
(DEFPARAMETER |MultivariateTaylorSeriesCategory;CAT| 'NIL) 

(DECLAIM (NOTINLINE |MultivariateTaylorSeriesCategory;|)) 

(DEFPARAMETER |MultivariateTaylorSeriesCategory;AL| 'NIL) 

(DEFUN |MultivariateTaylorSeriesCategory| (|t#1| |t#2|)
  (LET (#1=#:G692 (#2=#:G693 (LIST (|devaluate| |t#1|) (|devaluate| |t#2|))))
    (COND
     ((SETQ #1# (|assoc| #2# |MultivariateTaylorSeriesCategory;AL|)) (CDR #1#))
     (T
      (SETQ |MultivariateTaylorSeriesCategory;AL|
              (|cons5|
               (CONS #2#
                     (SETQ #1#
                             (APPLY #'|MultivariateTaylorSeriesCategory;|
                                    #2#)))
               |MultivariateTaylorSeriesCategory;AL|))
      #1#)))) 

(DEFUN |MultivariateTaylorSeriesCategory;| (|t#1| |t#2|)
  (SPROG ((#1=#:G691 NIL))
         (PROG1
             (LETT #1#
                   (|sublisV| (PAIR '(|t#1| |t#2|) (LIST |t#1| |t#2|))
                              (|sublisV|
                               (PAIR '(#2=#:G690)
                                     (LIST '(|IndexedExponents| |t#2|)))
                               (COND (|MultivariateTaylorSeriesCategory;CAT|)
                                     ('T
                                      (LETT
                                       |MultivariateTaylorSeriesCategory;CAT|
                                       (|Join|
                                        (|PartialDifferentialRing| '|t#2|)
                                        (|PowerSeriesCategory| '|t#1| '#2#
                                                               '|t#2|)
                                        (|InnerEvalable| '|t#2| '$)
                                        (|Evalable| '$)
                                        (|mkCategory|
                                         '(((|coefficient|
                                             ($ $ |t#2|
                                              (|NonNegativeInteger|)))
                                            T)
                                           ((|coefficient|
                                             ($ $ (|List| |t#2|)
                                              (|List| (|NonNegativeInteger|))))
                                            T)
                                           ((|extend|
                                             ($ $ (|NonNegativeInteger|)))
                                            T)
                                           ((|monomial|
                                             ($ $ |t#2|
                                              (|NonNegativeInteger|)))
                                            T)
                                           ((|monomial|
                                             ($ $ (|List| |t#2|)
                                              (|List| (|NonNegativeInteger|))))
                                            T)
                                           ((|order|
                                             ((|NonNegativeInteger|) $ |t#2|))
                                            T)
                                           ((|order|
                                             ((|NonNegativeInteger|) $ |t#2|
                                              (|NonNegativeInteger|)))
                                            T)
                                           ((|polynomial|
                                             ((|Polynomial| |t#1|) $
                                              (|NonNegativeInteger|)))
                                            T)
                                           ((|polynomial|
                                             ((|Polynomial| |t#1|) $
                                              (|NonNegativeInteger|)
                                              (|NonNegativeInteger|)))
                                            T)
                                           ((|integrate| ($ $ |t#2|))
                                            (|has| |t#1|
                                                   (|Algebra|
                                                    (|Fraction|
                                                     (|Integer|))))))
                                         '(((|RadicalCategory|)
                                            (|has| |t#1|
                                                   (|Algebra|
                                                    (|Fraction| (|Integer|)))))
                                           ((|TranscendentalFunctionCategory|)
                                            (|has| |t#1|
                                                   (|Algebra|
                                                    (|Fraction|
                                                     (|Integer|))))))
                                         NIL NIL))))))))
           (SETELT #1# 0
                   (LIST '|MultivariateTaylorSeriesCategory| |t#1| |t#2|))))) 
