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(DEFPARAMETER |AlgebraicallyClosedField;AL| NIL) 

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(DEFUN |AlgebraicallyClosedField;| ()

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  (LET ((#1=#:G553

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         (|Join| (|Field|) (|RadicalCategory|)

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                 (|mkCategory| '|domain|

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                               '(((|rootOf| ($ (|Polynomial| $))) T)

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                                 ((|rootOf|

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                                   ($ (|SparseUnivariatePolynomial| $)))

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                                  T)

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                                 ((|rootOf|

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                                   ($ (|SparseUnivariatePolynomial| $)

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                                    (|Symbol|)))

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                                  T)

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                                 ((|rootsOf| ((|List| $) (|Polynomial| $))) T)

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                                 ((|rootsOf|

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                                   ((|List| $)

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                                    (|SparseUnivariatePolynomial| $)))

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                                  T)

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                                 ((|rootsOf|

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                                   ((|List| $) (|SparseUnivariatePolynomial| $)

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                                    (|Symbol|)))

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                                  T)

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                                 ((|zeroOf| ($ (|Polynomial| $))) T)

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                                 ((|zeroOf|

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                                   ($ (|SparseUnivariatePolynomial| $)))

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                                  T)

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                                 ((|zeroOf|

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                                   ($ (|SparseUnivariatePolynomial| $)

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                                    (|Symbol|)))

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                                  T)

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                                 ((|zerosOf| ((|List| $) (|Polynomial| $))) T)

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                                 ((|zerosOf|

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                                   ((|List| $)

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                                    (|SparseUnivariatePolynomial| $)))

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                                  T)

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                                 ((|zerosOf|

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                                   ((|List| $) (|SparseUnivariatePolynomial| $)

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                                    (|Symbol|)))

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                                  T))

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                               NIL

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                               '((|List| $) (|SparseUnivariatePolynomial| $)

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                                 (|Symbol|) (|Polynomial| $))

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                               NIL))))

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    (PROGN (SETF (|shellEntry| #1# 0) '(|AlgebraicallyClosedField|)) #1#))) 

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(DEFUN |AlgebraicallyClosedField| ()

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  (COND (|AlgebraicallyClosedField;AL|)

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        (T (SETQ |AlgebraicallyClosedField;AL| (|AlgebraicallyClosedField;|))))) 

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(SETF (|dbConstructorDefault| (|constructorDB| '|AlgebraicallyClosedField|))

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        '|AlgebraicallyClosedField&|) 

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(SETF (|dbConstructorForm| (|constructorDB| '|AlgebraicallyClosedField|))

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        '(|AlgebraicallyClosedField|)) 

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(SETF (|dbConstructorKind| (|constructorDB| '|AlgebraicallyClosedField|))

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        '|category|) 

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(SETF (|dbConstructorModemap| (|constructorDB| '|AlgebraicallyClosedField|))

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        '(((|AlgebraicallyClosedField|) (|Category|))

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          (T |AlgebraicallyClosedField|))) 

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(SETF (|dbDualSignature| (|constructorDB| '|AlgebraicallyClosedField|)) '(T)) 

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(SETF (|dbCategory| (|constructorDB| '|AlgebraicallyClosedField|))

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        '(|Join| (|Field|) (|RadicalCategory|)

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                 (CATEGORY |domain| (SIGNATURE |rootOf| ($ (|Polynomial| $)))

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                  (SIGNATURE |rootOf| ($ (|SparseUnivariatePolynomial| $)))

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                  (SIGNATURE |rootOf|

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                   ($ (|SparseUnivariatePolynomial| $) (|Symbol|)))

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                  (SIGNATURE |rootsOf| ((|List| $) (|Polynomial| $)))

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                  (SIGNATURE |rootsOf|

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                   ((|List| $) (|SparseUnivariatePolynomial| $)))

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                  (SIGNATURE |rootsOf|

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                   ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))

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                  (SIGNATURE |zeroOf| ($ (|Polynomial| $)))

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                  (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $)))

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                  (SIGNATURE |zeroOf|

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                   ($ (|SparseUnivariatePolynomial| $) (|Symbol|)))

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                  (SIGNATURE |zerosOf| ((|List| $) (|Polynomial| $)))

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                  (SIGNATURE |zerosOf|

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                   ((|List| $) (|SparseUnivariatePolynomial| $)))

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                  (SIGNATURE |zerosOf|

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                   ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))))) 

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(SETF (|dbSourceFile| (|constructorDB| '|AlgebraicallyClosedField|))

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        '"algfunc.spad") 

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(SETF (|dbModemaps| (|constructorDB| '|AlgebraicallyClosedField|))

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        '((|rootOf| (*1 *1 *2)

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           (AND (|isDomain| *2 (|Polynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|rootOf| (*1 *1 *2)

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           (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|rootOf| (*1 *1 *2 *3)

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           (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))

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                (|isDomain| *3 (|Symbol|))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|rootsOf| (*1 *2 *3)

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           (AND (|isDomain| *3 (|Polynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1))))

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          (|rootsOf| (*1 *2 *3)

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           (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1))))

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          (|rootsOf| (*1 *2 *3 *4)

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           (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))

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                (|isDomain| *4 (|Symbol|))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1))))

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          (|zeroOf| (*1 *1 *2)

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           (AND (|isDomain| *2 (|Polynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|zeroOf| (*1 *1 *2)

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           (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|zeroOf| (*1 *1 *2 *3)

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           (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))

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                (|isDomain| *3 (|Symbol|))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))))

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          (|zerosOf| (*1 *2 *3)

