
(/VERSIONCHECK 2) 

(DEFUN |FRNAALG-;leftRankPolynomial;Sup;1| ($)
  (PROG (|res| |i| |vectorOfCoef| |cond| |y| |k| |x| #1=#:G1856 #2=#:G1855
         #3=#:G1854 |genGamma| |mo| |symbolsForCoef| #4=#:G1853 #5=#:G1852
         #6=#:G1851 |listOfNumbers| |q| #7=#:G1850 |gamma| |b| |n|)
    (RETURN
     (SEQ
      (LETT |n| (SPADCALL (QREFELT $ 9))
            . #8=(|FRNAALG-;leftRankPolynomial;Sup;1|))
      (LETT |b| (SPADCALL (QREFELT $ 11)) . #8#)
      (LETT |gamma| (SPADCALL |b| (QREFELT $ 13)) . #8#)
      (LETT |listOfNumbers|
            (PROGN
             (LETT #7# NIL . #8#)
             (SEQ (LETT |q| 1 . #8#) G190
                  (COND ((QSGREATERP |q| |n|) #9=(GO G191)))
                  (SEQ (EXIT (LETT #7# (CONS (STRINGIMAGE |q|) #7#) . #8#)))
                  (LETT |q| (QSADD1 |q|) . #8#) #10=(GO G190) G191
                  (EXIT (NREVERSE0 #7#))))
            . #8#)
      (LETT |symbolsForCoef|
            (PROGN
             (LETT #6# (GETREFV (SIZE |listOfNumbers|)) . #8#)
             (SEQ (LETT #5# 0 . #8#) (LETT |i| NIL . #8#)
                  (LETT #4# |listOfNumbers| . #8#) G190
                  (COND
                   ((OR (ATOM #4#) (PROGN (LETT |i| (CAR #4#) . #8#) NIL))
                    #9#))
                  (SEQ
                   (EXIT
                    (SETELT #6# #5#
                            (SPADCALL (STRCONC "%" (STRCONC "x" |i|))
                                      (QREFELT $ 16)))))
                  (LETT #4# (PROG1 (CDR #4#) (LETT #5# (QSADD1 #5#) . #8#))
                        . #8#)
                  #10# G191 (EXIT NIL))
             #6#)
            . #8#)
      (LETT |x| (SPADCALL 1 |n| (|spadConstant| $ 21) (QREFELT $ 24)) . #8#)
      (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |n|) #9#))
           (SEQ
            (LETT |mo|
                  (SPADCALL (|spadConstant| $ 25)
                            (LIST
                             (SPADCALL |symbolsForCoef| |i| (QREFELT $ 28)))
                            (LIST 1) (QREFELT $ 31))
                  . #8#)
            (EXIT (QSETAREF2O |x| 1 |i| |mo| 1 1)))
           (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
      (LETT |y| (SPADCALL |x| (QREFELT $ 32)) . #8#) (LETT |k| 1 . #8#)
      (LETT |cond| (SPADCALL |x| (QREFELT $ 32)) . #8#)
      (LETT |genGamma| (SPADCALL |gamma| (QREFELT $ 35)) . #8#)
      (LETT |x|
            (SPADCALL (ELT $ 36)
                      (PROGN
                       (LETT #3# (GETREFV #11=(QVSIZE |genGamma|)) . #8#)
                       (SEQ (LETT #2# 0 . #8#) (LETT |i| 1 . #8#)
                            (LETT #1# #11# . #8#) G190
                            (COND ((QSGREATERP |i| #1#) #9#))
                            (SEQ
                             (EXIT
                              (SETELT #3# #2#
                                      (SPADCALL |x|
                                                (SPADCALL |genGamma| |i|
                                                          (QREFELT $ 37))
                                                (QREFELT $ 38)))))
                            (LETT |i|
                                  (PROG1 (QSADD1 |i|)
                                    (LETT #2# (QSADD1 #2#) . #8#))
                                  . #8#)
                            #10# G191 (EXIT NIL))
                       #3#)
                      (QREFELT $ 40))
            . #8#)
      (SEQ G190 (COND ((NULL (EQL (SPADCALL |cond| (QREFELT $ 41)) |k|)) #9#))
           (SEQ (LETT |k| (+ |k| 1) . #8#)
                (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |n|) #9#))
                     (SEQ
                      (EXIT
                       (SPADCALL |xx| (LIST 1) (LIST |i|)
                                 (SPADCALL |x| (SPADCALL |y| (QREFELT $ 42))
                                           (QREFELT $ 38))
                                 (QREFELT $ 44))))
                     (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
                (LETT |y| (SPADCALL |xx| (QREFELT $ 32)) . #8#)
                (EXIT
                 (LETT |cond| (SPADCALL |cond| |xx| (QREFELT $ 36)) . #8#)))
           NIL #10# G191 (EXIT NIL))
      (LETT |vectorOfCoef| (|SPADfirst| (SPADCALL |cond| (QREFELT $ 46)))
            . #8#)
      (LETT |res| (|spadConstant| $ 47) . #8#)
      (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |k|) #9#))
           (SEQ
            (EXIT
             (LETT |res|
                   (SPADCALL |res|
                             (SPADCALL
                              (SPADCALL |vectorOfCoef| |i| (QREFELT $ 49)) |i|
                              (QREFELT $ 50))
                             (QREFELT $ 51))
                   . #8#)))
           (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
      (EXIT |res|))))) 

