
(/VERSIONCHECK 2) 

(PUT '|UTS;stream| '|SPADreplace| '(XLAM (|x|) |x|)) 

(DEFUN |UTS;stream| (|x| $) |x|) 

(DEFUN |UTS;coerce;V$;2| (|v| $)
  (COND
   ((SPADCALL (QREFELT $ 8) (QREFELT $ 11))
    (SPADCALL (|spadConstant| $ 12) 1 (QREFELT $ 15)))
   ('T
    (SPADCALL (SPADCALL (|spadConstant| $ 12) 1 (QREFELT $ 15))
              (SPADCALL (QREFELT $ 8) 0 (QREFELT $ 15)) (QREFELT $ 18))))) 

(DEFUN |UTS;coerce;I$;3| (|n| $)
  (SPADCALL (SPADCALL |n| (QREFELT $ 22)) (QREFELT $ 23))) 

(DEFUN |UTS;coerce;Coef$;4| (|r| $) (SPADCALL |r| (QREFELT $ 27))) 

(DEFUN |UTS;monomial;CoefNni$;5| (|c| |n| $) (SPADCALL |c| |n| (QREFELT $ 28))) 

(PUT '|UTS;getExpon| '|SPADreplace| 'QCAR) 

(DEFUN |UTS;getExpon| (|term| $) (QCAR |term|)) 

(PUT '|UTS;getCoef| '|SPADreplace| 'QCDR) 

(DEFUN |UTS;getCoef| (|term| $) (QCDR |term|)) 

(PUT '|UTS;rec| '|SPADreplace| 'CONS) 

(DEFUN |UTS;rec| (|expon| |coef| $) (CONS |expon| |coef|)) 

(DEFUN |UTS;recs| (|st| |n| $)
  (PROG ()
    (RETURN
     (SPADCALL (CONS #'|UTS;recs!0| (VECTOR |n| $ |st|)) (QREFELT $ 41))))) 

(DEFUN |UTS;recs!0| ($$)
  (PROG (|st| $ |n|)
    (LETT |st| (QREFELT $$ 2) . #1=(|UTS;recs|))
    (LETT $ (QREFELT $$ 1) . #1#)
    (LETT |n| (QREFELT $$ 0) . #1#)
    (RETURN
     (PROGN
      (PROG (|coef|)
        (RETURN
         (COND ((SPADCALL |st| (QREFELT $ 29)) (SPADCALL (QREFELT $ 38)))
               ((SPADCALL (LETT |coef| (SPADCALL |st| (QREFELT $ 31)) NIL)
                          (QREFELT $ 11))
                (|UTS;recs| (SPADCALL |st| (QREFELT $ 32))
                 (SPADCALL |n| (|spadConstant| $ 33) (QREFELT $ 34)) $))
               ('T
                (SPADCALL (|UTS;rec| |n| |coef| $)
                          (|UTS;recs| (SPADCALL |st| (QREFELT $ 32))
                           (SPADCALL |n| (|spadConstant| $ 33) (QREFELT $ 34))
                           $)
                          (QREFELT $ 39)))))))))) 

(DEFUN |UTS;terms;$S;10| (|x| $) (|UTS;recs| (|UTS;stream| |x| $) 0 $)) 

(DEFUN |UTS;recsToCoefs| (|st| |n| $)
  (PROG ()
    (RETURN
     (SEQ
      (SPADCALL (CONS #'|UTS;recsToCoefs!0| (VECTOR |n| $ |st|))
                (QREFELT $ 52)))))) 

(DEFUN |UTS;recsToCoefs!0| ($$)
  (PROG (|st| $ |n|)
    (LETT |st| (QREFELT $$ 2) . #1=(|UTS;recsToCoefs|))
    (LETT $ (QREFELT $$ 1) . #1#)
    (LETT |n| (QREFELT $$ 0) . #1#)
    (RETURN
     (PROGN
      (PROG (|term| |expon|)
        (RETURN
         (SEQ
          (COND ((SPADCALL |st| (QREFELT $ 43)) (SPADCALL (QREFELT $ 48)))
                ('T
                 (SEQ (LETT |term| (SPADCALL |st| (QREFELT $ 44)) NIL)
                      (LETT |expon| (|UTS;getExpon| |term| $) NIL)
                      (EXIT
                       (COND
                        ((SPADCALL |n| |expon| (QREFELT $ 45))
                         (SPADCALL (|UTS;getCoef| |term| $)
                                   (|UTS;recsToCoefs|
                                    (SPADCALL |st| (QREFELT $ 46))
                                    (SPADCALL |n| (|spadConstant| $ 33)
                                              (QREFELT $ 34))
                                    $)
                                   (QREFELT $ 49)))
                        ('T
                         (SPADCALL (|spadConstant| $ 16)
                                   (|UTS;recsToCoefs| |st|
                                    (SPADCALL |n| (|spadConstant| $ 33)
                                              (QREFELT $ 34))
                                    $)
                                   (QREFELT $ 49))))))))))))))) 

(DEFUN |UTS;series;S$;12| (|st| $) (|UTS;recsToCoefs| |st| 0 $)) 