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           (AND (|isDomain| *3 (|Polynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1))))

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          (|zerosOf| (*1 *2 *3)

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           (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1))))

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          (|zerosOf| (*1 *2 *3 *4)

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           (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))

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                (|isDomain| *4 (|Symbol|))

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                (|ofCategory| *1 (|AlgebraicallyClosedField|))

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                (|isDomain| *2 (|List| *1)))))) 

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(SETF (|dbOperations| (|constructorDB| '|AlgebraicallyClosedField|))

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        '((~= (#1=((|Boolean|) $ $) 7 T ELT))

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          (|zerosOf| (((|List| $) (|Polynomial| $)) 99 T ELT)

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           (((|List| $) (|SparseUnivariatePolynomial| $)) 98 T ELT)

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           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 97 T ELT))

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          (|zeroOf| (($ (|Polynomial| $)) 102 T ELT)

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           (($ (|SparseUnivariatePolynomial| $)) 101 T ELT)

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           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 100 T ELT))

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          (|zero?| ((#2=(|Boolean|) $) 22 T ELT))

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          (|unitNormal|

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           (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))

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             $)

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            56 T ELT))

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          (|unitCanonical| (($ $) 55 T ELT))

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          (|unit?| ((#3=(|Boolean|) $) 53 T ELT))

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          (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT))

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          (|squareFreePart| (($ $) 92 T ELT))

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          (|squareFree| (#4=((|Factored| $) $) 91 T ELT))

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          (|sqrt| (($ $) 111 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT))

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          (|sample| (#5=($) 23 T CONST))

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          (|rootsOf| (((|List| $) (|Polynomial| $)) 105 T ELT)

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           (((|List| $) (|SparseUnivariatePolynomial| $)) 104 T ELT)

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           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 103 T

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            ELT))

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          (|rootOf| (($ (|Polynomial| $)) 108 T ELT)

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           (($ (|SparseUnivariatePolynomial| $)) 107 T ELT)

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           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 106 T ELT))

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          (|rem| (#6=($ $ $) 72 T ELT))

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          (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT))

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          (|principalIdeal|

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           (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67

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            T ELT))

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          (|prime?| (((|Boolean|) $) 90 T ELT))

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          (|opposite?| ((#2# $ $) 20 T ELT))

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          (|one?| (((|Boolean|) $) 45 T ELT))

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          (|nthRoot| (($ $ #8=(|Integer|)) 110 T ELT))

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          (|multiEuclidean|

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           (((|Union| #9=(|List| $) #10="failed") #9# $) 69 T ELT))

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          (|lcm| (#11=($ $ $) 61 T ELT) (#12=($ (|List| $)) 60 T ELT))

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          (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT))

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          (|hash| (((|SingleInteger|) $) 12 T ELT))

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          (|gcdPolynomial|

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           ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 59 T ELT))

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          (|gcd| (#11# 63 T ELT) (#12# 62 T ELT)) (|factor| (#4# 93 T ELT))

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          (|extendedEuclidean|

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           (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $)

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                       (|:| |generator| $))

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             $ $)

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            71 T ELT)

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           (((|Union| (|Record| #14# #15#) #10#) $ $ $) 70 T ELT))

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          (|exquo| (((|Union| $ "failed") $ $) 57 T ELT))

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          (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT))

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          (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT))

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          (|divide|

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           (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT))

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          (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)

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                    (($ $) 58 T ELT)

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                    (($ #16=(|Fraction| #17=(|Integer|))) 85 T ELT))

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          (|characteristic| (((|NonNegativeInteger|)) 41 T CONST))

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          (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT))

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          (|annihilate?| (((|Boolean|) $ $) 34 T ELT))

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          (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT))

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          (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT))

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          (+ (($ $ $) 18 T ELT))

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          (** (($ $ (|PositiveInteger|)) 36 T ELT)

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           (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #17#) 88 T ELT)

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           (($ $ (|Fraction| #8#)) 109 T ELT))

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          (* (($ (|PositiveInteger|) $) 17 T ELT)

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             (($ (|NonNegativeInteger|) $) 21 T ELT)

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             (($ (|Integer|) . #18=($)) 31 T ELT) (($ $ $) 35 T ELT)

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             (($ $ #16#) 87 T ELT) (($ #16# . #18#) 86 T ELT)))) 

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(SETF (|dbAttributes| (|constructorDB| '|AlgebraicallyClosedField|))

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        '((|canonicalUnitNormal| . T) (|noZeroDivisors| . T)

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          ((|commutative| "*") . T))) 

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(SETF (|dbAbbreviation| (|constructorDB| '|AlgebraicallyClosedField|)) 'ACF) 

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(SETF (|dbPrincipals| (|constructorDB| '|AlgebraicallyClosedField|))

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        '(((|Field|) . T) ((|RadicalCategory|) . T))) 

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(SETF (|dbAncestors| (|constructorDB| '|AlgebraicallyClosedField|))

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        '(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T)

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          ((|AbelianSemiGroup|) . T)

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          ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T)

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          ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T)

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          ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T)

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          ((|CoercibleFrom| $) . T) ((|CoercibleFrom| (|Integer|)) . T)

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          ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T)

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          ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T)

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          ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T)

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          ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T)

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          ((|LeftLinearSet| (|Integer|)) . T) ((|LeftModule| #1#) . T)

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          ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T)

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          ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T)

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          ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T)

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          ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T)

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          ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T)

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          ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T)

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          ((|SetCategory|) . T) ((|Type|) . T)

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          ((|UniqueFactorizationDomain|) . T))) 

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