(DEFUN |FRNAALG-;rightRankPolynomial;Sup;2| ($)
  (PROG (|res| |i| |vectorOfCoef| |cond| |y| |k| |x| #1=#:G1874 #2=#:G1873
         #3=#:G1872 |genGamma| |mo| |symbolsForCoef| #4=#:G1871 #5=#:G1870
         #6=#:G1869 |listOfNumbers| |q| #7=#:G1868 |gamma| |b| |n|)
    (RETURN
     (SEQ
      (LETT |n| (SPADCALL (QREFELT $ 9))
            . #8=(|FRNAALG-;rightRankPolynomial;Sup;2|))
      (LETT |b| (SPADCALL (QREFELT $ 11)) . #8#)
      (LETT |gamma| (SPADCALL |b| (QREFELT $ 13)) . #8#)
      (LETT |listOfNumbers|
            (PROGN
             (LETT #7# NIL . #8#)
             (SEQ (LETT |q| 1 . #8#) G190
                  (COND ((QSGREATERP |q| |n|) #9=(GO G191)))
                  (SEQ (EXIT (LETT #7# (CONS (STRINGIMAGE |q|) #7#) . #8#)))
                  (LETT |q| (QSADD1 |q|) . #8#) #10=(GO G190) G191
                  (EXIT (NREVERSE0 #7#))))
            . #8#)
      (LETT |symbolsForCoef|
            (PROGN
             (LETT #6# (GETREFV (SIZE |listOfNumbers|)) . #8#)
             (SEQ (LETT #5# 0 . #8#) (LETT |i| NIL . #8#)
                  (LETT #4# |listOfNumbers| . #8#) G190
                  (COND
                   ((OR (ATOM #4#) (PROGN (LETT |i| (CAR #4#) . #8#) NIL))
                    #9#))
                  (SEQ
                   (EXIT
                    (SETELT #6# #5#
                            (SPADCALL (STRCONC "%" (STRCONC "x" |i|))
                                      (QREFELT $ 16)))))
                  (LETT #4# (PROG1 (CDR #4#) (LETT #5# (QSADD1 #5#) . #8#))
                        . #8#)
                  #10# G191 (EXIT NIL))
             #6#)
            . #8#)
      (LETT |x| (SPADCALL 1 |n| (|spadConstant| $ 21) (QREFELT $ 24)) . #8#)
      (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |n|) #9#))
           (SEQ
            (LETT |mo|
                  (SPADCALL (|spadConstant| $ 25)
                            (LIST
                             (SPADCALL |symbolsForCoef| |i| (QREFELT $ 28)))
                            (LIST 1) (QREFELT $ 31))
                  . #8#)
            (EXIT (QSETAREF2O |x| 1 |i| |mo| 1 1)))
           (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
      (LETT |y| (SPADCALL |x| (QREFELT $ 32)) . #8#) (LETT |k| 1 . #8#)
      (LETT |cond| (SPADCALL |x| (QREFELT $ 32)) . #8#)
      (LETT |genGamma| (SPADCALL |gamma| (QREFELT $ 35)) . #8#)
      (LETT |x|
            (SPADCALL (ELT $ 36)
                      (PROGN
                       (LETT #3# (GETREFV #11=(QVSIZE |genGamma|)) . #8#)
                       (SEQ (LETT #2# 0 . #8#) (LETT |i| 1 . #8#)
                            (LETT #1# #11# . #8#) G190
                            (COND ((QSGREATERP |i| #1#) #9#))
                            (SEQ
                             (EXIT
                              (SETELT #3# #2#
                                      (SPADCALL
                                       (SPADCALL |genGamma| |i| (QREFELT $ 37))
                                       (SPADCALL |x| (QREFELT $ 42))
                                       (QREFELT $ 38)))))
                            (LETT |i|
                                  (PROG1 (QSADD1 |i|)
                                    (LETT #2# (QSADD1 #2#) . #8#))
                                  . #8#)
                            #10# G191 (EXIT NIL))
                       #3#)
                      (QREFELT $ 40))
            . #8#)
      (SEQ G190 (COND ((NULL (EQL (SPADCALL |cond| (QREFELT $ 41)) |k|)) #9#))
           (SEQ (LETT |k| (+ |k| 1) . #8#)
                (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |n|) #9#))
                     (SEQ
                      (EXIT
                       (SPADCALL |xx| (LIST 1) (LIST |i|)
                                 (SPADCALL |y| (SPADCALL |x| (QREFELT $ 42))
                                           (QREFELT $ 38))
                                 (QREFELT $ 44))))
                     (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
                (LETT |y| (SPADCALL |xx| (QREFELT $ 32)) . #8#)
                (EXIT
                 (LETT |cond| (SPADCALL |cond| |xx| (QREFELT $ 36)) . #8#)))
           NIL #10# G191 (EXIT NIL))
      (LETT |vectorOfCoef| (|SPADfirst| (SPADCALL |cond| (QREFELT $ 46)))
            . #8#)
      (LETT |res| (|spadConstant| $ 47) . #8#)
      (SEQ (LETT |i| 1 . #8#) G190 (COND ((QSGREATERP |i| |k|) #9#))
           (SEQ
            (EXIT
             (LETT |res|
                   (SPADCALL |res|
                             (SPADCALL
                              (SPADCALL |vectorOfCoef| |i| (QREFELT $ 49)) |i|
                              (QREFELT $ 50))
                             (QREFELT $ 51))
                   . #8#)))
           (LETT |i| (QSADD1 |i|) . #8#) #10# G191 (EXIT NIL))
      (EXIT |res|))))) 