(DEFUN |UTS;stToPoly| (|st| |term| |n| |n0| $)
  (COND
   ((OR (< |n0| |n|) (SPADCALL |st| (QREFELT $ 29))) (|spadConstant| $ 55))
   ('T
    (SPADCALL
     (SPADCALL (SPADCALL |st| (QREFELT $ 31))
               (SPADCALL |term| |n| (QREFELT $ 56)) (QREFELT $ 57))
     (|UTS;stToPoly| (SPADCALL |st| (QREFELT $ 32)) |term| (+ |n| 1) |n0| $)
     (QREFELT $ 58))))) 

(DEFUN |UTS;polynomial;$NniP;14| (|x| |n| $)
  (|UTS;stToPoly| (|UTS;stream| |x| $)
   (SPADCALL (SPADCALL (QREFELT $ 7) (QREFELT $ 60))
             (SPADCALL (QREFELT $ 8) (QREFELT $ 61)) (QREFELT $ 62))
   0 |n| $)) 

(DEFUN |UTS;polynomial;$2NniP;15| (|x| |n1| |n2| $)
  (PROG (|#G31| |#G30|)
    (RETURN
     (SEQ
      (COND
       ((< |n2| |n1|)
        (PROGN
         (LETT |#G30| |n2| . #1=(|UTS;polynomial;$2NniP;15|))
         (LETT |#G31| |n1| . #1#)
         (LETT |n1| |#G30| . #1#)
         (LETT |n2| |#G31| . #1#))))
      (EXIT
       (|UTS;stToPoly| (SPADCALL (|UTS;stream| |x| $) |n1| (QREFELT $ 64))
        (SPADCALL (SPADCALL (QREFELT $ 7) (QREFELT $ 60))
                  (SPADCALL (QREFELT $ 8) (QREFELT $ 61)) (QREFELT $ 62))
        |n1| |n2| $)))))) 

(DEFUN |UTS;stToUPoly| (|st| |term| |n| |n0| $)
  (COND
   ((OR (< |n0| |n|) (SPADCALL |st| (QREFELT $ 29))) (|spadConstant| $ 67))
   ('T
    (SPADCALL
     (SPADCALL (SPADCALL |st| (QREFELT $ 31))
               (SPADCALL |term| |n| (QREFELT $ 68)) (QREFELT $ 69))
     (|UTS;stToUPoly| (SPADCALL |st| (QREFELT $ 32)) |term| (+ |n| 1) |n0| $)
     (QREFELT $ 70))))) 

(DEFUN |UTS;univariatePolynomial;$NniUp;17| (|x| |n| $)
  (|UTS;stToUPoly| (|UTS;stream| |x| $)
   (SPADCALL (SPADCALL (|spadConstant| $ 12) 1 (QREFELT $ 71))
             (SPADCALL (QREFELT $ 8) 0 (QREFELT $ 71)) (QREFELT $ 72))
   0 |n| $)) 

(DEFUN |UTS;coerce;Up$;18| (|p| $)
  (PROG (|st| |i| |oldDeg| |delta| #1=#:G725 |deg|)
    (RETURN
     (SEQ
      (COND ((SPADCALL |p| (QREFELT $ 74)) (|spadConstant| $ 17))
            ('T
             (SEQ
              (COND
               ((NULL (SPADCALL (QREFELT $ 8) (QREFELT $ 11)))
                (LETT |p|
                      (SPADCALL |p|
                                (SPADCALL
                                 (SPADCALL (|spadConstant| $ 12) 1
                                           (QREFELT $ 71))
                                 (SPADCALL (QREFELT $ 8) 0 (QREFELT $ 71))
                                 (QREFELT $ 70))
                                (QREFELT $ 75))
                      . #2=(|UTS;coerce;Up$;18|))))
              (LETT |st| (SPADCALL (QREFELT $ 48)) . #2#)
              (LETT |oldDeg| (+ (SPADCALL |p| (QREFELT $ 76)) 1) . #2#)
              (SEQ G190
                   (COND
                    ((NULL (COND ((SPADCALL |p| (QREFELT $ 74)) 'NIL) ('T 'T)))
                     #3=(GO G191)))
                   (SEQ (LETT |deg| (SPADCALL |p| (QREFELT $ 76)) . #2#)
                        (LETT |delta|
                              (PROG1 (LETT #1# (- (- |oldDeg| |deg|) 1) . #2#)
                                (|check-subtype| (>= #1# 0)
                                                 '(|NonNegativeInteger|) #1#))
                              . #2#)
                        (SEQ (LETT |i| 1 . #2#) G190
                             (COND ((QSGREATERP |i| |delta|) #3#))
                             (SEQ
                              (EXIT
                               (LETT |st|
                                     (SPADCALL (|spadConstant| $ 16) |st|
                                               (QREFELT $ 49))
                                     . #2#)))
                             (LETT |i| (QSADD1 |i|) . #2#) #4=(GO G190) G191
                             (EXIT NIL))
                        (LETT |st|
                              (SPADCALL (SPADCALL |p| (QREFELT $ 77)) |st|
                                        (QREFELT $ 49))
                              . #2#)
                        (LETT |oldDeg| |deg| . #2#)
                        (EXIT (LETT |p| (SPADCALL |p| (QREFELT $ 78)) . #2#)))
                   NIL #4# G191 (EXIT NIL))
              (SEQ (LETT |i| 1 . #2#) G190
                   (COND ((QSGREATERP |i| |oldDeg|) #3#))
                   (SEQ
                    (EXIT
                     (LETT |st|
                           (SPADCALL (|spadConstant| $ 16) |st| (QREFELT $ 49))
                           . #2#)))
                   (LETT |i| (QSADD1 |i|) . #2#) #4# G191 (EXIT NIL))
              (EXIT |st|)))))))) 

