CoCalc -- code.lsp

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open-axiom-build / src / algebra / ACF-.NRLIB / code.lsp
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(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;zeroOf;Sup$;1|)) 
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(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;rootOf;Sup$;2|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;zerosOf;SupL;3|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;rootsOf;SupL;4|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) (|%List| *))
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  |ACF-;rootsOf;SupSL;5|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) (|%List| *))
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  |ACF-;zerosOf;SupSL;6|)) 
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(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |ACF-;assign|)) 
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(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;zeroOf;P$;8|)) 
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(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;rootOf;P$;9|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;zerosOf;PL;10|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;rootsOf;PL;11|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
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  |ACF-;zeroOf;SupS$;12|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|) (|%List| *))
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  |ACF-;binomialRoots|)) 
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(DECLAIM
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 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|) (|%List| *))
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  |ACF-;allroots|)) 
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(DEFUN |ACF-;zeroOf;Sup$;1| (|p| $)
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  (PROG (|x|)
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    (RETURN
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     (|ACF-;assign|
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      (LETT |x| (SPADCALL (|shellEntry| $ 8)) |ACF-;zeroOf;Sup$;1|)
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      (SPADCALL |p| |x| (|shellEntry| $ 10)) $)))) 
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(DEFUN |ACF-;rootOf;Sup$;2| (|p| $)
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  (PROG (|x|)
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    (RETURN
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     (|ACF-;assign|
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      (LETT |x| (SPADCALL (|shellEntry| $ 8)) |ACF-;rootOf;Sup$;2|)
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      (SPADCALL |p| |x| (|shellEntry| $ 12)) $)))) 
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(DEFUN |ACF-;zerosOf;SupL;3| (|p| $)
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  (SPADCALL |p| (SPADCALL (|shellEntry| $ 8)) (|shellEntry| $ 15))) 
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(DEFUN |ACF-;rootsOf;SupL;4| (|p| $)
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  (SPADCALL |p| (SPADCALL (|shellEntry| $ 8)) (|shellEntry| $ 17))) 
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(DEFUN |ACF-;rootsOf;SupSL;5| (|p| |y| $)
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  (|ACF-;allroots| |p| |y| (|shellEntry| $ 12) $)) 
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(DEFUN |ACF-;zerosOf;SupSL;6| (|p| |y| $)
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  (|ACF-;allroots| |p| |y| (|shellEntry| $ 10) $)) 
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(DEFUN |ACF-;assign| (|x| |f| $)
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  (PROGN (|assignSymbol| |x| |f| (|shellEntry| $ 6)) |f|)) 
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(DEFUN |ACF-;zeroOf;P$;8| (|p| $)
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  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
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    (COND ((NULL |l|) (|error| "zeroOf: constant polynomial"))
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          (T
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           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
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                     (|shellEntry| $ 10)))))) 
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(DEFUN |ACF-;rootOf;P$;9| (|p| $)
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  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
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    (COND ((NULL |l|) (|error| "rootOf: constant polynomial"))
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          (T
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           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
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                     (|shellEntry| $ 12)))))) 
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(DEFUN |ACF-;zerosOf;PL;10| (|p| $)
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  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
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    (COND ((NULL |l|) (|error| "zerosOf: constant polynomial"))
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          (T
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           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
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                     (|shellEntry| $ 15)))))) 
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(DEFUN |ACF-;rootsOf;PL;11| (|p| $)
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  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
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    (COND ((NULL |l|) (|error| "rootsOf: constant polynomial"))
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          (T
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           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
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                     (|shellEntry| $ 17)))))) 
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(DEFUN |ACF-;zeroOf;SupS$;12| (|p| |y| $)
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  (PROG (|r| |b| |a|)
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    (RETURN
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     (LET ((|d| (SPADCALL |p| (|shellEntry| $ 35))))
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       (COND ((ZEROP |d|) (|error| "zeroOf: constant polynomial"))
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             ((SPADCALL (SPADCALL |p| 0 (|shellEntry| $ 40))
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                        (|shellEntry| $ 41))
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              (|spadConstant| $ 37))
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             (T
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              (SEQ
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               (LETT |a| (SPADCALL |p| (|shellEntry| $ 42))
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                     . #1=(|ACF-;zeroOf;SupS$;12|))
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               (EXIT
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                (COND
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                 ((EQL |d| 2)
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                  (PROGN
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                   (LETT |b| (SPADCALL |p| 1 (|shellEntry| $ 40)) . #1#)
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                   (SPADCALL
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                    (SPADCALL