(DEFUN |FRNAALG-;leftUnitsInternal| ($)
  (PROG (|j| |addOn| |z| |i| |k| |rhs| |cond| |gamma| |b| |n|)
    (RETURN
     (SEQ
      (LETT |n| (SPADCALL (QREFELT $ 9)) . #1=(|FRNAALG-;leftUnitsInternal|))
      (LETT |b| (SPADCALL (QREFELT $ 11)) . #1#)
      (LETT |gamma| (SPADCALL |b| (QREFELT $ 13)) . #1#)
      (LETT |cond|
            (SPADCALL (SPADCALL |n| 2 (QREFELT $ 54)) |n| (|spadConstant| $ 55)
                      (QREFELT $ 57))
            . #1#)
      (LETT |rhs|
            (MAKEARR1 (SPADCALL |n| 2 (QREFELT $ 54)) (|spadConstant| $ 55))
            . #1#)
      (LETT |z| 0 . #1#) (LETT |addOn| (|spadConstant| $ 55) . #1#)
      (SEQ (LETT |k| 1 . #1#) G190 (COND ((QSGREATERP |k| |n|) #2=(GO G191)))
           (SEQ
            (EXIT
             (SEQ (LETT |i| 1 . #1#) G190 (COND ((QSGREATERP |i| |n|) #2#))
                  (SEQ (LETT |z| (+ |z| 1) . #1#)
                       (LETT |addOn|
                             (COND ((EQL |k| |i|) (|spadConstant| $ 17))
                                   ('T (|spadConstant| $ 55)))
                             . #1#)
                       (SPADCALL |rhs| |z| |addOn| (QREFELT $ 59))
                       (EXIT
                        (SEQ (LETT |j| 1 . #1#) G190
                             (COND ((QSGREATERP |j| |n|) #2#))
                             (SEQ
                              (EXIT
                               (SPADCALL |cond| |z| |j|
                                         (SPADCALL
                                          (SPADCALL |gamma| |k| (QREFELT $ 60))
                                          |j| |i| (QREFELT $ 61))
                                         (QREFELT $ 62))))
                             (LETT |j| (QSADD1 |j|) . #1#) #3=(GO G190) G191
                             (EXIT NIL))))
                  (LETT |i| (QSADD1 |i|) . #1#) #3# G191 (EXIT NIL))))
           (LETT |k| (QSADD1 |k|) . #1#) #3# G191 (EXIT NIL))
      (EXIT (SPADCALL |cond| |rhs| (QREFELT $ 66))))))) 