(DEFUN |UTS;stToCoef| (|st| |term| |n| |n0| $)
  (COND
   ((OR (< |n0| |n|) (SPADCALL |st| (QREFELT $ 29))) (|spadConstant| $ 16))
   ('T
    (SPADCALL
     (SPADCALL (SPADCALL |st| (QREFELT $ 31))
               (SPADCALL |term| |n| (QREFELT $ 80)) (QREFELT $ 81))
     (|UTS;stToCoef| (SPADCALL |st| (QREFELT $ 32)) |term| (+ |n| 1) |n0| $)
     (QREFELT $ 82))))) 

(DEFUN |UTS;approximate;$NniCoef;20| (|x| |n| $)
  (|UTS;stToCoef| (|UTS;stream| |x| $)
   (SPADCALL (SPADCALL (QREFELT $ 7) (QREFELT $ 83)) (QREFELT $ 8)
             (QREFELT $ 84))
   0 |n| $)) 

(DEFUN |UTS;variable;$S;21| (|x| $) (QREFELT $ 7)) 

(DEFUN |UTS;center;$Coef;22| (|s| $) (QREFELT $ 8)) 

(DEFUN |UTS;coefficient;$NniCoef;23| (|x| |n| $)
  (PROG (#1=#:G740 |u|)
    (RETURN
     (SEQ (LETT |u| (|UTS;stream| |x| $) . #2=(|UTS;coefficient;$NniCoef;23|))
          (SEQ G190
               (COND
                ((NULL
                  (COND ((SPADCALL |u| (QREFELT $ 29)) 'NIL) ('T (< 0 |n|))))
                 (GO G191)))
               (SEQ (LETT |u| (SPADCALL |u| (QREFELT $ 35)) . #2#)
                    (EXIT
                     (LETT |n|
                           (PROG1 (LETT #1# (- |n| 1) . #2#)
                             (|check-subtype| (>= #1# 0)
                                              '(|NonNegativeInteger|) #1#))
                           . #2#)))
               NIL (GO G190) G191 (EXIT NIL))
          (COND
           ((OR (SPADCALL |u| (QREFELT $ 29)) (NULL (EQL |n| 0)))
            (EXIT (|spadConstant| $ 16))))
          (EXIT (SPADCALL |u| (QREFELT $ 31))))))) 

(DEFUN |UTS;elt;$NniCoef;24| (|x| |n| $) (SPADCALL |x| |n| (QREFELT $ 88))) 

(DEFUN |UTS;map;M2$;25| (|f| |x| $) (SPADCALL |f| |x| (QREFELT $ 91))) 

(DEFUN |UTS;eval;$CoefS;26| (|x| |r| $)
  (SPADCALL (|UTS;stream| |x| $) (SPADCALL |r| (QREFELT $ 8) (QREFELT $ 84))
            (QREFELT $ 93))) 

(DEFUN |UTS;differentiate;2$;27| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 95))) 

(DEFUN |UTS;differentiate;$V$;28| (|x| |v| $) (SPADCALL |x| (QREFELT $ 96))) 

(DEFUN |UTS;differentiate;$S$;29| (|x| |s| $)
  (PROG ()
    (RETURN
     (COND
      ((EQUAL |s| (SPADCALL |x| (QREFELT $ 86))) (SPADCALL |x| (QREFELT $ 96)))
      ('T
       (SPADCALL
        (SPADCALL (CONS #'|UTS;differentiate;$S$;29!0| (VECTOR $ |s|)) |x|
                  (QREFELT $ 92))
        (SPADCALL (SPADCALL (SPADCALL |x| (QREFELT $ 87)) |s| (QREFELT $ 98))
                  (SPADCALL |x| (QREFELT $ 96)) (QREFELT $ 99))
        (QREFELT $ 100))))))) 

(DEFUN |UTS;differentiate;$S$;29!0| (|y| $$)
  (PROG (|s| $)
    (LETT |s| (QREFELT $$ 1) . #1=(|UTS;differentiate;$S$;29|))
    (LETT $ (QREFELT $$ 0) . #1#)
    (RETURN (PROGN (SPADCALL |y| |s| (QREFELT $ 98)))))) 

(DEFUN |UTS;multiplyCoefficients;M2$;30| (|f| |x| $)
  (SPADCALL |f| (|UTS;stream| |x| $) (QREFELT $ 103))) 

