEQ (LETT |h| (|spadConstant| $ 32) . #4#)
                    (SEQ (LETT |i| 1 . #4#) (LETT #2# (QREFELT $ 7) . #4#) G190
                         (COND ((|greater_SI| |i| #2#) (GO G191)))
                         (SEQ
                          (EXIT
                           (SEQ (LETT |j| 1 . #4#)
                                (LETT #1# (QREFELT $ 7) . #4#) G190
                                (COND ((|greater_SI| |j| #1#) (GO G191)))
                                (SEQ
                                 (EXIT
                                  (LETT |h|
                                        (SPADCALL |h|
                                                  (SPADCALL
                                                   (SPADCALL
                                                    (SPADCALL |x| |i|
                                                              (QREFELT $ 47))
                                                    (SPADCALL |y| |j|
                                                              (QREFELT $ 47))
                                                    (QREFELT $ 65))
                                                   (SPADCALL
                                                    (SPADCALL (QREFELT $ 9) |k|
                                                              (QREFELT $ 66))
                                                    |i| |j| (QREFELT $ 67))
                                                   (QREFELT $ 65))
                                                  (QREFELT $ 68))
                                        . #4#)))
                                (LETT |j| (|inc_SI| |j|) . #4#) (GO G190) G191
                                (EXIT NIL))))
                         (LETT |i| (|inc_SI| |i|) . #4#) (GO G190) G191
                         (EXIT NIL))
                    (EXIT (SPADCALL |v| |k| |h| (QREFELT $ 69))))
               (LETT |k| (|inc_SI| |k|) . #4#) (GO G190) G191 (EXIT NIL))
          (EXIT (SPADCALL |v| (QREFELT $ 21)))))) 

(SDEFUN |ALGSC;alternative?;B;13| (($ |Boolean|))
        (SPROG
         ((#1=#:G740 NIL) (#2=#:G744 NIL) (|res| (R)) (#3=#:G758 NIL) (|l| NIL)
          (#4=#:G757 NIL) (|r| NIL) (#5=#:G741 NIL) (#6=#:G756 NIL)
          (#7=#:G755 NIL) (#8=#:G754 NIL) (|k| NIL) (#9=#:G742 NIL)
          (#10=#:G753 NIL) (#11=#:G752 NIL) (#12=#:G751 NIL) (#13=#:G750 NIL)
          (|j| NIL) (#14=#:G743 NIL) (#15=#:G749 NIL) (#16=#:G748 NIL)
          (#17=#:G747 NIL) (#18=#:G746 NIL) (#19=#:G745 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #20=(|ALGSC;alternative?;B;13|))
                 (LETT #19# (QREFELT $ 7) . #20#) G190
                 (COND ((|greater_SI| |i| #19#) (GO G191)))
                 (SEQ
                  (SEQ (LETT |j| 1 . #20#) (LETT #18# (- |i| 1) . #20#) G190
                       (COND ((|greater_SI| |j| #18#) (GO G191)))
                       (SEQ
                        (EXIT
                         (SEQ (LETT |k| |j| . #20#)
                              (LETT #17# (QREFELT $ 7) . #20#) G190
                              (COND ((> |k| #17#) (GO G191)))
                              (SEQ
                               (EXIT
                                (SEQ (LETT |r| 1 . #20#)
                                     (LETT #16# (QREFELT $ 7) . #20#) G190
                                     (COND ((|greater_SI| |r| #16#) (GO G191)))
                                     (SEQ
                                      (EXIT
                                       (SEQ
                                        (LETT |res| (|spadConstant| $ 32)
                                              . #20#)
                                        (SEQ (LETT |l| 1 . #20#)
                                             (LETT #15# (QREFELT $ 7) . #20#)
                                             G190
                                             (COND
                                              ((|greater_SI| |l| #15#)
                                               (GO G191)))
                                             (SEQ
                                              (EXIT
                                               (LETT |res|
                                                     (SPADCALL
                                                      (SPADCALL |res|
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |j| |k|
                                                                   (QREFELT $
                                                                            67))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |k| |j|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           68))
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT $
                                                                            9)
                                                                   |r|
                                                                   (QREFELT $
                                                                            66))
                                                                  |i| |l|
                                                                  (QREFELT $
                                                                           67))
                                                                 (QREFELT $
                                                                          65))
                                                                (QREFELT $ 71))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |i| |j|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |l| |k|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |i| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |l| |j|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 68))
                                                     . #20#)))
                                             (LETT |l| (|inc_SI| |l|) . #20#)
                                             (GO G190) G191 (EXIT NIL))
                                        (EXIT
                                         (COND
                                          ((NULL
                                            (SPADCALL |res| (QREFELT $ 52)))
                                           (PROGN
                                            (LETT #14#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not right alternative"
                                                    (QREFELT $ 74))
                                                   (EXIT
                                                    (PROGN
                                                     (LETT #2# 'NIL . #20#)
                                                     (GO #21=#:G739))))
                                                  . #20#)
                                            (GO #22=#:G715)))))))
                                      #22# (EXIT #14#))
                                     (LETT |r| (|inc_SI| |r|) . #20#) (GO G190)
                                     G191 (EXIT NIL))))
                              (LETT |k| (+ |k| 1) . #20#) (GO G190) G191
                              (EXIT NIL))))
                       (LETT |j| (|inc_SI| |j|) . #20#) (GO G190) G191
                       (EXIT NIL))
                  (EXIT
                   (SEQ (LETT |j| |i| . #20#) (LETT #13# (QREFELT $ 7) . #20#)
                        G190 (COND ((> |j| #13#) (GO G191)))
                        (SEQ
                         (SEQ (LETT |k| 1 . #20#) (LETT #12# (- |j| 1) . #20#)
                              G190 (COND ((|greater_SI| |k| #12#) (GO G191)))
                              (SEQ
                               (EXIT
                                (SEQ (LETT |r| 1 . #20#)
                                     (LETT #11# (QREFELT $ 7) . #20#) G190
                                     (COND ((|greater_SI| |r| #11#) (GO G191)))
                                     (SEQ
                                      (EXIT
                                       (SEQ
                                        (LETT |res| (|spadConstant| $ 32)
                                              . #20#)
                                        (SEQ (LETT |l| 1 . #20#)
                                             (LETT #10# (QREFELT $ 7) . #20#)
                                             G190
                                             (COND
                                              ((|greater_SI| |l| #10#)
                                               (GO G191)))
                                             (SEQ
                                              (EXIT
                                               (LETT |res|
                                                     (SPADCALL
                                                      (SPADCALL |res|
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |j|
                                                                   (QREFELT $
                                                                            67))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |j| |i|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           68))
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT $
                                                                            9)
                                                                   |r|
                                                                   (QREFELT $
                                                                            66))
                                                                  |l| |k|
                                                                  (QREFELT $
                                                                           67))
                                                                 (QREFELT $
                                                                          65))
                                                                (QREFELT $ 68))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |j| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |i| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |i| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |j| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     . #20#)))
                                             (LETT |l| (|inc_SI| |l|) . #20#)
                                             (GO G190) G191 (EXIT NIL))
                                        (EXIT
                                         (COND
                                          ((NULL
                                            (SPADCALL |res| (QREFELT $ 52)))
                                           (PROGN
                                            (LETT #9#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not left alternative"
                                                    (QREFELT $ 74))
                                                   (EXIT
                                                    (PROGN
                                                     (LETT #2# 'NIL . #20#)
                                                     (GO #21#))))
                                                  . #20#)
                                            (GO #23=#:G721)))))))
                                      #23# (EXIT #9#))
                                     (LETT |r| (|inc_SI| |r|) . #20#) (GO G190)
                                     G191 (EXIT NIL))))
                              (LETT |k| (|inc_SI| |k|) . #20#) (GO G190) G191
                              (EXIT NIL))
                         (EXIT
                          (SEQ (LETT |k| |j| . #20#)
                               (LETT #8# (QREFELT $ 7) . #20#) G190
                               (COND ((> |k| #8#) (GO G191)))
                               (SEQ
                                (SEQ (LETT |r| 1 . #20#)
                                     (LETT #7# (QREFELT $ 7) . #20#) G190
                                     (COND ((|greater_SI| |r| #7#) (GO G191)))
                                     (SEQ
                                      (EXIT
                                       (SEQ
                                        (LETT |res| (|spadConstant| $ 32)
                                              . #20#)
                                        (SEQ (LETT |l| 1 . #20#)
                                             (LETT #6# (QREFELT $ 7) . #20#)
                                             G190