(DEFUN |FRNAALG-;leftUnit;U;4| ($)
  (PROG (#1=#:G1893 |res|)
    (RETURN
     (SEQ
      (LETT |res| (|FRNAALG-;leftUnitsInternal| $)
            . #2=(|FRNAALG-;leftUnit;U;4|))
      (EXIT
       (COND
        ((QEQCAR (QCAR |res|) 1)
         (SEQ (SPADCALL "this algebra has no left unit" (QREFELT $ 69))
              (EXIT (CONS 1 "failed"))))
        ('T
         (CONS 0
               (SPADCALL
                (PROG2
                    (LETT #1# (QCAR |res|) . #2#)
                    (QCDR #1#)
                  (|check-union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 7)) #1#))
                (QREFELT $ 70)))))))))) 

(DEFUN |FRNAALG-;leftUnits;U;5| ($)
  (PROG (#1=#:G1907 |res|)
    (RETURN
     (SEQ
      (LETT |res| (|FRNAALG-;leftUnitsInternal| $)
            . #2=(|FRNAALG-;leftUnits;U;5|))
      (EXIT
       (COND
        ((QEQCAR (QCAR |res|) 1)
         (SEQ (SPADCALL "this algebra has no left unit" (QREFELT $ 69))
              (EXIT (CONS 1 "failed"))))
        ('T
         (CONS 0
               (CONS
                (SPADCALL
                 (PROG2
                     (LETT #1# (QCAR |res|) . #2#)
                     (QCDR #1#)
                   (|check-union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 7)) #1#))
                 (QREFELT $ 70))
                (SPADCALL (ELT $ 70) (QCDR |res|) (QREFELT $ 77))))))))))) 

(DEFUN |FRNAALG-;rightUnitsInternal| ($)
  (PROG (|j| |addOn| |z| |i| |k| |rhs| |condo| |gamma| |b| |n|)
    (RETURN
     (SEQ
      (LETT |n| (SPADCALL (QREFELT $ 9)) . #1=(|FRNAALG-;rightUnitsInternal|))
      (LETT |b| (SPADCALL (QREFELT $ 11)) . #1#)
      (LETT |gamma| (SPADCALL |b| (QREFELT $ 13)) . #1#)
      (LETT |condo|
            (SPADCALL (SPADCALL |n| 2 (QREFELT $ 54)) |n| (|spadConstant| $ 55)
                      (QREFELT $ 57))
            . #1#)
      (LETT |rhs|
            (MAKEARR1 (SPADCALL |n| 2 (QREFELT $ 54)) (|spadConstant| $ 55))
            . #1#)
      (LETT |z| 0 . #1#) (LETT |addOn| (|spadConstant| $ 55) . #1#)
      (SEQ (LETT |k| 1 . #1#) G190 (COND ((QSGREATERP |k| |n|) #2=(GO G191)))
           (SEQ
            (EXIT
             (SEQ (LETT |i| 1 . #1#) G190 (COND ((QSGREATERP |i| |n|) #2#))
                  (SEQ (LETT |z| (+ |z| 1) . #1#)
                       (LETT |addOn|
                             (COND ((EQL |k| |i|) (|spadConstant| $ 17))
                                   ('T (|spadConstant| $ 55)))
                             . #1#)
                       (SPADCALL |rhs| |z| |addOn| (QREFELT $ 59))
                       (EXIT
                        (SEQ (LETT |j| 1 . #1#) G190
                             (COND ((QSGREATERP |j| |n|) #2#))
                             (SEQ
                              (EXIT
                               (SPADCALL |condo| |z| |j|
                                         (SPADCALL
                                          (SPADCALL |gamma| |k| (QREFELT $ 60))
                                          |i| |j| (QREFELT $ 61))
                                         (QREFELT $ 62))))
                             (LETT |j| (QSADD1 |j|) . #1#) #3=(GO G190) G191
                             (EXIT NIL))))
                  (LETT |i| (QSADD1 |i|) . #1#) #3# G191 (EXIT NIL))))
           (LETT |k| (QSADD1 |k|) . #1#) #3# G191 (EXIT NIL))
      (EXIT (SPADCALL |condo| |rhs| (QREFELT $ 66))))))) 