(DEFUN |UTS;lagrange;2$;31| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 105))) 

(DEFUN |UTS;lambert;2$;32| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 107))) 

(DEFUN |UTS;oddlambert;2$;33| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 109))) 

(DEFUN |UTS;evenlambert;2$;34| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 111))) 

(DEFUN |UTS;generalLambert;$2I$;35| (|x| |a| |d| $)
  (SPADCALL (|UTS;stream| |x| $) |a| |d| (QREFELT $ 113))) 

(DEFUN |UTS;extend;$Nni$;36| (|x| |n| $)
  (SPADCALL |x| (+ |n| 1) (QREFELT $ 115))) 

(DEFUN |UTS;complete;2$;37| (|x| $) (SPADCALL |x| (QREFELT $ 117))) 

(DEFUN |UTS;truncate;$Nni$;38| (|x| |n| $)
  (SPADCALL (|UTS;stream| |x| $) (+ |n| 1) (QREFELT $ 119))) 

(DEFUN |UTS;truncate;$2Nni$;39| (|x| |n1| |n2| $)
  (PROG (|st| |i| |m| #1=#:G764 |#G80| |#G79|)
    (RETURN
     (SEQ
      (COND
       ((< |n2| |n1|)
        (PROGN
         (LETT |#G79| |n2| . #2=(|UTS;truncate;$2Nni$;39|))
         (LETT |#G80| |n1| . #2#)
         (LETT |n1| |#G79| . #2#)
         (LETT |n2| |#G80| . #2#))))
      (LETT |m|
            (PROG1 (LETT #1# (- |n2| |n1|) . #2#)
              (|check-subtype| (>= #1# 0) '(|NonNegativeInteger|) #1#))
            . #2#)
      (LETT |st|
            (SPADCALL (SPADCALL (|UTS;stream| |x| $) |n1| (QREFELT $ 121))
                      (+ |m| 1) (QREFELT $ 119))
            . #2#)
      (SEQ (LETT |i| 1 . #2#) G190 (COND ((QSGREATERP |i| |n1|) (GO G191)))
           (SEQ
            (EXIT
             (LETT |st| (SPADCALL (|spadConstant| $ 16) |st| (QREFELT $ 47))
                   . #2#)))
           (LETT |i| (QSADD1 |i|) . #2#) (GO G190) G191 (EXIT NIL))
      (EXIT |st|))))) 

(DEFUN |UTS;elt;3$;40| (|x| |y| $)
  (SPADCALL (|UTS;stream| |x| $) (|UTS;stream| |y| $) (QREFELT $ 123))) 

(DEFUN |UTS;revert;2$;41| (|x| $)
  (SPADCALL (|UTS;stream| |x| $) (QREFELT $ 125))) 

(DEFUN |UTS;multisect;2I2$;42| (|a| |b| |x| $)
  (SPADCALL |a| |b| (|UTS;stream| |x| $) (QREFELT $ 127))) 

(DEFUN |UTS;invmultisect;2I2$;43| (|a| |b| |x| $)
  (SPADCALL |a| |b| (|UTS;stream| |x| $) (QREFELT $ 129))) 

(DEFUN |UTS;multiplyExponents;$Pi$;44| (|x| |n| $)
  (SPADCALL |n| 0 |x| (QREFELT $ 130))) 

(DEFUN |UTS;quoByVar;2$;45| (|x| $)
  (COND ((SPADCALL |x| (QREFELT $ 29)) (|spadConstant| $ 17))
        ('T (SPADCALL |x| (QREFELT $ 35))))) 

(DEFUN |UTS;unit?;$B;46| (|x| $)
  (SPADCALL (SPADCALL |x| 0 (QREFELT $ 88)) (QREFELT $ 134))) 

(DEFUN |UTS;^;$Coef$;47| (|x| |s| $)
  (SPADCALL |s| (|UTS;stream| |x| $) (QREFELT $ 137))) 

(DEFUN |UTS;^;$Coef$;48| (|x| |s| $)
  (SPADCALL |s| (|UTS;stream| |x| $) (QREFELT $ 139))) 

(DEFUN |UTS;coerce;F$;49| (|r| $)
  (SPADCALL (SPADCALL |r| (QREFELT $ 140)) (QREFELT $ 23))) 

(DEFUN |UTS;integrate;2$;50| (|x| $)
  (SPADCALL (|spadConstant| $ 16) (|UTS;stream| |x| $) (QREFELT $ 142))) 

(DEFUN |UTS;integrate;$V$;51| (|x| |v| $) (SPADCALL |x| (QREFELT $ 143))) 

(DEFUN |UTS;integrate;$S$;52| (|x| |s| $)
  (PROG ()
    (RETURN
     (COND
      ((EQUAL |s| (SPADCALL |x| (QREFELT $ 86)))
       (SPADCALL |x| (QREFELT $ 143)))
      ((NULL
        (SPADCALL |s| (SPADCALL (SPADCALL |x| (QREFELT $ 87)) (QREFELT $ 146))
                  (QREFELT $ 147)))
       (SPADCALL (CONS #'|UTS;integrate;$S$;52!0| (VECTOR $ |s|)) |x|
                 (QREFELT $ 92)))
      ('T
       (|error|
        "integrate: center is a function of variable of integration")))))) 