                                             (COND
                                              ((|greater_SI| |l| #6#)
                                               (GO G191)))
                                             (SEQ
                                              (EXIT
                                               (LETT |res|
                                                     (SPADCALL
                                                      (SPADCALL |res|
                                                                (SPADCALL
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |j|
                                                                   (QREFELT $
                                                                            67))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |j| |i|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           68))
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (QREFELT $
                                                                            9)
                                                                   |r|
                                                                   (QREFELT $
                                                                            66))
                                                                  |l| |k|
                                                                  (QREFELT $
                                                                           67))
                                                                 (QREFELT $
                                                                          65))
                                                                (QREFELT $ 68))
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |j| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |i| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |i| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |j| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      (QREFELT $ 71))
                                                     . #20#)))
                                             (LETT |l| (|inc_SI| |l|) . #20#)
                                             (GO G190) G191 (EXIT NIL))
                                        (EXIT
                                         (COND
                                          ((NULL
                                            (SPADCALL |res| (QREFELT $ 52)))
                                           (PROGN
                                            (LETT #5#
                                                  (SEQ
                                                   (SPADCALL
                                                    "algebra is not left alternative"
                                                    (QREFELT $ 74))
                                                   (EXIT
                                                    (PROGN
                                                     (LETT #2# 'NIL . #20#)
                                                     (GO #21#))))
                                                  . #20#)
                                            (GO #24=#:G726)))))))
                                      #24# (EXIT #5#))
                                     (LETT |r| (|inc_SI| |r|) . #20#) (GO G190)
                                     G191 (EXIT NIL))
                                (EXIT
                                 (SEQ (LETT |r| 1 . #20#)
                                      (LETT #4# (QREFELT $ 7) . #20#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #20#)
                                         (SEQ (LETT |l| 1 . #20#)
                                              (LETT #3# (QREFELT $ 7) . #20#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |j| |k|
                                                                    (QREFELT $
                                                                             67))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |k| |j|
                                                                    (QREFELT $
                                                                             67))
                                                                   (QREFELT $
                                                                            68))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |r|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |l|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           65))
                                                                 (QREFELT $
                                                                          71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |j|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |k|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |k|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |j|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 68))
                                                      . #20#)))
                                              (LETT |l| (|inc_SI| |l|) . #20#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not right alternative"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #20#)
                                                      (GO #21#))))
                                                   . #20#)
                                             (GO #25=#:G730)))))))
                                       #25# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #20#)
                                      (GO G190) G191 (EXIT NIL))))
                               (LETT |k| (+ |k| 1) . #20#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (+ |j| 1) . #20#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #20#) (GO G190) G191 (EXIT NIL))
            (SPADCALL
             "algebra satisfies 2*associator(a,b,b) = 0 = 2*associator(a,a,b) = 0"
             (QREFELT $ 74))
            (EXIT 'T)))
          #21# (EXIT #2#)))) 

(SDEFUN |ALGSC;associative?;B;14| (($ |Boolean|))
        (SPROG
         ((#1=#:G768 NIL) (#2=#:G769 NIL) (|res| (R)) (#3=#:G774 NIL) (|l| NIL)
          (#4=#:G773 NIL) (|r| NIL) (#5=#:G772 NIL) (|k| NIL) (#6=#:G771 NIL)
          (|j| NIL) (#7=#:G770 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;associative?;B;14|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((|greater_SI| |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |j|
                                                                   (QREFELT $
                                                                            67))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |r|
                                                                    (QREFELT $
                                                                             66))
                                                                   |l| |k|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           65))
                                                                 (QREFELT $
                                                                          68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |j| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |i| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 71))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not associative"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G767))))
                                                   . #8#)
                                             (GO #10=#:G761)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (|inc_SI| |k|) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is associative" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;antiAssociative?;B;15| (($ |Boolean|))
        (SPROG
         ((#1=#:G784 NIL) (#2=#:G785 NIL) (|res| (R)) (#3=#:G790 NIL) (|l| NIL)
          (#4=#:G789 NIL) (|r| NIL) (#5=#:G788 NIL) (|k| NIL) (#6=#:G787 NIL)
          (|j| NIL) (#7=#:G786 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;antiAssociative?;B;15|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((|greater_SI| |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |l|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |j|
                                                                   (QREFELT $
                                                                            67))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |r|
                                                                    (QREFELT $
                                                                             66))
                                                                   |l| |k|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           65))
                                                                 (QREFELT $
                                                                          68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |j| |k|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |i| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not anti-associative"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G783))))
                                                   . #8#)
                                             (GO #10=#:G777)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (|inc_SI| |k|) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is anti-associative" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;commutative?;B;16| (($ |Boolean|))
        (SPROG
         ((#1=#:G798 NIL) (#2=#:G799 NIL) (#3=#:G802 NIL) (|k| NIL)
          (#4=#:G801 NIL) (|j| NIL) (#5=#:G800 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #6=(|ALGSC;commutative?;B;16|))
                 (LETT #5# (QREFELT $ 7) . #6#) G190
                 (COND ((|greater_SI| |i| #5#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| (+ |i| 1) . #6#)
                        (LETT #4# (QREFELT $ 7) . #6#) G190
                        (COND ((> |j| #4#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #6#)
                               (LETT #3# (QREFELT $ 7) . #6#) G190
                               (COND ((|greater_SI| |k| #3#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (COND
                                  ((NULL
                                    (SPADCALL
                                     (SPADCALL
                                      (SPADCALL (QREFELT $ 9) |k|
                                                (QREFELT $ 66))
                                      |i| |j| (QREFELT $ 67))
                                     (SPADCALL
                                      (SPADCALL (QREFELT $ 9) |k|
                                                (QREFELT $ 66))
                                      |j| |i| (QREFELT $ 67))
                                     (QREFELT $ 54)))
                                   (PROGN
                                    (LETT #1#
                                          (SEQ
                                           (SPADCALL
                                            "algebra is not commutative"
                                            (QREFELT $ 74))
                                           (EXIT
                                            (PROGN
                                             (LETT #2# 'NIL . #6#)
                                             (GO #7=#:G797))))
                                          . #6#)
                                    (GO #8=#:G793))))))
                               (LETT |k| (|inc_SI| |k|) . #6#) (GO G190) G191
                               (EXIT NIL)))
                         #8# (EXIT #1#))
                        (LETT |j| (+ |j| 1) . #6#) (GO G190) G191 (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #6#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is commutative" (QREFELT $ 74)) (EXIT 'T)))
          #7# (EXIT #2#)))) 

(SDEFUN |ALGSC;antiCommutative?;B;17| (($ |Boolean|))
        (SPROG
         ((#1=#:G810 NIL) (#2=#:G811 NIL) (#3=#:G814 NIL) (|k| NIL)
          (#4=#:G813 NIL) (|j| NIL) (#5=#:G812 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #6=(|ALGSC;antiCommutative?;B;17|))
                 (LETT #5# (QREFELT $ 7) . #6#) G190
                 (COND ((|greater_SI| |i| #5#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| |i| . #6#) (LETT #4# (QREFELT $ 7) . #6#)
                        G190 (COND ((> |j| #4#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #6#)