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                     (SPADCALL
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                      (SPADCALL (SPADCALL |b| 2 (|shellEntry| $ 48))
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                                (SPADCALL (SPADCALL 4 |a| (|shellEntry| $ 49))
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                                          (SPADCALL |p| 0 (|shellEntry| $ 40))
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                                          (|shellEntry| $ 50))
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                                (|shellEntry| $ 51))
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                      (|shellEntry| $ 52))
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                     |b| (|shellEntry| $ 51))
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                    (SPADCALL 2 |a| (|shellEntry| $ 49)) (|shellEntry| $ 53))))
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                 (T
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                  (PROGN
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                   (LETT |r|
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                         (SPADCALL (SPADCALL |p| (|shellEntry| $ 54))
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                                   (|shellEntry| $ 56))
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                         . #1#)
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                   (COND
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                    ((EQL (CAR |r|) 1) (SPADCALL |p| |y| (|shellEntry| $ 12)))
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                    (T
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                     (SPADCALL
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                      (SPADCALL (SPADCALL (CDR |r|) |a| (|shellEntry| $ 53))
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                                (|shellEntry| $ 57))
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                      |d| (|shellEntry| $ 59))))))))))))))) 
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(DEFUN |ACF-;binomialRoots| (|p| |y| |fn| $)
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  (PROG (|beta| |cyclo|)
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    (RETURN
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     (LET* ((|x| (SPADCALL |y| (|shellEntry| $ 61)))
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            (|alpha|
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             (|ACF-;assign| |x| (FUNCALL (CAR |fn|) |p| |x| (CDR |fn|)) $))
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            (|n| (SPADCALL |p| (|shellEntry| $ 35))))
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       (COND ((EQL |n| 1) (LIST |alpha|))
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             (T
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              (PROGN
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               (LETT |cyclo|
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                     (SPADCALL |n|
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                               (SPADCALL (|spadConstant| $ 44) 1
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                                         (|shellEntry| $ 64))
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                               (|shellEntry| $ 66))
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                     . #1=(|ACF-;binomialRoots|))
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               (SETQ |x| (SPADCALL |y| (|shellEntry| $ 61)))
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               (LETT |beta|
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                     (|ACF-;assign| |x|
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                      (FUNCALL (CAR |fn|) |cyclo| |x| (CDR |fn|)) $)
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                     . #1#)
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               (LET ((|i| 0)
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                     (#2=#:G615
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                      (LET ((#3=#:G589 (- |n| 1)))
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                        (COND ((NOT (MINUSP #3#)) #3#)
168
                              (T
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                               (|moanRetract| #3# '(|NonNegativeInteger|))))))
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                     (#4=#:G583 NIL))
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                 (LOOP
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                  (COND ((< #2# |i|) (RETURN (|reverse!| #4#)))
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                        (T
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                         (SETQ #4#
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                                 (CONS
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                                  (SPADCALL |alpha|
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                                            (SPADCALL |beta| |i|
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                                                      (|shellEntry| $ 68))
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                                            (|shellEntry| $ 50))
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                                  #4#))))
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                  (SETQ |i| (+ |i| 1))))))))))) 
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(DEFUN |ACF-;allroots| (|p| |y| |fn| $)
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  (PROG (|q| |alpha| |x| |ans| |groots| |g| |h| |decompList|)
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    (RETURN
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     (COND
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      ((SPADCALL |p| (|shellEntry| $ 69))
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       (|error| "allroots: polynomial must be nonzero"))
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      ((SPADCALL (SPADCALL |p| 0 (|shellEntry| $ 40)) (|shellEntry| $ 41))
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       (CONS (|spadConstant| $ 37)
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             (|ACF-;allroots|
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              (SPADCALL |p|
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                        (SPADCALL (|spadConstant| $ 44) 1 (|shellEntry| $ 64))
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                        (|shellEntry| $ 70))
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              |y| |fn| $)))
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      (T
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       (LET ((|p1| (SPADCALL |p| (|shellEntry| $ 54))))
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         (COND ((SPADCALL |p1| (|shellEntry| $ 69)) NIL)
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               ((SPADCALL (SPADCALL |p1| (|shellEntry| $ 54))
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                          (|shellEntry| $ 69))
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                (|ACF-;binomialRoots| |p| |y| |fn| $))
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               (T