(DEFUN |UTS;integrate;$S$;52!0| (|y| $$)
  (PROG (|s| $)
    (LETT |s| (QREFELT $$ 1) . #1=(|UTS;integrate;$S$;52|))
    (LETT $ (QREFELT $$ 0) . #1#)
    (RETURN (PROGN (SPADCALL |y| |s| (QREFELT $ 148)))))) 

(DEFUN |UTS;integrateWithOneAnswer| (|f| |s| $)
  (PROG (|res|)
    (RETURN
     (SEQ
      (LETT |res| (SPADCALL |f| |s| (QREFELT $ 152))
            |UTS;integrateWithOneAnswer|)
      (EXIT
       (COND ((QEQCAR |res| 0) (QCDR |res|))
             ('T (|SPADfirst| (QCDR |res|))))))))) 

(DEFUN |UTS;integrate;$S$;54| (|x| |s| $)
  (PROG ()
    (RETURN
     (COND
      ((EQUAL |s| (SPADCALL |x| (QREFELT $ 86)))
       (SPADCALL |x| (QREFELT $ 143)))
      ((NULL
        (SPADCALL |s| (SPADCALL (SPADCALL |x| (QREFELT $ 87)) (QREFELT $ 146))
                  (QREFELT $ 147)))
       (SPADCALL (CONS #'|UTS;integrate;$S$;54!0| (VECTOR $ |s|)) |x|
                 (QREFELT $ 92)))
      ('T
       (|error|
        "integrate: center is a function of variable of integration")))))) 

(DEFUN |UTS;integrate;$S$;54!0| (|y| $$)
  (PROG (|s| $)
    (LETT |s| (QREFELT $$ 1) . #1=(|UTS;integrate;$S$;54|))
    (LETT $ (QREFELT $$ 0) . #1#)
    (RETURN (PROGN (|UTS;integrateWithOneAnswer| |y| |s| $))))) 

(DEFUN |UnivariateTaylorSeries| (&REST #1=#:G804)
  (PROG ()
    (RETURN
     (PROG (#2=#:G805)
       (RETURN
        (COND
         ((LETT #2#
                (|lassocShiftWithFunction| (|devaluateList| #1#)
                                           (HGET |$ConstructorCache|
                                                 '|UnivariateTaylorSeries|)
                                           '|domainEqualList|)
                . #3=(|UnivariateTaylorSeries|))
          (|CDRwithIncrement| #2#))
         ('T
          (UNWIND-PROTECT
              (PROG1 (APPLY (|function| |UnivariateTaylorSeries;|) #1#)
                (LETT #2# T . #3#))
            (COND
             ((NOT #2#)
              (HREM |$ConstructorCache| '|UnivariateTaylorSeries|))))))))))) 