(DEFUN |FRNAALG-;rightUnit;U;7| ($)
  (PROG (#1=#:G1929 |res|)
    (RETURN
     (SEQ
      (LETT |res| (|FRNAALG-;rightUnitsInternal| $)
            . #2=(|FRNAALG-;rightUnit;U;7|))
      (EXIT
       (COND
        ((QEQCAR (QCAR |res|) 1)
         (SEQ (SPADCALL "this algebra has no right unit" (QREFELT $ 69))
              (EXIT (CONS 1 "failed"))))
        ('T
         (CONS 0
               (SPADCALL
                (PROG2
                    (LETT #1# (QCAR |res|) . #2#)
                    (QCDR #1#)
                  (|check-union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 7)) #1#))
                (QREFELT $ 70)))))))))) 

(DEFUN |FRNAALG-;rightUnits;U;8| ($)
  (PROG (#1=#:G1940 |res|)
    (RETURN
     (SEQ
      (LETT |res| (|FRNAALG-;rightUnitsInternal| $)
            . #2=(|FRNAALG-;rightUnits;U;8|))
      (EXIT
       (COND
        ((QEQCAR (QCAR |res|) 1)
         (SEQ (SPADCALL "this algebra has no right unit" (QREFELT $ 69))
              (EXIT (CONS 1 "failed"))))
        ('T
         (CONS 0
               (CONS
                (SPADCALL
                 (PROG2
                     (LETT #1# (QCAR |res|) . #2#)
                     (QCDR #1#)
                   (|check-union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 7)) #1#))
                 (QREFELT $ 70))
                (SPADCALL (ELT $ 70) (QCDR |res|) (QREFELT $ 77))))))))))) 

(DEFUN |FRNAALG-;unit;U;9| ($)
  (PROG (#1=#:G1955 |res| |j| |addOn| |z| |i| |k| |u| |rhs| |cond| |gamma| |b|
         |n|)
    (RETURN
     (SEQ (LETT |n| (SPADCALL (QREFELT $ 9)) . #2=(|FRNAALG-;unit;U;9|))
          (LETT |b| (SPADCALL (QREFELT $ 11)) . #2#)
          (LETT |gamma| (SPADCALL |b| (QREFELT $ 13)) . #2#)
          (LETT |cond|
                (SPADCALL (* 2 (SPADCALL |n| 2 (QREFELT $ 54))) |n|
                          (|spadConstant| $ 55) (QREFELT $ 57))
                . #2#)
          (LETT |rhs|
                (MAKEARR1 (* 2 (SPADCALL |n| 2 (QREFELT $ 54)))
                          (|spadConstant| $ 55))
                . #2#)
          (LETT |z| 0 . #2#) (LETT |u| (* |n| |n|) . #2#)
          (LETT |addOn| (|spadConstant| $ 55) . #2#)
          (SEQ (LETT |k| 1 . #2#) G190
               (COND ((QSGREATERP |k| |n|) #3=(GO G191)))
               (SEQ
                (EXIT
                 (SEQ (LETT |i| 1 . #2#) G190 (COND ((QSGREATERP |i| |n|) #3#))
                      (SEQ (LETT |z| (+ |z| 1) . #2#)
                           (LETT |addOn|
                                 (COND ((EQL |k| |i|) (|spadConstant| $ 17))
                                       ('T (|spadConstant| $ 55)))
                                 . #2#)
                           (SPADCALL |rhs| |z| |addOn| (QREFELT $ 59))
                           (SPADCALL |rhs| |u| |addOn| (QREFELT $ 59))
                           (EXIT
                            (SEQ (LETT |j| 1 . #2#) G190
                                 (COND ((QSGREATERP |j| |n|) #3#))
                                 (SEQ
                                  (SPADCALL |cond| |z| |j|
                                            (SPADCALL
                                             (SPADCALL |gamma| |k|
                                                       (QREFELT $ 60))
                                             |j| |i| (QREFELT $ 61))
                                            (QREFELT $ 62))
                                  (EXIT
                                   (SPADCALL |cond| |u| |j|
                                             (SPADCALL
                                              (SPADCALL |gamma| |k|
                                                        (QREFELT $ 60))
                                              |i| |j| (QREFELT $ 61))
                                             (QREFELT $ 62))))
                                 (LETT |j| (QSADD1 |j|) . #2#) #4=(GO G190)
                                 G191 (EXIT NIL))))
                      (LETT |i| (QSADD1 |i|) . #2#) #4# G191 (EXIT NIL))))
               (LETT |k| (QSADD1 |k|) . #2#) #4# G191 (EXIT NIL))
          (LETT |res| (SPADCALL |cond| |rhs| (QREFELT $ 66)) . #2#)
          (EXIT
           (COND
            ((QEQCAR (QCAR |res|) 1)
             (SEQ (SPADCALL "this algebra has no unit" (QREFELT $ 69))
                  (EXIT (CONS 1 "failed"))))
            ('T
             (CONS 0
                   (SPADCALL
                    (PROG2
                        (LETT #1# (QCAR |res|) . #2#)
                        (QCDR #1#)
                      (|check-union| (QEQCAR #1# 0) (|Vector| (QREFELT $ 7))
                                     #1#))
                    (QREFELT $ 70)))))))))) 