                               (LETT #3# (QREFELT $ 7) . #6#) G190
                               (COND ((|greater_SI| |k| #3#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (COND
                                  ((NULL
                                    (SPADCALL
                                     (COND
                                      ((EQL |i| |j|)
                                       (SPADCALL
                                        (SPADCALL (QREFELT $ 9) |k|
                                                  (QREFELT $ 66))
                                        |i| |i| (QREFELT $ 67)))
                                      ('T
                                       (SPADCALL
                                        (SPADCALL
                                         (SPADCALL (QREFELT $ 9) |k|
                                                   (QREFELT $ 66))
                                         |i| |j| (QREFELT $ 67))
                                        (SPADCALL
                                         (SPADCALL (QREFELT $ 9) |k|
                                                   (QREFELT $ 66))
                                         |j| |i| (QREFELT $ 67))
                                        (QREFELT $ 68))))
                                     (QREFELT $ 52)))
                                   (PROGN
                                    (LETT #1#
                                          (SEQ
                                           (SPADCALL
                                            "algebra is not anti-commutative"
                                            (QREFELT $ 74))
                                           (EXIT
                                            (PROGN
                                             (LETT #2# 'NIL . #6#)
                                             (GO #7=#:G809))))
                                          . #6#)
                                    (GO #8=#:G805))))))
                               (LETT |k| (|inc_SI| |k|) . #6#) (GO G190) G191
                               (EXIT NIL)))
                         #8# (EXIT #1#))
                        (LETT |j| (+ |j| 1) . #6#) (GO G190) G191 (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #6#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is anti-commutative" (QREFELT $ 74)) (EXIT 'T)))
          #7# (EXIT #2#)))) 

(SDEFUN |ALGSC;leftAlternative?;B;18| (($ |Boolean|))
        (SPROG
         ((#1=#:G824 NIL) (#2=#:G825 NIL) (|res| (R)) (#3=#:G830 NIL) (|l| NIL)
          (#4=#:G829 NIL) (|r| NIL) (#5=#:G828 NIL) (|k| NIL) (#6=#:G827 NIL)
          (|j| NIL) (#7=#:G826 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;leftAlternative?;B;18|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| |i| . #8#) (LETT #6# (QREFELT $ 7) . #8#)
                        G190 (COND ((> |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((|greater_SI| |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |i| |j|
                                                                    (QREFELT $
                                                                             67))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |j| |i|
                                                                    (QREFELT $
                                                                             67))
                                                                   (QREFELT $
                                                                            68))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |r|
                                                                    (QREFELT $
                                                                             66))
                                                                   |l| |k|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           65))
                                                                 (QREFELT $
                                                                          68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |j| |k|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |i| |l|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |k|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |j| |l|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 71))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not left alternative"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G823))))
                                                   . #8#)
                                             (GO #10=#:G817)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (|inc_SI| |k|) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (+ |j| 1) . #8#) (GO G190) G191 (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is left alternative" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;rightAlternative?;B;19| (($ |Boolean|))
        (SPROG
         ((#1=#:G840 NIL) (#2=#:G841 NIL) (|res| (R)) (#3=#:G846 NIL) (|l| NIL)
          (#4=#:G845 NIL) (|r| NIL) (#5=#:G844 NIL) (|k| NIL) (#6=#:G843 NIL)
          (|j| NIL) (#7=#:G842 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;rightAlternative?;B;19|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| |j| . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((> |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL |res|
                                                                 (SPADCALL
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |j| |k|
                                                                    (QREFELT $
                                                                             67))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |l|
                                                                     (QREFELT $
                                                                              66))
                                                                    |k| |j|
                                                                    (QREFELT $
                                                                             67))
                                                                   (QREFELT $
                                                                            68))
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (QREFELT $
                                                                             9)
                                                                    |r|
                                                                    (QREFELT $
                                                                             66))
                                                                   |i| |l|
                                                                   (QREFELT $
                                                                            67))
                                                                  (QREFELT $
                                                                           65))
                                                                 (QREFELT $
                                                                          71))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |j|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |k|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |k|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |j|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (QREFELT $ 68))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not right alternative"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G839))))
                                                   . #8#)
                                             (GO #10=#:G833)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (+ |k| 1) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is right alternative" (QREFELT $ 74))
            (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;flexible?;B;20| (($ |Boolean|))
        (SPROG
         ((#1=#:G856 NIL) (#2=#:G857 NIL) (|res| (R)) (#3=#:G862 NIL) (|l| NIL)
          (#4=#:G861 NIL) (|r| NIL) (#5=#:G860 NIL) (|k| NIL) (#6=#:G859 NIL)
          (|j| NIL) (#7=#:G858 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;flexible?;B;20|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| |i| . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((> |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL |res|
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |l|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |i| |j|
                                                                     (QREFELT $
                                                                              67))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |r|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |l| |k|
                                                                     (QREFELT $
                                                                              67))
                                                                    (QREFELT $
                                                                             65))
                                                                   (QREFELT $
                                                                            68))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |l|
                                                            (QREFELT $ 66))
                                                           |j| |k|
                                                           (QREFELT $ 67))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |r|
                                                            (QREFELT $ 66))
                                                           |i| |l|
                                                           (QREFELT $ 67))
                                                          (QREFELT $ 65))
                                                         (QREFELT $ 71))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |k| |j|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |i|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |l|
                                                          (QREFELT $ 66))
                                                         |j| |i|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |k| |l|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 71))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not flexible"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G855))))
                                                   . #8#)
                                             (GO #10=#:G849)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (+ |k| 1) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is flexible" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;lieAdmissible?;B;21| (($ |Boolean|))
        (SPROG
         ((#1=#:G872 NIL) (#2=#:G873 NIL) (|res| (R)) (#3=#:G878 NIL) (|l| NIL)
          (#4=#:G877 NIL) (|r| NIL) (#5=#:G876 NIL) (|k| NIL) (#6=#:G875 NIL)
          (|j| NIL) (#7=#:G874 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;lieAdmissible?;B;21|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((|greater_SI| |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |l| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |l| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL |res|
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |l|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |i| |j|
                                                                     (QREFELT $
                                                                              67))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |l|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |j| |i|
                                                                     (QREFELT $
                                                                              67))
                                                                    (QREFELT $
                                                                             71))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |r|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |l| |k|
                                                                     (QREFELT $
