
(/VERSIONCHECK 2) 

(DEFUN |RCFIELD-;sqrt;2S;1| (|a| $) (SPADCALL |a| 2 (QREFELT $ 8))) 

(DEFUN |RCFIELD-;sqrt;FS;2| (|a| $)
  (SPADCALL (SPADCALL |a| (QREFELT $ 11)) 2 (QREFELT $ 8))) 

(DEFUN |RCFIELD-;sqrt;IS;3| (|a| $)
  (SPADCALL (SPADCALL |a| (QREFELT $ 14)) 2 (QREFELT $ 8))) 

(PUT '|RCFIELD-;characteristic;Nni;4| '|SPADreplace| '(XLAM NIL 0)) 

(DEFUN |RCFIELD-;characteristic;Nni;4| ($) 0) 

(DEFUN |RCFIELD-;rootOf;SupPiOfU;5| (|pol| |n| |o| $)
  (PROG (|r|)
    (RETURN
     (SEQ
      (LETT |r| (SPADCALL |pol| |n| (QREFELT $ 20))
            |RCFIELD-;rootOf;SupPiOfU;5|)
      (EXIT
       (COND ((QEQCAR |r| 1) (CONS 1 "failed"))
             ('T (CONS 0 (SPADCALL (QCDR |r|) |o| (QREFELT $ 22)))))))))) 

(DEFUN |RCFIELD-;rootOf;SupPiU;6| (|pol| |n| $)
  (PROG (|liste|)
    (RETURN
     (SEQ
      (LETT |liste| (SPADCALL |pol| (QREFELT $ 25)) |RCFIELD-;rootOf;SupPiU;6|)
      (EXIT
       (COND ((< |n| (LENGTH |liste|)) (CONS 1 "failed"))
             ('T (CONS 0 (SPADCALL |liste| |n| (QREFELT $ 27)))))))))) 

(DEFUN |RCFIELD-;sqrt;SPiS;7| (|x| |n| $)
  (PROG (|r|)
    (RETURN
     (SEQ
      (COND ((EQL |n| 1) |x|)
            ((SPADCALL |x| (QREFELT $ 31)) (|spadConstant| $ 32))
            ((SPADCALL |x| (QREFELT $ 33)) (|spadConstant| $ 29))
            (#1='T
             (SEQ
              (COND
               ((ODDP |n|)
                (LETT |r|
                      (SPADCALL
                       (SPADCALL
                        (SPADCALL (|spadConstant| $ 29) |n| (QREFELT $ 35))
                        (SPADCALL |x| (QREFELT $ 36)) (QREFELT $ 37))
                       1 (QREFELT $ 20))
                      . #2=(|RCFIELD-;sqrt;SPiS;7|)))
               (#1#
                (LETT |r|
                      (SPADCALL
                       (SPADCALL
                        (SPADCALL (|spadConstant| $ 29) |n| (QREFELT $ 35))
                        (SPADCALL |x| (QREFELT $ 36)) (QREFELT $ 37))
                       2 (QREFELT $ 20))
                      . #2#)))
              (EXIT
               (COND ((QEQCAR |r| 1) (|error| "no roots"))
                     ((EQL |n| 2)
                      (SPADCALL (QCDR |r|)
                                (SPADCALL (SPADCALL |x| (QREFELT $ 38))
                                          (QREFELT $ 39))
                                (QREFELT $ 40)))
                     (#1#
                      (SPADCALL (QCDR |r|)
                                (SPADCALL (SPADCALL |x| (QREFELT $ 38))
                                          (SPADCALL |n| (QREFELT $ 41))
                                          (QREFELT $ 42))
                                (QREFELT $ 40)))))))))))) 

(DEFUN |RCFIELD-;^;SFS;8| (|x| |rn| $)
  (PROG (#1=#:G10832)
    (RETURN
     (SPADCALL (SPADCALL |x| (SPADCALL |rn| (QREFELT $ 44)) (QREFELT $ 45))
               (PROG1
                   (LETT #1# (SPADCALL |rn| (QREFELT $ 46)) |RCFIELD-;^;SFS;8|)
                 (|check-subtype| (> #1# 0) '(|PositiveInteger|) #1#))
               (QREFELT $ 8))))) 

(DEFUN |RCFIELD-;nthRoot;SIS;9| (|x| |n| $)
  (PROG (#1=#:G10835 #2=#:G10834)
    (RETURN
     (COND ((ZEROP |n|) |x|)
           ((MINUSP |n|)
            (SPADCALL
             (SPADCALL |x|
                       (PROG1
                           (LETT #2# (- |n|) . #3=(|RCFIELD-;nthRoot;SIS;9|))
                         (|check-subtype| (> #2# 0) '(|PositiveInteger|) #2#))
                       (QREFELT $ 8))
             (QREFELT $ 48)))
           ('T
            (SPADCALL |x|
                      (PROG1 (LETT #1# |n| . #3#)
                        (|check-subtype| (> #1# 0) '(|PositiveInteger|) #1#))
                      (QREFELT $ 8))))))) 

