
(/VERSIONCHECK 2) 

(DEFPARAMETER |RealClosedField;AL| 'NIL) 

(DEFUN |RealClosedField| ()
  (LET (#:G10795)
    (COND (|RealClosedField;AL|)
          (T (SETQ |RealClosedField;AL| (|RealClosedField;|)))))) 

(DEFUN |RealClosedField;| ()
  (PROG (#1=#:G10793)
    (RETURN
     (PROG1
         (LETT #1#
               (|sublisV|
                (PAIR '(#2=#:G10790 #3=#:G10791 #4=#:G10792)
                      (LIST '(|Fraction| (|Integer|)) '(|Integer|)
                            '(|Fraction| (|Integer|))))
                (|Join| (|CharacteristicZero|) (|OrderedRing|)
                        (|CommutativeRing|) (|Field|)
                        (|FullyRetractableTo| '#2#) (|Algebra| '#3#)
                        (|Algebra| '#4#) (|RadicalCategory|)
                        (|mkCategory| '|domain|
                                      '(((|mainForm|
                                          ((|Union| (|OutputForm|) "failed")
                                           $))
                                         T)
                                        ((|mainDefiningPolynomial|
                                          ((|Union|
                                            (|SparseUnivariatePolynomial| $)
                                            "failed")
                                           $))
                                         T)
                                        ((|mainValue|
                                          ((|Union|
                                            (|SparseUnivariatePolynomial| $)
                                            "failed")
                                           $))
                                         T)
                                        ((|rootOf|
                                          ((|Union| $ "failed")
                                           (|SparseUnivariatePolynomial| $)
                                           (|PositiveInteger|) (|OutputForm|)))
                                         T)
                                        ((|rootOf|
                                          ((|Union| $ "failed")
                                           (|SparseUnivariatePolynomial| $)
                                           (|PositiveInteger|)))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $)
                                           (|SparseUnivariatePolynomial| $)))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $)
                                           (|SparseUnivariatePolynomial|
                                            (|Fraction| (|Integer|)))))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $)
                                           (|SparseUnivariatePolynomial|
                                            (|Integer|))))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $) (|Polynomial| $)))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $)
                                           (|Polynomial|
                                            (|Fraction| (|Integer|)))))
                                         T)
                                        ((|allRootsOf|
                                          ((|List| $)
                                           (|Polynomial| (|Integer|))))
                                         T)
                                        ((|sqrt| ($ $ (|PositiveInteger|))) T)
                                        ((|sqrt| ($ $)) T)
                                        ((|sqrt| ($ (|Fraction| (|Integer|))))
                                         T)
                                        ((|sqrt| ($ (|Integer|))) T)
                                        ((|rename!| ($ $ (|OutputForm|))) T)
                                        ((|rename| ($ $ (|OutputForm|))) T)
                                        ((|approximate|
                                          ((|Fraction| (|Integer|)) $ $))
                                         T))
                                      NIL
                                      '((|Fraction| (|Integer|)) (|OutputForm|)
                                        (|Integer|) (|PositiveInteger|)
                                        (|List| $) (|Polynomial| (|Integer|))
                                        (|Polynomial| (|Fraction| (|Integer|)))
                                        (|Polynomial| $)
                                        (|SparseUnivariatePolynomial|
                                         (|Integer|))
                                        (|SparseUnivariatePolynomial|
                                         (|Fraction| (|Integer|)))
                                        (|SparseUnivariatePolynomial| $))
                                      NIL)))
               |RealClosedField|)
       (SETELT #1# 0 '(|RealClosedField|)))))) 

(MAKEPROP '|RealClosedField| 'NILADIC T) 