                                                                              67))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |r|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |k| |l|
                                                                     (QREFELT $
                                                                              67))
                                                                    (QREFELT $
                                                                             71))
                                                                   (QREFELT $
                                                                            65))
                                                                  (QREFELT $
                                                                           68))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |l|
                                                            (QREFELT $ 66))
                                                           |j| |k|
                                                           (QREFELT $ 67))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |l|
                                                            (QREFELT $ 66))
                                                           |k| |j|
                                                           (QREFELT $ 67))
                                                          (QREFELT $ 71))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |r|
                                                            (QREFELT $ 66))
                                                           |l| |i|
                                                           (QREFELT $ 67))
                                                          (SPADCALL
                                                           (SPADCALL
                                                            (QREFELT $ 9) |r|
                                                            (QREFELT $ 66))
                                                           |i| |l|
                                                           (QREFELT $ 67))
                                                          (QREFELT $ 71))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |k| |i|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |l|
                                                           (QREFELT $ 66))
                                                          |i| |k|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 71))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |l| |j|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |j| |l|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 71))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      . #8#)))
                                              (LETT |l| (|inc_SI| |l|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "algebra is not Lie admissible"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G871))))
                                                   . #8#)
                                             (GO #10=#:G865)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (|inc_SI| |k|) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "algebra is Lie admissible" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(SDEFUN |ALGSC;jordanAdmissible?;B;22| (($ |Boolean|))
        (SPROG
         ((#1=#:G895 NIL) (#2=#:G896 NIL) (|res| (R)) (#3=#:G903 NIL) (|r| NIL)
          (#4=#:G902 NIL) (|l| NIL) (#5=#:G901 NIL) (|t| NIL) (#6=#:G900 NIL)
          (|w| NIL) (#7=#:G899 NIL) (|k| NIL) (#8=#:G898 NIL) (|j| NIL)
          (#9=#:G897 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (COND
            ((QEQCAR
              (SPADCALL (SPADCALL 2 (|spadConstant| $ 53) (QREFELT $ 84))
                        (QREFELT $ 85))
              1)
             (SEQ
              (SPADCALL
               "this algebra is not Jordan admissible, as 2 is not invertible in the ground ring"
               (QREFELT $ 74))
              (EXIT 'NIL)))
            ('T
             (SEQ
              (SEQ (LETT |i| 1 . #10=(|ALGSC;jordanAdmissible?;B;22|))
                   (LETT #9# (QREFELT $ 7) . #10#) G190
                   (COND ((|greater_SI| |i| #9#) (GO G191)))
                   (SEQ
                    (EXIT
                     (SEQ (LETT |j| 1 . #10#) (LETT #8# (QREFELT $ 7) . #10#)
                          G190 (COND ((|greater_SI| |j| #8#) (GO G191)))
                          (SEQ
                           (EXIT
                            (SEQ (LETT |k| 1 . #10#)
                                 (LETT #7# (QREFELT $ 7) . #10#) G190
                                 (COND ((|greater_SI| |k| #7#) (GO G191)))
                                 (SEQ
                                  (EXIT
                                   (SEQ (LETT |w| 1 . #10#)
                                        (LETT #6# (QREFELT $ 7) . #10#) G190
                                        (COND
                                         ((|greater_SI| |w| #6#) (GO G191)))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |t| 1 . #10#)
                                               (LETT #5# (QREFELT $ 7) . #10#)
                                               G190
                                               (COND
                                                ((|greater_SI| |t| #5#)
                                                 (GO G191)))
                                               (SEQ
                                                (EXIT
                                                 (SEQ
                                                  (LETT |res|
                                                        (|spadConstant| $ 32)
                                                        . #10#)
                                                  (SEQ (LETT |l| 1 . #10#)
                                                       (LETT #4# (QREFELT $ 7)
                                                             . #10#)
                                                       G190
                                                       (COND
                                                        ((|greater_SI| |l| #4#)
                                                         (GO G191)))
                                                       (SEQ
                                                        (EXIT
                                                         (SEQ
                                                          (LETT |r| 1 . #10#)
                                                          (LETT #3#
                                                                (QREFELT $ 7)
                                                                . #10#)
                                                          G190
                                                          (COND
                                                           ((|greater_SI| |r|
                                                                          #3#)
                                                            (GO G191)))
                                                          (SEQ
                                                           (EXIT
                                                            (LETT |res|
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        |res|
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (SPADCALL
                                                                             (QREFELT
                                                                              $
                                                                              9)
                                                                             |l|
                                                                             (QREFELT
                                                                              $
                                                                              66))
                                                                            |i|
                                                                            |j|
                                                                            (QREFELT
                                                                             $
                                                                             67))
                                                                           (SPADCALL
                                                                            (SPADCALL
                                                                             (QREFELT
                                                                              $
                                                                              9)
                                                                             |l|
                                                                             (QREFELT
                                                                              $
                                                                              66))
                                                                            |j|
                                                                            |i|
                                                                            (QREFELT
                                                                             $
                                                                             67))
                                                                           (QREFELT
                                                                            $
                                                                            68))
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (SPADCALL
                                                                             (QREFELT
                                                                              $
                                                                              9)
                                                                             |r|
                                                                             (QREFELT
                                                                              $
                                                                              66))
                                                                            |w|
                                                                            |k|
                                                                            (QREFELT
                                                                             $
                                                                             67))
                                                                           (SPADCALL
                                                                            (SPADCALL
                                                                             (QREFELT
                                                                              $
                                                                              9)
                                                                             |r|
                                                                             (QREFELT
                                                                              $
                                                                              66))
                                                                            |k|
                                                                            |w|
                                                                            (QREFELT
                                                                             $
                                                                             67))
                                                                           (QREFELT
                                                                            $
                                                                            68))
                                                                          (QREFELT
                                                                           $
                                                                           65))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |t|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |l|
