
(DEFPARAMETER |XFreeAlgebra;CAT| 'NIL) 

(DECLAIM (NOTINLINE |XFreeAlgebra;|)) 

(DEFPARAMETER |XFreeAlgebra;AL| 'NIL) 

(DEFUN |XFreeAlgebra| (|t#1| |t#2|)
  (LET (#1=#:G3 (#2=#:G4 (LIST (|devaluate| |t#1|) (|devaluate| |t#2|))))
    (COND ((SETQ #1# (|assoc| #2# |XFreeAlgebra;AL|)) (CDR #1#))
          (T
           (SETQ |XFreeAlgebra;AL|
                   (|cons5| (CONS #2# (SETQ #1# (APPLY #'|XFreeAlgebra;| #2#)))
                            |XFreeAlgebra;AL|))
           #1#)))) 

(DEFUN |XFreeAlgebra;| (|t#1| |t#2|)
  (SPROG ((#1=#:G2 NIL))
         (PROG1
             (LETT #1#
                   (|subst_in_cat| '(|t#1| |t#2|) (LIST |t#1| |t#2|)
                                   (|subst_in_cat| '(#2=#:G1)
                                                   (LIST '(|FreeMonoid| |t#1|))
                                                   (COND (|XFreeAlgebra;CAT|)
                                                         ('T
                                                          (LETT
                                                           |XFreeAlgebra;CAT|
                                                           (|Join|
                                                            (|XAlgebra| '|t#2|)
                                                            (|RetractableTo|
                                                             '|t#2|)
                                                            (|RetractableTo|
                                                             '#2#)
                                                            (|mkCategory|
                                                             '(((* (% |t#1| %))
                                                                T)
                                                               ((* (% % |t#2|))
                                                                T)
                                                               ((|mindeg|
                                                                 ((|FreeMonoid|
                                                                   |t#1|)
                                                                  %))
                                                                T)
                                                               ((|mindegTerm|
                                                                 ((|Record|
                                                                   (|:| |k|
                                                                        (|FreeMonoid|
                                                                         |t#1|))
                                                                   (|:| |c|
                                                                        |t#2|))
                                                                  %))
                                                                T)
                                                               ((|coef|
                                                                 (|t#2| %
                                                                  (|FreeMonoid|
                                                                   |t#1|)))
                                                                T)
                                                               ((|coef|
                                                                 (|t#2| % %))
                                                                T)
                                                               ((|lquo|
                                                                 (% % |t#1|))
                                                                T)
                                                               ((|lquo|
                                                                 (% %
                                                                  (|FreeMonoid|
                                                                   |t#1|)))
                                                                T)
                                                               ((|lquo|
                                                                 (% % %))
                                                                T)
                                                               ((|rquo|
                                                                 (% % |t#1|))
                                                                T)
                                                               ((|rquo|
                                                                 (% %
                                                                  (|FreeMonoid|
                                                                   |t#1|)))
                                                                T)
                                                               ((|rquo|
                                                                 (% % %))
                                                                T)
                                                               ((|monomial|
                                                                 (% |t#2|
                                                                  (|FreeMonoid|
                                                                   |t#1|)))
                                                                T)
                                                               ((|monomial?|
                                                                 ((|Boolean|)
                                                                  %))
                                                                T)
                                                               ((|mirror|
                                                                 (% %))
                                                                T)
                                                               ((|coerce|
                                                                 (% |t#1|))
                                                                T)
                                                               ((|constant?|
                                                                 ((|Boolean|)
                                                                  %))
                                                                T)
                                                               ((|constant|
                                                                 (|t#2| %))
                                                                T)
                                                               ((|quasiRegular?|
                                                                 ((|Boolean|)
                                                                  %))
                                                                T)
                                                               ((|quasiRegular|
                                                                 (% %))
                                                                T)
                                                               ((|sh| (% % %))
                                                                (|has| |t#2|
                                                                       (|CommutativeRing|)))
                                                               ((|sh|
                                                                 (% %
                                                                  (|NonNegativeInteger|)))
                                                                (|has| |t#2|
                                                                       (|CommutativeRing|)))
                                                               ((|map|
                                                                 (%
                                                                  (|Mapping|
                                                                   |t#2| |t#2|)
                                                                  %))
                                                                T)
                                                               ((|varList|
                                                                 ((|List|
                                                                   |t#1|)
                                                                  %))
                                                                T))
                                                             '(((|noZeroDivisors|)
                                                                (|has| |t#2|
                                                                       (|noZeroDivisors|))))
                                                             NIL NIL))))))))
           (SETELT #1# 0 (LIST '|XFreeAlgebra| |t#1| |t#2|))))) 