(DEFUN |FRNAALG-;apply;M2S;10| (|m| |a| $)
  (PROG (|v|)
    (RETURN
     (SEQ
      (LETT |v| (SPADCALL |a| (QREFELT $ 84)) . #1=(|FRNAALG-;apply;M2S;10|))
      (LETT |v| (SPADCALL |m| |v| (QREFELT $ 85)) . #1#)
      (EXIT (SPADCALL |v| (QREFELT $ 86))))))) 

(DEFUN |FRNAALG-;structuralConstants;V;11| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 13))) 

(DEFUN |FRNAALG-;conditionsForIdempotents;L;12| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 90))) 

(DEFUN |FRNAALG-;convert;SV;13| (|x| $)
  (SPADCALL |x| (SPADCALL (QREFELT $ 11)) (QREFELT $ 92))) 

(DEFUN |FRNAALG-;convert;VS;14| (|v| $)
  (SPADCALL |v| (SPADCALL (QREFELT $ 11)) (QREFELT $ 94))) 

(DEFUN |FRNAALG-;leftTraceMatrix;M;15| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 96))) 

(DEFUN |FRNAALG-;rightTraceMatrix;M;16| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 98))) 

(DEFUN |FRNAALG-;leftDiscriminant;R;17| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 100))) 

(DEFUN |FRNAALG-;rightDiscriminant;R;18| ($)
  (SPADCALL (SPADCALL (QREFELT $ 11)) (QREFELT $ 102))) 

(DEFUN |FRNAALG-;leftRegularRepresentation;SM;19| (|x| $)
  (SPADCALL |x| (SPADCALL (QREFELT $ 11)) (QREFELT $ 104))) 

(DEFUN |FRNAALG-;rightRegularRepresentation;SM;20| (|x| $)
  (SPADCALL |x| (SPADCALL (QREFELT $ 11)) (QREFELT $ 106))) 

(DEFUN |FRNAALG-;coordinates;VM;21| (|x| $)
  (SPADCALL |x| (SPADCALL (QREFELT $ 11)) (QREFELT $ 108))) 

(DEFUN |FRNAALG-;represents;VS;22| (|v| $)
  (SPADCALL |v| (SPADCALL (QREFELT $ 11)) (QREFELT $ 94))) 

(DEFUN |FRNAALG-;coordinates;VM;23| (|v| $)
  (PROG (#1=#:G1977 |i| |j| |m|)
    (RETURN
     (SEQ
      (LETT |m|
            (SPADCALL (QVSIZE |v|) (SPADCALL (QREFELT $ 9))
                      (|spadConstant| $ 55) (QREFELT $ 57))
            . #2=(|FRNAALG-;coordinates;VM;23|))
      (SEQ (LETT |j| 1 . #2#) (LETT |i| (SPADCALL |v| (QREFELT $ 112)) . #2#)
           (LETT #1# (QVSIZE |v|) . #2#) G190 (COND ((> |i| #1#) (GO G191)))
           (SEQ
            (EXIT
             (SPADCALL |m| |j| (SPADCALL (QAREF1O |v| |i| 1) (QREFELT $ 84))
                       (QREFELT $ 113))))
           (LETT |i| (PROG1 (+ |i| 1) (LETT |j| (QSADD1 |j|) . #2#)) . #2#)
           (GO G190) G191 (EXIT NIL))
      (EXIT |m|))))) 