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                (SEQ
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                 (LETT |decompList| (SPADCALL |p| (|shellEntry| $ 76))
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                       . #1=(|ACF-;allroots|))
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                 (EXIT
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                  (COND
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                   ((< 1 (LIST-LENGTH |decompList|))
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                    (PROGN
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                     (LETT |h| (SPADCALL |decompList| (|shellEntry| $ 79))
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                           . #1#)
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                     (LETT |g|
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                           (LET ((#2=#:G613
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                                  (SPADCALL |p| |h| (|shellEntry| $ 81))))
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                             (COND ((ZEROP (CAR #2#)) (CDR #2#))
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                                   (T
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                                    (|moanRetract| #2#
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                                                   (LIST
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                                                    '|SparseUnivariatePolynomial|
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                                                    (|shellEntry| $ 6))))))
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                           . #1#)
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                     (LETT |groots| (|ACF-;allroots| |g| |y| |fn| $) . #1#)
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                     (LET ((#3=#:G593 NIL) (#4=#:G594 T) (#5=#:G616 |groots|))
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                       (LOOP
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                        (COND
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                         ((NOT (CONSP #5#)) (RETURN (COND (#4# NIL) (T #3#))))
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                         (T
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                          (LET ((#6=#:G592
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                                 (|ACF-;allroots|
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                                  (SPADCALL |h|
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                                            (SPADCALL (CAR #5#)
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                                                      (|shellEntry| $ 82))
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                                            (|shellEntry| $ 83))
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                                  |y| |fn| $)))
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                            (PROGN
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                             (COND (#4# (SETQ #3# #6#))
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                                   (T (SETQ #3# (APPEND #3# #6#))))
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                             (SETQ #4# NIL)))))
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                        (SETQ #5# (CDR #5#))))))
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                   (T
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                    (SEQ (LETT |ans| NIL . #1#)
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                         (LOOP
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                          (COND
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                           ((SPADCALL |p| (|shellEntry| $ 86)) (RETURN NIL))
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                           (T
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                            (SEQ
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                             (LETT |x| (SPADCALL |y| (|shellEntry| $ 61))
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                                   . #1#)
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                             (LETT |alpha|
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                                   (|ACF-;assign| |x|
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                                    (FUNCALL (CAR |fn|) |p| |x| (CDR |fn|)) $)
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                                   . #1#)
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                             (LETT |q|
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                                   (SPADCALL
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                                    (SPADCALL (|spadConstant| $ 44) 1
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                                              (|shellEntry| $ 64))
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                                    (SPADCALL |alpha| (|shellEntry| $ 82))
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                                    (|shellEntry| $ 83))
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                                   . #1#)
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                             (EXIT
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                              (COND
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                               ((SPADCALL
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                                 (SPADCALL |p| |alpha| (|shellEntry| $ 88))
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                                 (|shellEntry| $ 41))
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                                (LOOP
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                                 (COND
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                                  ((NOT
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                                    (SPADCALL
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                                     (SPADCALL |p| |alpha| (|shellEntry| $ 88))
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                                     (|shellEntry| $ 41)))
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                                   (RETURN NIL))
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                                  (T
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                                   (PROGN
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                                    (SETQ |p|
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                                            (LET ((#7=#:G614
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                                                   (SPADCALL |p| |q|
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                                                             (|shellEntry| $
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                                                                           90))))