                                                                           |r|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |t|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |r|
                                                                           |l|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (QREFELT
                                                                           $
                                                                           68))
                                                                         (QREFELT
                                                                          $
                                                                          65))
                                                                        (QREFELT
                                                                         $ 68))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |r|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |w|
                                                                           |k|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |r|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |k|
                                                                           |w|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (QREFELT
                                                                           $
                                                                           68))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |l|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |j|
                                                                           |r|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |l|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |r|
                                                                           |j|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (QREFELT
                                                                           $
                                                                           68))
                                                                         (QREFELT
                                                                          $
                                                                          65))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |t|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |i|
                                                                          |l|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |t|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |l|
                                                                          |i|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (QREFELT
                                                                          $
                                                                          68))
                                                                        (QREFELT
                                                                         $ 65))
                                                                       (QREFELT
                                                                        $ 71))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |l|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |w|
                                                                          |j|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |l|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |j|
                                                                          |w|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (QREFELT
                                                                          $
                                                                          68))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |r|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |k|
                                                                          |i|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |r|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |i|
                                                                          |k|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (QREFELT
                                                                          $
                                                                          68))
                                                                        (QREFELT
                                                                         $ 65))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |t|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |l|
                                                                         |r|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |t|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |r|
                                                                         |l|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (QREFELT
                                                                         $ 68))
                                                                       (QREFELT
                                                                        $ 65))
                                                                      (QREFELT
                                                                       $ 68))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |r|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |k|
                                                                         |i|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |r|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |k|
                                                                         |i|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (QREFELT
                                                                         $ 68))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |l|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |j|
                                                                         |r|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |l|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |r|
                                                                         |j|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (QREFELT
                                                                         $ 68))
                                                                       (QREFELT
                                                                        $ 65))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |t|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |w| |l|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |t|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |l| |w|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (QREFELT
                                                                        $ 68))
                                                                      (QREFELT
                                                                       $ 65))
                                                                     (QREFELT $
                                                                              71))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |l|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |k| |j|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |l|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |j| |k|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (QREFELT
                                                                        $ 68))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |r|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |i| |w|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |r|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |w| |i|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (QREFELT
                                                                        $ 68))
                                                                      (QREFELT
                                                                       $ 65))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |t|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |l| |r|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |t|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |r| |l|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (QREFELT
                                                                       $ 68))
                                                                     (QREFELT $
                                                                              65))
                                                                    (QREFELT $
                                                                             68))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |r|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |i| |w|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |r|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |w| |i|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (QREFELT
                                                                       $ 68))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |l|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |j| |r|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |l|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |r| |j|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (QREFELT
                                                                       $ 68))
                                                                     (QREFELT $
                                                                              65))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (QREFELT
                                                                        $ 9)
                                                                       |t|
                                                                       (QREFELT
                                                                        $ 66))
                                                                      |k| |l|
                                                                      (QREFELT
                                                                       $ 67))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (QREFELT
                                                                        $ 9)
                                                                       |t|
                                                                       (QREFELT
                                                                        $ 66))
                                                                      |l| |k|
                                                                      (QREFELT
                                                                       $ 67))
                                                                     (QREFELT $
                                                                              68))
                                                                    (QREFELT $
                                                                             65))
                                                                   (QREFELT $
                                                                            71))
                                                                  . #10#)))
                                                          (LETT |r|
                                                                (|inc_SI| |r|)
                                                                . #10#)
                                                          (GO G190) G191
                                                          (EXIT NIL))))
                                                       (LETT |l| (|inc_SI| |l|)
                                                             . #10#)
                                                       (GO G190) G191
                                                       (EXIT NIL))
                                                  (EXIT
                                                   (COND
                                                    ((NULL