(DEFUN |UnivariateTaylorSeries;| (|#1| |#2| |#3|)
  (PROG (|pv$| #1=#:G803 $ |dv$| DV$3 DV$2 DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #2=(|UnivariateTaylorSeries|))
      (LETT DV$2 (|devaluate| |#2|) . #2#)
      (LETT DV$3 (|devaluate| |#3|) . #2#)
      (LETT |dv$| (LIST '|UnivariateTaylorSeries| DV$1 DV$2 DV$3) . #2#)
      (LETT $ (GETREFV 161) . #2#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3
                (LETT |pv$|
                      (|buildPredVector| 0 0
                                         (LIST
                                          (|HasCategory| |#1|
                                                         '(|Algebra|
                                                           (|Fraction|
                                                            (|Integer|))))
                                          (|HasCategory| |#1|
                                                         '(|IntegralDomain|))
                                          (LETT #1#
                                                (|HasCategory| |#1|
                                                               '(|CommutativeRing|))
                                                . #2#)
                                          (OR #1#
                                              (|HasCategory| |#1|
                                                             '(|IntegralDomain|)))
                                          (|HasCategory| |#1|
                                                         '(|CharacteristicNonZero|))
                                          (|HasCategory| |#1|
                                                         '(|CharacteristicZero|))
                                          (|HasSignature| |#1|
                                                          (LIST '*
                                                                (LIST
                                                                 (|devaluate|
                                                                  |#1|)
                                                                 '(|NonNegativeInteger|)
                                                                 (|devaluate|
                                                                  |#1|))))
                                          (AND
                                           (|HasCategory| |#1|
                                                          '(|PartialDifferentialRing|
                                                            (|Symbol|)))
                                           (|HasSignature| |#1|
                                                           (LIST '*
                                                                 (LIST
                                                                  (|devaluate|
                                                                   |#1|)
                                                                  '(|NonNegativeInteger|)
                                                                  (|devaluate|
                                                                   |#1|)))))
                                          (|HasCategory| (|NonNegativeInteger|)
                                                         '(|SemiGroup|))
                                          (|HasSignature| |#1|
                                                          (LIST '^
                                                                (LIST
                                                                 (|devaluate|
                                                                  |#1|)
                                                                 (|devaluate|
                                                                  |#1|)
                                                                 '(|NonNegativeInteger|))))
                                          (AND
                                           (|HasSignature| |#1|
                                                           (LIST '^
                                                                 (LIST
                                                                  (|devaluate|
                                                                   |#1|)
                                                                  (|devaluate|
                                                                   |#1|)
                                                                  '(|NonNegativeInteger|))))
                                           (|HasSignature| |#1|
                                                           (LIST '|coerce|
                                                                 (LIST
                                                                  (|devaluate|
                                                                   |#1|)
                                                                  '(|Symbol|)))))
                                          (|HasCategory| |#1| '(|Field|))
                                          (OR
                                           (AND
                                            (|HasCategory| |#1|
                                                           '(|PrimitiveFunctionCategory|))
                                            (|HasCategory| |#1|
                                                           '(|TranscendentalFunctionCategory|))
                                            (|HasCategory| |#1|
                                                           '(|AlgebraicallyClosedFunctionSpace|
                                                             (|Integer|)))
                                            (|HasCategory| |#1|
                                                           '(|Algebra|
                                                             (|Fraction|
                                                              (|Integer|)))))
                                           (AND
                                            (|HasCategory| |#1|
                                                           '(|Algebra|
                                                             (|Fraction|
                                                              (|Integer|))))
                                            (|HasSignature| |#1|
                                                            (LIST '|integrate|
                                                                  (LIST
                                                                   (|devaluate|
                                                                    |#1|)
                                                                   (|devaluate|
                                                                    |#1|)
                                                                   '(|Symbol|))))
                                            (|HasSignature| |#1|
                                                            (LIST '|variables|
                                                                  (LIST
                                                                   '(|List|
                                                                     (|Symbol|))
                                                                   (|devaluate|
                                                                    |#1|))))))))
                      . #2#))
      (|haddProp| |$ConstructorCache| '|UnivariateTaylorSeries|
                  (LIST DV$1 DV$2 DV$3) (CONS 1 $))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      (QSETREFV $ 7 |#2|)
      (QSETREFV $ 8 |#3|)
      (QSETREFV $ 9 (|Stream| |#1|))
      (COND
       ((|HasSignature| |#1|
                        (LIST '|coerce| (LIST (|devaluate| |#1|) '(|Symbol|))))
        (COND
         ((|testBitVector| |pv$| 10)
          (PROGN
           (QSETREFV $ 85
                     (CONS (|dispatchFunction| |UTS;approximate;$NniCoef;20|)
                           $)))))))
      (COND
       ((|HasCategory| |#1| '(|PartialDifferentialRing| (|Symbol|)))
        (QSETREFV $ 101
                  (CONS (|dispatchFunction| |UTS;differentiate;$S$;29|) $))))
      (COND
       ((|testBitVector| |pv$| 2)
        (QSETREFV $ 135 (CONS (|dispatchFunction| |UTS;unit?;$B;46|) $))))
      (COND
       ((|testBitVector| |pv$| 12)
        (COND
         ((|domainEqual| |#1| (|Fraction| (|Integer|)))
          (QSETREFV $ 138 (CONS (|dispatchFunction| |UTS;^;$Coef$;47|) $)))
         ('T
          (QSETREFV $ 138 (CONS (|dispatchFunction| |UTS;^;$Coef$;48|) $))))))
      (COND
       ((|testBitVector| |pv$| 1)
        (PROGN
         (QSETREFV $ 141 (CONS (|dispatchFunction| |UTS;coerce;F$;49|) $))
         (QSETREFV $ 143 (CONS (|dispatchFunction| |UTS;integrate;2$;50|) $))
         (QSETREFV $ 144 (CONS (|dispatchFunction| |UTS;integrate;$V$;51|) $))
         (COND
          ((|HasSignature| |#1|
                           (LIST '|integrate|
                                 (LIST (|devaluate| |#1|) (|devaluate| |#1|)
                                       '(|Symbol|))))
           (COND
            ((|HasSignature| |#1|
                             (LIST '|variables|
                                   (LIST '(|List| (|Symbol|))
                                         (|devaluate| |#1|))))
             (QSETREFV $ 149
                       (CONS (|dispatchFunction| |UTS;integrate;$S$;52|)
                             $))))))
         (COND
          ((|HasCategory| |#1| '(|TranscendentalFunctionCategory|))
           (COND
            ((|HasCategory| |#1| '(|PrimitiveFunctionCategory|))
             (COND
              ((|HasCategory| |#1|
                              '(|AlgebraicallyClosedFunctionSpace|
                                (|Integer|)))
               (PROGN
                (QSETREFV $ 149
                          (CONS (|dispatchFunction| |UTS;integrate;$S$;54|)
                                $))))))))))))
      $)))) 