(DEFUN |FramedNonAssociativeAlgebra&| (|#1| |#2|)
  (PROG (|pv$| $ |dv$| DV$2 DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #1=(|FramedNonAssociativeAlgebra&|))
      (LETT DV$2 (|devaluate| |#2|) . #1#)
      (LETT |dv$| (LIST '|FramedNonAssociativeAlgebra&| DV$1 DV$2) . #1#)
      (LETT $ (GETREFV 114) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3
                (LETT |pv$|
                      (|buildPredVector| 0 0
                                         (LIST
                                          (|HasCategory| |#2| '(|Field|))))
                      . #1#))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      (QSETREFV $ 7 |#2|)
      (COND
       ((|testBitVector| |pv$| 1)
        (PROGN
         (QSETREFV $ 52
                   (CONS
                    (|dispatchFunction| |FRNAALG-;leftRankPolynomial;Sup;1|)
                    $))
         (QSETREFV $ 53
                   (CONS
                    (|dispatchFunction| |FRNAALG-;rightRankPolynomial;Sup;2|)
                    $))
         NIL
         (QSETREFV $ 72 (CONS (|dispatchFunction| |FRNAALG-;leftUnit;U;4|) $))
         (QSETREFV $ 80 (CONS (|dispatchFunction| |FRNAALG-;leftUnits;U;5|) $))
         NIL
         (QSETREFV $ 81 (CONS (|dispatchFunction| |FRNAALG-;rightUnit;U;7|) $))
         (QSETREFV $ 82
                   (CONS (|dispatchFunction| |FRNAALG-;rightUnits;U;8|) $))
         (QSETREFV $ 83 (CONS (|dispatchFunction| |FRNAALG-;unit;U;9|) $)))))
      $)))) 

