
(DECLAIM (NOTINLINE |RealClosedField;|)) 

(DEFPARAMETER |RealClosedField;AL| 'NIL) 

(DEFUN |RealClosedField| ()
  (COND (|RealClosedField;AL|)
        (T (SETQ |RealClosedField;AL| (|RealClosedField;|))))) 

(DEFUN |RealClosedField;| ()
  (SPROG ((#1=#:G9 NIL))
         (PROG1
             (LETT #1#
                   (|subst_in_cat| '(#2=#:G6 #3=#:G7 #4=#:G8)
                                   (LIST '(|Fraction| (|Integer|)) '(|Integer|)
                                         '(|Fraction| (|Integer|)))
                                   (|Join| (|OrderedRing|) (|CommutativeRing|)
                                           (|Field|)
                                           (|FullyRetractableTo| '#2#)
                                           (|Algebra| '#3#) (|Algebra| '#4#)
                                           (|RadicalCategory|)
                                           (|mkCategory|
                                            '(((|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 NIL NIL))))
           (SETELT #1# 0 '(|RealClosedField|))))) 