(MAKEPROP '|UnivariateTaylorSeries| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL (|InnerTaylorSeries| 6) (|local| |#1|)
              (|local| |#2|) (|local| |#3|) '|Rep| (|Boolean|) (0 . |zero?|)
              (5 . |One|) (9 . |One|) (|NonNegativeInteger|)
              |UTS;monomial;CoefNni$;5| (13 . |Zero|) (17 . |Zero|) (21 . +)
              (|Variable| 7) |UTS;coerce;V$;2| (|Integer|) (27 . |coerce|)
              |UTS;coerce;Coef$;4| |UTS;coerce;I$;3| (|Stream| 6)
              (|StreamTaylorSeriesOperations| 6) (32 . |coerce|) (37 . |monom|)
              (43 . |empty?|) (48 . |empty|) (52 . |frst|) (57 . |rst|)
              (62 . |One|) (66 . +) (72 . |rst|)
              (|Record| (|:| |k| 14) (|:| |c| 6)) (|Stream| 36) (77 . |empty|)
              (81 . |concat|) (|Mapping| $) (87 . |delay|) |UTS;terms;$S;10|
              (92 . |empty?|) (97 . |frst|) (102 . =) (108 . |rst|)
              (113 . |concat|) (119 . |empty|) (123 . |concat|) (129 . |Zero|)
              (133 . |Zero|) (137 . |delay|) |UTS;series;S$;12|
              (|Polynomial| 6) (142 . |Zero|) (146 . ^) (152 . *) (158 . +)
              (|Symbol|) (164 . |coerce|) (169 . |coerce|) (174 . -)
              |UTS;polynomial;$NniP;14| (180 . |rest|)
              |UTS;polynomial;$2NniP;15| (|UnivariatePolynomial| 7 6)
              (186 . |Zero|) (190 . ^) (196 . *) (202 . +) (208 . |monomial|)
              (214 . -) |UTS;univariatePolynomial;$NniUp;17| (220 . |zero?|)
              (225 . |elt|) (231 . |degree|) (236 . |leadingCoefficient|)
              (241 . |reductum|) |UTS;coerce;Up$;18| (246 . ^) (252 . *)
              (258 . +) (264 . |coerce|) (269 . -) (275 . |approximate|)
              |UTS;variable;$S;21| |UTS;center;$Coef;22|
              |UTS;coefficient;$NniCoef;23| |UTS;elt;$NniCoef;24|
              (|Mapping| 6 6) (281 . |map|) |UTS;map;M2$;25| (287 . |eval|)
              |UTS;eval;$CoefS;26| (293 . |deriv|) |UTS;differentiate;2$;27|
              |UTS;differentiate;$V$;28| (298 . |differentiate|) (304 . *)
              (310 . -) (316 . |differentiate|) (|Mapping| 6 21)
              (322 . |gderiv|) |UTS;multiplyCoefficients;M2$;30|
              (328 . |lagrange|) |UTS;lagrange;2$;31| (333 . |lambert|)
              |UTS;lambert;2$;32| (338 . |oddlambert|) |UTS;oddlambert;2$;33|
              (343 . |evenlambert|) |UTS;evenlambert;2$;34|
              (348 . |generalLambert|) |UTS;generalLambert;$2I$;35|
              (355 . |extend|) |UTS;extend;$Nni$;36| (361 . |complete|)
              |UTS;complete;2$;37| (366 . |first|) |UTS;truncate;$Nni$;38|
              (372 . |rest|) |UTS;truncate;$2Nni$;39| (378 . |compose|)
              |UTS;elt;3$;40| (384 . |revert|) |UTS;revert;2$;41|
              (389 . |multisect|) |UTS;multisect;2I2$;42|
              (396 . |invmultisect|) |UTS;invmultisect;2I2$;43|
              (|PositiveInteger|) |UTS;multiplyExponents;$Pi$;44|
              |UTS;quoByVar;2$;45| (403 . |unit?|) (408 . |unit?|)
              (|Fraction| 21) (413 . |powern|) (419 . ^) (425 . |power|)
              (431 . |coerce|) (436 . |coerce|) (441 . |integrate|)
              (447 . |integrate|) (452 . |integrate|) (|List| 59)
              (458 . |variables|) (463 . |entry?|) (469 . |integrate|)
              (475 . |integrate|) (|Union| 6 (|List| 6))
              (|FunctionSpaceIntegration| 21 6) (481 . |integrate|) (|List| 14)
              (|Union| $ '"failed")
              (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))
              (|List| 157) (|SingletonAsOrderedSet|) (|SingleInteger|)
              (|String|) (|OutputForm|))
           '#(~= 487 |zero?| 493 |variables| 498 |variable| 503
              |univariatePolynomial| 508 |unitNormal| 514 |unitCanonical| 519
              |unit?| 524 |truncate| 529 |terms| 542 |tanh| 547 |tan| 552
              |subtractIfCan| 557 |sqrt| 563 |sinh| 568 |sin| 573 |series| 578
              |sech| 588 |sec| 593 |sample| 598 |revert| 602 |reductum| 607
              |recip| 612 |quoByVar| 617 |polynomial| 622 |pole?| 635 |pi| 640
              |order| 644 |one?| 655 |oddlambert| 660 |nthRoot| 665 |multisect|
              671 |multiplyExponents| 678 |multiplyCoefficients| 684