                                                      (SPADCALL |res|
                                                                (QREFELT $
                                                                         52)))
                                                     (PROGN
                                                      (LETT #1#
                                                            (SEQ
                                                             (SPADCALL
                                                              "algebra is not Jordan admissible"
                                                              (QREFELT $ 74))
                                                             (EXIT
                                                              (PROGN
                                                               (LETT #2# 'NIL
                                                                     . #10#)
                                                               (GO
                                                                #11=#:G894))))
                                                            . #10#)
                                                      (GO #12=#:G886)))))))
                                                #12# (EXIT #1#))
                                               (LETT |t| (|inc_SI| |t|) . #10#)
                                               (GO G190) G191 (EXIT NIL))))
                                        (LETT |w| (|inc_SI| |w|) . #10#)
                                        (GO G190) G191 (EXIT NIL))))
                                 (LETT |k| (|inc_SI| |k|) . #10#) (GO G190)
                                 G191 (EXIT NIL))))
                          (LETT |j| (|inc_SI| |j|) . #10#) (GO G190) G191
                          (EXIT NIL))))
                   (LETT |i| (|inc_SI| |i|) . #10#) (GO G190) G191 (EXIT NIL))
              (SPADCALL "algebra is Jordan admissible" (QREFELT $ 74))
              (EXIT 'T)))))
          #11# (EXIT #2#)))) 

(SDEFUN |ALGSC;jordanAlgebra?;B;23| (($ |Boolean|))
        (SPROG
         ((#1=#:G922 NIL) (#2=#:G923 NIL) (|res| (R)) (#3=#:G930 NIL) (|s| NIL)
          (#4=#:G929 NIL) (|r| NIL) (#5=#:G928 NIL) (|t| NIL) (#6=#:G927 NIL)
          (|l| NIL) (#7=#:G926 NIL) (|k| NIL) (#8=#:G925 NIL) (|j| NIL)
          (#9=#:G924 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (COND
            ((QEQCAR
              (SPADCALL (SPADCALL 2 (|spadConstant| $ 53) (QREFELT $ 84))
                        (QREFELT $ 85))
              1)
             (SEQ
              (SPADCALL
               "this is not a Jordan algebra, as 2 is not invertible in the ground ring"
               (QREFELT $ 74))
              (EXIT 'NIL)))
            ((SPADCALL (QREFELT $ 78))
             (SEQ
              (SEQ (LETT |i| 1 . #10=(|ALGSC;jordanAlgebra?;B;23|))
                   (LETT #9# (QREFELT $ 7) . #10#) G190
                   (COND ((|greater_SI| |i| #9#) (GO G191)))
                   (SEQ
                    (EXIT
                     (SEQ (LETT |j| 1 . #10#) (LETT #8# (QREFELT $ 7) . #10#)
                          G190 (COND ((|greater_SI| |j| #8#) (GO G191)))
                          (SEQ
                           (EXIT
                            (SEQ (LETT |k| 1 . #10#)
                                 (LETT #7# (QREFELT $ 7) . #10#) G190
                                 (COND ((|greater_SI| |k| #7#) (GO G191)))
                                 (SEQ
                                  (EXIT
                                   (SEQ (LETT |l| 1 . #10#)
                                        (LETT #6# (QREFELT $ 7) . #10#) G190
                                        (COND
                                         ((|greater_SI| |l| #6#) (GO G191)))
                                        (SEQ
                                         (EXIT
                                          (SEQ (LETT |t| 1 . #10#)
                                               (LETT #5# (QREFELT $ 7) . #10#)
                                               G190
                                               (COND
                                                ((|greater_SI| |t| #5#)
                                                 (GO G191)))
                                               (SEQ
                                                (LETT |res|
                                                      (|spadConstant| $ 32)
                                                      . #10#)
                                                (EXIT
                                                 (SEQ (LETT |r| 1 . #10#)
                                                      (LETT #4# (QREFELT $ 7)
                                                            . #10#)
                                                      G190
                                                      (COND
                                                       ((|greater_SI| |r| #4#)
                                                        (GO G191)))
                                                      (SEQ
                                                       (EXIT
                                                        (SEQ
                                                         (LETT |s| 1 . #10#)
                                                         (LETT #3#
                                                               (QREFELT $ 7)
                                                               . #10#)
                                                         G190
                                                         (COND
                                                          ((|greater_SI| |s|
                                                                         #3#)
                                                           (GO G191)))
                                                         (SEQ
                                                          (EXIT
                                                           (SEQ
                                                            (LETT |res|
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        |res|
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |r|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |i|
                                                                           |j|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (SPADCALL
                                                                           (SPADCALL
                                                                            (QREFELT
                                                                             $
                                                                             9)
                                                                            |s|
                                                                            (QREFELT
                                                                             $
                                                                             66))
                                                                           |l|
                                                                           |k|
                                                                           (QREFELT
                                                                            $
                                                                            67))
                                                                          (QREFELT
                                                                           $
                                                                           65))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |t|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |r|
                                                                          |s|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (QREFELT
                                                                          $
                                                                          65))
                                                                        (QREFELT
                                                                         $ 68))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |r|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |l|
                                                                          |k|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (SPADCALL
                                                                          (SPADCALL
                                                                           (QREFELT
                                                                            $
                                                                            9)
                                                                           |s|
                                                                           (QREFELT
                                                                            $
                                                                            66))
                                                                          |j|
                                                                          |r|
                                                                          (QREFELT
                                                                           $
                                                                           67))
                                                                         (QREFELT
                                                                          $
                                                                          65))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |t|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |i|
                                                                         |s|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (QREFELT
                                                                         $ 65))
                                                                       (QREFELT
                                                                        $ 71))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |r|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |l|
                                                                         |j|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (SPADCALL
                                                                         (SPADCALL
                                                                          (QREFELT
                                                                           $ 9)
                                                                          |s|
                                                                          (QREFELT
                                                                           $
                                                                           66))
                                                                         |k|
                                                                         |k|
                                                                         (QREFELT
                                                                          $
                                                                          67))
                                                                        (QREFELT
                                                                         $ 65))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |t|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |r| |s|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (QREFELT
                                                                        $ 65))
                                                                      (QREFELT
                                                                       $ 68))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |r|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |k| |i|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (SPADCALL
                                                                        (SPADCALL
                                                                         (QREFELT
