
(/VERSIONCHECK 2) 

(DEFPARAMETER |RealClosedField;AL| 'NIL) 

(DEFUN |RealClosedField| ()
  (LET (#:G1827)
    (COND
      (|RealClosedField;AL|)
      (T (SETQ |RealClosedField;AL| (|RealClosedField;|)))))) 

(DEFUN |RealClosedField;| ()
  (PROG (#0=#:G1825)
    (RETURN
      (PROG1 (LETT #0#
                   (|sublisV|
                       (PAIR '(#1=#:G1822 #2=#:G1823 #3=#:G1824)
                             (LIST '(|Fraction| (|Integer|))
                                   '(|Integer|)
                                   '(|Fraction| (|Integer|))))
                       (|Join| (|CharacteristicZero|) (|OrderedRing|)
                               (|CommutativeRing|) (|Field|)
                               (|FullyRetractableTo| '#1#)
                               (|Algebra| '#2#) (|Algebra| '#3#)
                               (|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 #0# 0 '(|RealClosedField|)))))) 

(MAKEPROP '|RealClosedField| 'NILADIC T) 