              |monomial?| 690 |monomial| 695 |map| 715 |log| 721
              |leadingMonomial| 726 |leadingCoefficient| 731 |latex| 736
              |lambert| 741 |lagrange| 746 |invmultisect| 751 |integrate| 758
              |hash| 775 |generalLambert| 780 |extend| 787 |exquo| 793 |exp|
              799 |evenlambert| 804 |eval| 809 |elt| 815 |differentiate| 827
              |degree| 870 |csch| 875 |csc| 880 |coth| 885 |cot| 890 |cosh| 895
              |cos| 900 |complete| 905 |coerce| 910 |coefficients| 945
              |coefficient| 950 |charthRoot| 956 |characteristic| 961 |center|
              965 |atanh| 970 |atan| 975 |associates?| 980 |asinh| 986 |asin|
              991 |asech| 996 |asec| 1001 |approximate| 1006 |acsch| 1012
              |acsc| 1017 |acoth| 1022 |acot| 1027 |acosh| 1032 |acos| 1037 ^
              1042 |Zero| 1072 |One| 1076 D 1080 = 1117 / 1123 - 1129 + 1140 *
              1146)
           'NIL
           (CONS
            (|makeByteWordVec2| 9
                                '(0 0 0 0 2 1 2 3 1 4 2 2 5 6 3 8 7 0 0 1 4 0 0
                                  0 0 1 1 3 0 0 0 0 0 0 0 0 0 1 0 0 0 3 2 9 1 1
                                  1 1 1 1))
            (CONS
             '#(|UnivariateTaylorSeriesCategory&|
                |UnivariatePowerSeriesCategory&| |PowerSeriesCategory&|
                |AbelianMonoidRing&| |IntegralDomain&| |Algebra&| |Algebra&|
                |Algebra&| |Module&| NIL |Module&| NIL NIL NIL |Module&|
                |PartialDifferentialRing&| |DifferentialRing&| |Ring&| NIL NIL
                NIL NIL NIL NIL NIL NIL NIL NIL |AbelianGroup&| NIL NIL
                |AbelianMonoid&| |Monoid&| NIL |SemiGroup&| |AbelianSemiGroup&|
                |SetCategory&| |TranscendentalFunctionCategory&| NIL
                |BasicType&| NIL NIL NIL NIL |TrigonometricFunctionCategory&|
                |ArcTrigonometricFunctionCategory&|
                |HyperbolicFunctionCategory&| NIL |ElementaryFunctionCategory&|
                |RadicalCategory&|)
             (CONS
              '#((|UnivariateTaylorSeriesCategory| 6)
                 (|UnivariatePowerSeriesCategory| 6 14)
                 (|PowerSeriesCategory| 6 14 157) (|AbelianMonoidRing| 6 14)
                 (|IntegralDomain|) (|Algebra| 136) (|Algebra| $$)
                 (|Algebra| 6) (|Module| 136) (|CommutativeRing|) (|Module| $$)
                 (|EntireRing|) (|CharacteristicNonZero|)
                 (|CharacteristicZero|) (|Module| 6)
                 (|PartialDifferentialRing| 59) (|DifferentialRing|) (|Ring|)
                 (|BiModule| 6 6) (|BiModule| 136 136) (|BiModule| $$ $$)
                 (|Rng|) (|LeftModule| 6) (|RightModule| 6) (|LeftModule| $$)
                 (|LeftModule| 136) (|RightModule| 136) (|RightModule| $$)
                 (|AbelianGroup|) (|CancellationAbelianMonoid|) (|SemiRing|)
                 (|AbelianMonoid|) (|Monoid|) (|SemiRng|) (|SemiGroup|)
                 (|AbelianSemiGroup|) (|SetCategory|)
                 (|TranscendentalFunctionCategory|) (|unitsKnown|)
                 (|BasicType|) (|CoercibleTo| 160) (|CommutativeStar|)
                 (|noZeroDivisors|) (|Eltable| $$ $$)
                 (|TrigonometricFunctionCategory|)
                 (|ArcTrigonometricFunctionCategory|)
                 (|HyperbolicFunctionCategory|)
                 (|ArcHyperbolicFunctionCategory|)
                 (|ElementaryFunctionCategory|) (|RadicalCategory|))
              (|makeByteWordVec2| 160
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                                    41 1 37 10 0 43 1 37 36 0 44 2 14 10 0 0 45
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                                    25 136 25 137 2 0 0 0 6 138 2 26 25 6 25
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                                    146 2 145 10 59 0 147 2 6 0 0 59 148 2 0 0
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                                    0 0 145 153 1 1 7 0 0 1 2 7 0 0 14 1 2 0 10
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                                    0 0 0 6 1 2 0 0 6 0 99 2 0 0 0 0 1 2 0 0 21
                                    0 1 2 0 0 14 0 1 2 0 0 131 0 1)))))
           '|lookupComplete|)) 