                                                                          $ 9)
                                                                         |s|
                                                                         (QREFELT
                                                                          $
                                                                          66))
                                                                        |j| |r|
                                                                        (QREFELT
                                                                         $ 67))
                                                                       (QREFELT
                                                                        $ 65))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |t|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |l| |s|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (QREFELT
                                                                       $ 65))
                                                                     (QREFELT $
                                                                              71))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |r|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |k| |j|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (SPADCALL
                                                                       (SPADCALL
                                                                        (QREFELT
                                                                         $ 9)
                                                                        |s|
                                                                        (QREFELT
                                                                         $ 66))
                                                                       |i| |k|
                                                                       (QREFELT
                                                                        $ 67))
                                                                      (QREFELT
                                                                       $ 65))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (QREFELT
                                                                        $ 9)
                                                                       |t|
                                                                       (QREFELT
                                                                        $ 66))
                                                                      |r| |s|
                                                                      (QREFELT
                                                                       $ 67))
                                                                     (QREFELT $
                                                                              65))
                                                                    (QREFELT $
                                                                             68))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (QREFELT
                                                                        $ 9)
                                                                       |r|
                                                                       (QREFELT
                                                                        $ 66))
                                                                      |i| |l|
                                                                      (QREFELT
                                                                       $ 67))
                                                                     (SPADCALL
                                                                      (SPADCALL
                                                                       (QREFELT
                                                                        $ 9)
                                                                       |s|
                                                                       (QREFELT
                                                                        $ 66))
                                                                      |j| |r|
                                                                      (QREFELT
                                                                       $ 67))
                                                                     (QREFELT $
                                                                              65))
                                                                    (SPADCALL
                                                                     (SPADCALL
                                                                      (QREFELT
                                                                       $ 9)
                                                                      |t|
                                                                      (QREFELT
                                                                       $ 66))
                                                                     |k| |s|
                                                                     (QREFELT $
                                                                              67))
                                                                    (QREFELT $
                                                                             65))
                                                                   (QREFELT $
                                                                            71))
                                                                  . #10#)
                                                            (EXIT
                                                             (COND
                                                              ((NULL
                                                                (SPADCALL |res|
                                                                          (QREFELT
                                                                           $
                                                                           52)))
                                                               (PROGN
                                                                (LETT #1#
                                                                      (SEQ
                                                                       (SPADCALL
                                                                        "this is not a Jordan algebra"
                                                                        (QREFELT
                                                                         $ 74))
                                                                       (EXIT
                                                                        (PROGN
                                                                         (LETT
                                                                          #2#
                                                                          'NIL
                                                                          . #10#)
                                                                         (GO
                                                                          #11=#:G921))))
                                                                      . #10#)
                                                                (GO
                                                                 #12=#:G909)))))))
                                                          #12# (EXIT #1#))
                                                         (LETT |s|
                                                               (|inc_SI| |s|)
                                                               . #10#)
                                                         (GO G190) G191
                                                         (EXIT NIL))))
                                                      (LETT |r| (|inc_SI| |r|)
                                                            . #10#)
                                                      (GO G190) G191
                                                      (EXIT NIL))))
                                               (LETT |t| (|inc_SI| |t|) . #10#)
                                               (GO G190) G191 (EXIT NIL))))
                                        (LETT |l| (|inc_SI| |l|) . #10#)
                                        (GO G190) G191 (EXIT NIL))))
                                 (LETT |k| (|inc_SI| |k|) . #10#) (GO G190)
                                 G191 (EXIT NIL))))
                          (LETT |j| (|inc_SI| |j|) . #10#) (GO G190) G191
                          (EXIT NIL))))
                   (LETT |i| (|inc_SI| |i|) . #10#) (GO G190) G191 (EXIT NIL))
              (SPADCALL "this is a Jordan algebra" (QREFELT $ 74)) (EXIT 'T)))
            ('T
             (SEQ (SPADCALL "this is not a Jordan algebra" (QREFELT $ 74))
                  (EXIT 'NIL)))))
          #11# (EXIT #2#)))) 

(SDEFUN |ALGSC;jacobiIdentity?;B;24| (($ |Boolean|))
        (SPROG
         ((#1=#:G940 NIL) (#2=#:G941 NIL) (|res| (R)) (#3=#:G946 NIL) (|s| NIL)
          (#4=#:G945 NIL) (|r| NIL) (#5=#:G944 NIL) (|k| NIL) (#6=#:G943 NIL)
          (|j| NIL) (#7=#:G942 NIL) (|i| NIL))
         (SEQ
          (EXIT
           (SEQ
            (SEQ (LETT |i| 1 . #8=(|ALGSC;jacobiIdentity?;B;24|))
                 (LETT #7# (QREFELT $ 7) . #8#) G190
                 (COND ((|greater_SI| |i| #7#) (GO G191)))
                 (SEQ
                  (EXIT
                   (SEQ (LETT |j| 1 . #8#) (LETT #6# (QREFELT $ 7) . #8#) G190
                        (COND ((|greater_SI| |j| #6#) (GO G191)))
                        (SEQ
                         (EXIT
                          (SEQ (LETT |k| 1 . #8#)
                               (LETT #5# (QREFELT $ 7) . #8#) G190
                               (COND ((|greater_SI| |k| #5#) (GO G191)))
                               (SEQ
                                (EXIT
                                 (SEQ (LETT |r| 1 . #8#)
                                      (LETT #4# (QREFELT $ 7) . #8#) G190
                                      (COND ((|greater_SI| |r| #4#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (SEQ
                                         (LETT |res| (|spadConstant| $ 32)
                                               . #8#)
                                         (SEQ (LETT |s| 1 . #8#)
                                              (LETT #3# (QREFELT $ 7) . #8#)
                                              G190
                                              (COND
                                               ((|greater_SI| |s| #3#)
                                                (GO G191)))
                                              (SEQ
                                               (EXIT
                                                (LETT |res|
                                                      (SPADCALL
                                                       (SPADCALL
                                                        (SPADCALL |res|
                                                                  (SPADCALL
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |r|
                                                                     (QREFELT $
                                                                              66))
                                                                    |i| |j|
                                                                    (QREFELT $
                                                                             67))
                                                                   (SPADCALL
                                                                    (SPADCALL
                                                                     (QREFELT $
                                                                              9)
                                                                     |s|