(DEFUN |RCFIELD-;allRootsOf;SupL;10| (|p| $)
  (SPADCALL (SPADCALL (ELT $ 11) |p| (QREFELT $ 53)) (QREFELT $ 25))) 

(DEFUN |RCFIELD-;allRootsOf;SupL;11| (|p| $)
  (SPADCALL (SPADCALL (ELT $ 14) |p| (QREFELT $ 58)) (QREFELT $ 25))) 

(DEFUN |RCFIELD-;allRootsOf;PL;12| (|p| $)
  (SPADCALL (SPADCALL |p| (QREFELT $ 61)) (QREFELT $ 25))) 

(DEFUN |RCFIELD-;allRootsOf;PL;13| (|p| $)
  (SPADCALL (SPADCALL |p| (QREFELT $ 65)) (QREFELT $ 66))) 

(DEFUN |RCFIELD-;allRootsOf;PL;14| (|p| $)
  (SPADCALL (SPADCALL |p| (QREFELT $ 69)) (QREFELT $ 70))) 

(DEFUN |RealClosedField&| (|#1|)
  (PROG (|pv$| $ |dv$| DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #1=(|RealClosedField&|))
      (LETT |dv$| (LIST '|RealClosedField&| DV$1) . #1#)
      (LETT $ (GETREFV 72) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      $)))) 

(MAKEPROP '|RealClosedField&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|PositiveInteger|)
              (0 . |sqrt|) |RCFIELD-;sqrt;2S;1| (|Fraction| 13) (6 . |coerce|)
              |RCFIELD-;sqrt;FS;2| (|Integer|) (11 . |coerce|)
              |RCFIELD-;sqrt;IS;3| (|NonNegativeInteger|)
              |RCFIELD-;characteristic;Nni;4| (|Union| $ '"failed")
              (|SparseUnivariatePolynomial| $) (16 . |rootOf|) (|OutputForm|)
              (22 . |rename!|) |RCFIELD-;rootOf;SupPiOfU;5| (|List| $)
              (28 . |allRootsOf|) (|List| 6) (33 . |elt|)
              |RCFIELD-;rootOf;SupPiU;6| (39 . |One|) (|Boolean|)
              (43 . |zero?|) (48 . |Zero|) (52 . |one?|)
              (|SparseUnivariatePolynomial| 6) (57 . |monomial|)
              (63 . |coerce|) (68 . -) (74 . |coerce|) (79 . |root|)
              (84 . |rename|) (90 . |coerce|) (95 . |root|)
              |RCFIELD-;sqrt;SPiS;7| (101 . |numer|) (106 . ^) (112 . |denom|)
              |RCFIELD-;^;SFS;8| (117 . |inv|) |RCFIELD-;nthRoot;SIS;9|
              (|Mapping| 6 10) (|SparseUnivariatePolynomial| 10)
              (|SparseUnivariatePolynomialFunctions2| 10 6) (122 . |map|)
              |RCFIELD-;allRootsOf;SupL;10| (|Mapping| 6 13)
              (|SparseUnivariatePolynomial| 13)
              (|SparseUnivariatePolynomialFunctions2| 13 6) (128 . |map|)
              |RCFIELD-;allRootsOf;SupL;11| (|Polynomial| 6)
              (134 . |univariate|) (|Polynomial| $) |RCFIELD-;allRootsOf;PL;12|
              (|Polynomial| 10) (139 . |univariate|) (144 . |allRootsOf|)
              |RCFIELD-;allRootsOf;PL;13| (|Polynomial| 13)
              (149 . |univariate|) (154 . |allRootsOf|)
              |RCFIELD-;allRootsOf;PL;14|)
           '#(|sqrt| 159 |rootOf| 180 |nthRoot| 193 |characteristic| 199
              |allRootsOf| 203 ^ 228)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 71
                                                 '(2 6 0 0 7 8 1 6 0 10 11 1 6
                                                   0 13 14 2 6 18 19 7 20 2 6 0
                                                   0 21 22 1 6 24 19 25 2 26 6
                                                   0 13 27 0 6 0 29 1 6 30 0 31
                                                   0 6 0 32 1 6 30 0 33 2 34 0
                                                   6 16 35 1 34 0 6 36 2 34 0 0
                                                   0 37 1 6 21 0 38 1 21 0 0 39
                                                   2 6 0 0 21 40 1 7 21 0 41 2
                                                   21 0 0 0 42 1 10 13 0 44 2 6
                                                   0 0 13 45 1 10 13 0 46 1 6 0
                                                   0 48 2 52 34 50 51 53 2 57
                                                   34 55 56 58 1 60 34 0 61 1
                                                   64 51 0 65 1 6 24 51 66 1 68
                                                   56 0 69 1 6 24 56 70 1 0 0
                                                   10 12 1 0 0 13 15 2 0 0 0 7
                                                   43 1 0 0 0 9 3 0 18 19 7 21
                                                   23 2 0 18 19 7 28 2 0 0 0 13
                                                   49 0 0 16 17 1 0 24 68 71 1
                                                   0 24 62 63 1 0 24 64 67 1 0
                                                   24 56 59 1 0 24 51 54 2 0 0
                                                   0 10 47)))))
           '|lookupComplete|)) 