(MAKEPROP '|FramedNonAssociativeAlgebra&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|PositiveInteger|) (0 . |rank|) (|Vector| $) (4 . |basis|)
              (|Vector| 56) (8 . |structuralConstants|) (|String|) (|Symbol|)
              (13 . |coerce|) (18 . |One|) (|SparseUnivariatePolynomial| 20)
              (22 . |One|) (|Polynomial| 7) (26 . |Zero|)
              (|NonNegativeInteger|) (|Matrix| 20) (30 . |new|) (37 . |One|)
              (|Integer|) (|Vector| 15) (41 . |elt|) (|List| 15) (|List| 22)
              (47 . |monomial|) (54 . |copy|) (|Vector| 23)
              (|CoerceVectorMatrixPackage| 7) (59 . |coerceP|)
              (64 . |horizConcat|) (70 . |elt|) (76 . *) (|Mapping| 23 23 23)
              (82 . |reduce|) (88 . |rank|) (93 . |transpose|) (|List| 26)
              (98 . |setelt|) (|List| 48) (106 . |nullSpace|) (111 . |Zero|)
              (|Vector| 20) (115 . |elt|) (121 . |monomial|) (127 . +)
              (133 . |leftRankPolynomial|) (137 . |rightRankPolynomial|)
              (141 . ^) (147 . |Zero|) (|Matrix| 7) (151 . |new|) (|Vector| 7)
              (158 . |setelt|) (165 . |elt|) (171 . |elt|) (178 . |setelt|)
              (|Union| 58 '"failed")
              (|Record| (|:| |particular| 63) (|:| |basis| 75))
              (|LinearSystemMatrixPackage| 7 58 58 56) (186 . |solve|) (|Void|)
              (|OutputForm|) (192 . |messagePrint|) (197 . |represents|)
              (|Union| $ '#1="failed") (202 . |leftUnit|) (|List| 6)
              (|Mapping| 6 58) (|List| 58) (|ListFunctions2| 58 6)
              (206 . |map|)
              (|Record| (|:| |particular| $) (|:| |basis| (|List| $)))
              (|Union| 78 '#1#) (212 . |leftUnits|) (216 . |rightUnit|)
              (220 . |rightUnits|) (224 . |unit|) (228 . |coordinates|)
              (233 . *) (239 . |convert|) |FRNAALG-;apply;M2S;10|
              |FRNAALG-;structuralConstants;V;11| (|List| 20)
              (244 . |conditionsForIdempotents|)
              |FRNAALG-;conditionsForIdempotents;L;12| (249 . |coordinates|)
              |FRNAALG-;convert;SV;13| (255 . |represents|)
              |FRNAALG-;convert;VS;14| (261 . |leftTraceMatrix|)
              |FRNAALG-;leftTraceMatrix;M;15| (266 . |rightTraceMatrix|)
              |FRNAALG-;rightTraceMatrix;M;16| (271 . |leftDiscriminant|)
              |FRNAALG-;leftDiscriminant;R;17| (276 . |rightDiscriminant|)
              |FRNAALG-;rightDiscriminant;R;18|
              (281 . |leftRegularRepresentation|)
              |FRNAALG-;leftRegularRepresentation;SM;19|
              (287 . |rightRegularRepresentation|)
              |FRNAALG-;rightRegularRepresentation;SM;20| (293 . |coordinates|)
              |FRNAALG-;coordinates;VM;23| |FRNAALG-;represents;VS;22|
              (|Vector| 6) (299 . |minIndex|) (304 . |setRow!|))
           '#(|unit| 311 |structuralConstants| 315 |rightUnits| 319 |rightUnit|
              323 |rightTraceMatrix| 327 |rightRegularRepresentation| 331
              |rightRankPolynomial| 336 |rightDiscriminant| 340 |represents|
              344 |leftUnits| 349 |leftUnit| 353 |leftTraceMatrix| 357
              |leftRegularRepresentation| 361 |leftRankPolynomial| 366
              |leftDiscriminant| 370 |coordinates| 374 |convert| 379
              |conditionsForIdempotents| 389 |apply| 393)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 113
                                                 '(0 6 8 9 0 6 10 11 1 6 12 10
                                                   13 1 15 0 14 16 0 7 0 17 0
                                                   18 0 19 0 20 0 21 3 23 0 22
                                                   22 20 24 0 20 0 25 2 27 15 0
                                                   26 28 3 20 0 0 29 30 31 1 23
                                                   0 0 32 1 34 33 12 35 2 23 0
                                                   0 0 36 2 33 23 0 26 37 2 23
                                                   0 0 0 38 2 33 23 39 0 40 1
                                                   23 22 0 41 1 23 0 0 42 4 23
                                                   0 0 43 43 0 44 1 23 45 0 46
                                                   0 18 0 47 2 48 20 0 26 49 2
                                                   18 0 20 22 50 2 18 0 0 0 51
                                                   0 0 18 52 0 0 18 53 2 8 0 0
                                                   8 54 0 7 0 55 3 56 0 22 22 7
                                                   57 3 58 7 0 26 7 59 2 12 56
                                                   0 26 60 3 56 7 0 26 26 61 4
                                                   56 7 0 26 26 7 62 2 65 64 56
                                                   58 66 1 68 67 14 69 1 6 0 58
                                                   70 0 0 71 72 2 76 73 74 75
                                                   77 0 0 79 80 0 0 71 81 0 0
                                                   79 82 0 0 71 83 1 6 58 0 84
                                                   2 56 58 0 58 85 1 6 0 58 86
                                                   1 6 89 10 90 2 6 58 0 10 92
                                                   2 6 0 58 10 94 1 6 56 10 96
                                                   1 6 56 10 98 1 6 7 10 100 1
                                                   6 7 10 102 2 6 56 0 10 104 2
                                                   6 56 0 10 106 2 6 56 10 10
                                                   108 1 111 26 0 112 3 56 0 0
                                                   26 58 113 0 0 71 83 0 0 12
                                                   88 0 0 79 82 0 0 71 81 0 0
                                                   56 99 1 0 56 0 107 0 0 18 53
                                                   0 0 7 103 1 0 0 58 110 0 0
                                                   79 80 0 0 71 72 0 0 56 97 1
                                                   0 56 0 105 0 0 18 52 0 0 7
                                                   101 1 0 56 10 109 1 0 0 58
                                                   95 1 0 58 0 93 0 0 89 91 2 0
                                                   0 56 0 87)))))
           '|lookupComplete|)) 