                                                                     (QREFELT $
                                                                              66))
                                                                    |j| |k|
                                                                    (QREFELT $
                                                                             67))
                                                                   (QREFELT $
                                                                            65))
                                                                  (QREFELT $
                                                                           68))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |r|
                                                           (QREFELT $ 66))
                                                          |j| |k|
                                                          (QREFELT $ 67))
                                                         (SPADCALL
                                                          (SPADCALL
                                                           (QREFELT $ 9) |s|
                                                           (QREFELT $ 66))
                                                          |k| |i|
                                                          (QREFELT $ 67))
                                                         (QREFELT $ 65))
                                                        (QREFELT $ 68))
                                                       (SPADCALL
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |r|
                                                          (QREFELT $ 66))
                                                         |k| |i|
                                                         (QREFELT $ 67))
                                                        (SPADCALL
                                                         (SPADCALL
                                                          (QREFELT $ 9) |s|
                                                          (QREFELT $ 66))
                                                         |i| |j|
                                                         (QREFELT $ 67))
                                                        (QREFELT $ 65))
                                                       (QREFELT $ 68))
                                                      . #8#)))
                                              (LETT |s| (|inc_SI| |s|) . #8#)
                                              (GO G190) G191 (EXIT NIL))
                                         (EXIT
                                          (COND
                                           ((NULL
                                             (SPADCALL |res| (QREFELT $ 52)))
                                            (PROGN
                                             (LETT #1#
                                                   (SEQ
                                                    (SPADCALL
                                                     "Jacobi identity does not hold"
                                                     (QREFELT $ 74))
                                                    (EXIT
                                                     (PROGN
                                                      (LETT #2# 'NIL . #8#)
                                                      (GO #9=#:G939))))
                                                   . #8#)
                                             (GO #10=#:G933)))))))
                                       #10# (EXIT #1#))
                                      (LETT |r| (|inc_SI| |r|) . #8#) (GO G190)
                                      G191 (EXIT NIL))))
                               (LETT |k| (|inc_SI| |k|) . #8#) (GO G190) G191
                               (EXIT NIL))))
                        (LETT |j| (|inc_SI| |j|) . #8#) (GO G190) G191
                        (EXIT NIL))))
                 (LETT |i| (|inc_SI| |i|) . #8#) (GO G190) G191 (EXIT NIL))
            (SPADCALL "Jacobi identity holds" (QREFELT $ 74)) (EXIT 'T)))
          #9# (EXIT #2#)))) 

(DECLAIM (NOTINLINE |AlgebraGivenByStructuralConstants;|)) 

(DEFUN |AlgebraGivenByStructuralConstants| (&REST #1=#:G955)
  (SPROG NIL
         (PROG (#2=#:G956)
           (RETURN
            (COND
             ((LETT #2#
                    (|lassocShiftWithFunction| (|devaluateList| #1#)
                                               (HGET |$ConstructorCache|
                                                     '|AlgebraGivenByStructuralConstants|)
                                               '|domainEqualList|)
                    . #3=(|AlgebraGivenByStructuralConstants|))
              (|CDRwithIncrement| #2#))
             ('T
              (UNWIND-PROTECT
                  (PROG1
                      (APPLY (|function| |AlgebraGivenByStructuralConstants;|)
                             #1#)
                    (LETT #2# T . #3#))
                (COND
                 ((NOT #2#)
                  (HREM |$ConstructorCache|
                        '|AlgebraGivenByStructuralConstants|)))))))))) 

(DEFUN |AlgebraGivenByStructuralConstants;| (|#1| |#2| |#3| |#4|)
  (SPROG
   ((|pv$| NIL) ($ NIL) (|dv$| NIL) (DV$4 NIL) (DV$3 NIL) (DV$2 NIL)
    (DV$1 NIL))
   (PROGN
    (LETT DV$1 (|devaluate| |#1|) . #1=(|AlgebraGivenByStructuralConstants|))
    (LETT DV$2 (|devaluate| |#2|) . #1#)
    (LETT DV$3 (|devaluate| |#3|) . #1#)
    (LETT DV$4 (|devaluate| |#4|) . #1#)
    (LETT |dv$| (LIST '|AlgebraGivenByStructuralConstants| DV$1 DV$2 DV$3 DV$4)
          . #1#)
    (LETT $ (GETREFV 98) . #1#)
    (QSETREFV $ 0 |dv$|)
    (QSETREFV $ 3
              (LETT |pv$|
                    (|buildPredVector| 0 0
                                       (LIST
                                        (|HasCategory| |#1|
                                                       '(|IntegralDomain|))
                                        (|HasCategory| |#1| '(|Field|))))
                    . #1#))
    (|haddProp| |$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|)
    (SETF |pv$| (QREFELT $ 3))
    (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|) (40 . |elt|) (46 . |setColumn!|)
              (|Union| 20 '"failed")
              (|Record| (|:| |particular| 35) (|:| |basis| 93))
              (|LinearSystemMatrixPackage| 6 20 20 15) (53 . |solve|)
              (|Vector| $) |ALGSC;basis;V;7| |ALGSC;coordinates;$VV;6|
              (|PositiveInteger|) (59 . |unitVector|) |ALGSC;someBasis;V;8|
              |ALGSC;rank;Pi;9| (64 . |elt|) |ALGSC;elt;$IR;10| (|Boolean|)
              (70 . |zero?|) (|OutputForm|) (75 . |coerce|) (80 . |zero?|)
              (85 . |One|) (89 . =) (|Symbol|) (|List| 55) (95 . |elt|)
              (101 . |coerce|) (106 . *) (112 . +) (|Mapping| 50 50 50)
              (|List| 50) (118 . |reduce|) |ALGSC;coerce;$Of;11| (124 . *)
              (130 . |elt|) (136 . |elt|) (143 . +) (149 . |setelt!|)
              |ALGSC;*;3$;12| (156 . -) (|Void|) (|String|)
              (162 . |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| (167 . *)
              (173 . |recip|) |ALGSC;jordanAdmissible?;B;22|
              |ALGSC;jordanAlgebra?;B;23| |ALGSC;jacobiIdentity?;B;24|
              (|SparseUnivariatePolynomial| (|Polynomial| 6))
              (|Record| (|:| |particular| $) (|:| |basis| (|List| $)))
              (|Union| 90 '"failed") (|SparseUnivariatePolynomial| 6)
              (|List| 20) (|List| (|Polynomial| 6)) (|NonNegativeInteger|)
              (|SingleInteger|) (|HashState|))
           '#(~= 178 |zero?| 184 |unit| 189 |subtractIfCan| 193
              |structuralConstants| 199 |someBasis| 208 |sample| 212
              |rightUnits| 216 |rightUnit| 220 |rightTraceMatrix| 224
              |rightTrace| 233 |rightRegularRepresentation| 238 |rightRecip|
              249 |rightRankPolynomial| 254 |rightPower| 258 |rightNorm| 264
              |rightMinimalPolynomial| 269 |rightDiscriminant| 274
              |rightCharacteristicPolynomial| 283 |rightAlternative?| 288
              |represents| 292 |recip| 303 |rank| 308 |powerAssociative?| 312
              |plenaryPower| 316 |opposite?| 322 |noncommutativeJordanAlgebra?|
              328 |lieAlgebra?| 332 |lieAdmissible?| 336 |leftUnits| 340
              |leftUnit| 344 |leftTraceMatrix| 348 |leftTrace| 357
              |leftRegularRepresentation| 362 |leftRecip| 373
              |leftRankPolynomial| 378 |leftPower| 382 |leftNorm| 388
              |leftMinimalPolynomial| 393 |leftDiscriminant| 398
              |leftCharacteristicPolynomial| 407 |leftAlternative?| 412 |latex|
              416 |jordanAlgebra?| 421 |jordanAdmissible?| 425
              |jacobiIdentity?| 429 |hashUpdate!| 433 |hash| 439 |flexible?|
              444 |elt| 448 |coordinates| 454 |convert| 476
              |conditionsForIdempotents| 486 |commutator| 495 |commutative?|
              501 |coerce| 505 |basis| 515 |associatorDependence| 519
              |associator| 523 |associative?| 530 |apply| 534 |antiCommutator|
              540 |antiCommutative?| 546 |antiAssociative?| 550 |alternative?|
              554 ^ 558 |Zero| 564 = 568 - 574 + 585 * 591)
           '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| 50) (|unitsKnown|))
                   (|makeByteWordVec2| 97
                                       '(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 2 30 2 0 29
                                         33 3 15 0 0 29 20 34 2 37 36 15 20 38
                                         1 10 0 42 43 2 10 6 0 29 46 1 10 48 0
                                         49 1 6 50 0 51 1 6 48 0 52 0 6 0 53 2
                                         6 48 0 0 54 2 56 55 0 29 57 1 55 50 0
                                         58 2 50 0 0 0 59 2 50 0 0 0 60 2 62 50
                                         61 0 63 2 6 0 0 0 65 2 23 15 0 29 66 3
                                         15 6 0 29 29 67 2 6 0 0 0 68 3 20 6 0
                                         29 6 69 2 6 0 0 0 71 1 50 72 73 74 2 6
                                         0 42 0 84 1 6 11 0 85 2 0 48 0 0 1 1 0
                                         48 0 1 0 1 11 1 2 0 11 0 0 1 0 0 23 24
                                         1 0 23 39 1 0 0 39 44 0 0 0 1 0 1 91 1
                                         0 1 11 1 0 0 15 1 1 0 15 39 1 1 0 6 0
                                         1 1 0 15 0 1 2 0 15 0 39 1 1 1 11 0 1
                                         0 2 89 1 2 0 0 0 42 1 1 0 6 0 1 1 1 92
                                         0 1 0 0 6 1 1 0 6 39 1 1 0 92 0 1 0 0
                                         48 81 1 0 0 20 1 2 0 0 20 39 1 1 1 11
                                         0 14 0 0 42 45 0 0 48 1 2 0 0 0 42 1 2
                                         0 48 0 0 1 0 0 48 1 0 0 48 1 0 0 48 83
                                         0 1 91 1 0 1 11 1 0 0 15 1 1 0 15 39 1
                                         1 0 6 0 1 1 0 15 0 1 2 0 15 0 39 1 1 1
                                         11 0 1 0 2 89 1 2 0 0 0 42 1 1 0 6 0 1
                                         1 1 92 0 1 0 0 6 1 1 0 6 39 1 1 0 92 0
                                         1 0 0 48 80 1 0 73 0 1 0 0 48 87 0 0
                                         48 86 0 0 48 88 2 0 97 97 0 1 1 0 96 0
                                         1 0 0 48 82 2 0 6 0 29 47 1 0 15 39 1
                                         1 0 20 0 28 2 0 15 39 39 1 2 0 20 0 39
                                         41 1 0 0 20 1 1 0 20 0 1 0 0 94 1 1 0
                                         94 39 1 2 0 0 0 0 1 0 0 48 78 1 0 0 20
                                         22 1 0 50 0 64 0 0 39 40 0 1 93 1 3 0
                                         0 0 0 0 1 0 0 48 76 2 0 0 15 0 18 2 0
                                         0 0 0 1 0 0 48 79 0 0 48 77 0 0 48 75
                                         2 0 0 0 42 1 0 0 0 1 2 0 48 0 0 1 2 0
                                         0 0 0 1 1 0 0 0 1 2 0 0 0 0 1 2 0 0 16
                                         0 19 2 0 0 6 0 1 2 0 0 0 6 1 2 0 0 0 0
                                         70 2 0 0 29 0 1 2 0 0 95 0 1 2 0 0 42
                                         0 1)))))
           '|lookupComplete|)) 