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                                              (COND
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                                               ((ZEROP (CAR #7#)) (CDR #7#))
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                                               (T
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                                                (|moanRetract| #7#
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                                                               (LIST
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                                                                '|SparseUnivariatePolynomial|
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                                                                (|shellEntry| $
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                                                                              6)))))))
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                                    (SETQ |ans| (CONS |alpha| |ans|)))))))
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                               (T
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                                (PROGN
290
                                 (SETQ |p|
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                                         (SPADCALL |p| |q|
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                                                   (|shellEntry| $ 70)))
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                                 (SETQ |ans| (CONS |alpha| |ans|))))))))))
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                         (EXIT (|reverse!| |ans|))))))))))))))) 
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(DEFUN |AlgebraicallyClosedField&| (|#1|)
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  (LET* ((|dv$1| (|devaluate| |#1|))
298
         (|dv$| (LIST '|AlgebraicallyClosedField&| |dv$1|))
299
         ($ (|newShell| 92))
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         (|pv$| (|buildPredVector| 0 0 NIL)))
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    (PROGN
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     (SETF (|shellEntry| $ 0) |dv$|)
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     (SETF (|shellEntry| $ 3) |pv$|)
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     (|stuffDomainSlots| $)
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     (SETF (|shellEntry| $ 6) |#1|)
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     $))) 
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(MAKEPROP '|AlgebraicallyClosedField&| '|infovec|
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          (LIST
310
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Symbol|) (0 . |new|)
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              (|SparseUnivariatePolynomial| $) (4 . |zeroOf|)
312
              |ACF-;zeroOf;Sup$;1| (10 . |rootOf|) |ACF-;rootOf;Sup$;2|
313
              (|List| $) (16 . |zerosOf|) |ACF-;zerosOf;SupL;3|
314
              (22 . |rootsOf|) |ACF-;rootsOf;SupL;4| |ACF-;rootsOf;SupSL;5|
315
              |ACF-;zerosOf;SupSL;6| (|Polynomial| 6) (|List| 7)
316
              (28 . |variables|) (|Boolean|) (33 . |empty?|)
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              (|SparseUnivariatePolynomial| 6) (38 . |univariate|)
318
              (43 . |first|) (|Polynomial| $) |ACF-;zeroOf;P$;8|
319
              |ACF-;rootOf;P$;9| |ACF-;zerosOf;PL;10| |ACF-;rootsOf;PL;11|
320
              (|NonNegativeInteger|) (48 . |degree|) (53 . |zero?|)
321
              (58 . |Zero|) (62 . |Zero|) (66 . |Zero|) (70 . |coefficient|)
322
              (76 . |zero?|) (81 . |leadingCoefficient|) (86 . =) (92 . |One|)
323
              (96 . |One|) (|PositiveInteger|) (100 . |One|) (104 . **)
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              (110 . *) (116 . *) (122 . -) (128 . |sqrt|) (133 . /)
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              (139 . |reductum|) (|Union| 6 '#1="failed")
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              (144 . |retractIfCan|) (149 . -) (|Integer|) (154 . |nthRoot|)
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              |ACF-;zeroOf;SupS$;12| (160 . |new|) (165 . |one?|) (170 . |One|)
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              (174 . |monomial|) (|NumberTheoreticPolynomialFunctions| 26)
329
              (180 . |cyclotomic|) (186 . -) (192 . **) (198 . |zero?|)
330
              (203 . |quo|) (|List| 6) (209 . |concat|) (215 . |empty|)
331
              (|PolynomialDecomposition| 26 6) (|List| 26) (219 . |decompose|)
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              (224 . |#|) (229 . >) (235 . |last|) (|Union| 26 '"failed")
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              (240 . |leftFactor|) (246 . |coerce|) (251 . -) (257 . |append|)
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              (263 . |nil|) (267 . |ground?|) (272 . |not|) (277 . |elt|)
335
              (|Union| $ '#1#) (283 . |exquo|) (289 . |reverse!|))
336
           '#(|zerosOf| 294 |zeroOf| 310 |rootsOf| 326 |rootOf| 342) 'NIL
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           (CONS (|makeByteWordVec2| 1 'NIL)
338
                 (CONS '#()
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                       (CONS '#()
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                             (|makeByteWordVec2| 91
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                                                 '(0 7 0 8 2 6 0 9 7 10 2 6 0 9
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                                                   7 12 2 6 14 9 7 15 2 6 14 9
343
                                                   7 17 1 21 22 0 23 1 22 24 0
344
                                                   25 1 21 26 0 27 1 22 7 0 28
345
                                                   1 26 34 0 35 1 34 24 0 36 0
346
                                                   6 0 37 0 26 0 38 0 34 0 39 2
347
                                                   26 6 0 34 40 1 6 24 0 41 1
348
                                                   26 6 0 42 2 34 24 0 0 43 0 6
349
                                                   0 44 0 26 0 45 0 46 0 47 2 6
350
                                                   0 0 46 48 2 6 0 46 0 49 2 6
351
                                                   0 0 0 50 2 6 0 0 0 51 1 6 0
352
                                                   0 52 2 6 0 0 0 53 1 26 0 0
353
                                                   54 1 26 55 0 56 1 6 0 0 57 2
354
                                                   6 0 0 58 59 1 7 0 0 61 1 34
355
                                                   24 0 62 0 34 0 63 2 26 0 6
356
                                                   34 64 2 65 26 34 26 66 2 58
357
                                                   0 0 0 67 2 6 0 0 34 68 1 26
358
                                                   24 0 69 2 26 0 0 0 70 2 71 0
359
                                                   6 0 72 0 71 0 73 1 74 75 26
360
                                                   76 1 75 34 0 77 2 34 24 0 0
361
                                                   78 1 75 26 0 79 2 74 80 26
362
                                                   26 81 1 26 0 6 82 2 26 0 0 0
363
                                                   83 2 71 0 0 0 84 0 71 0 85 1
364
                                                   26 24 0 86 1 24 0 0 87 2 26
365
                                                   6 0 6 88 2 26 89 0 0 90 1 71
366
                                                   0 0 91 2 0 14 9 7 20 1 0 14
367
                                                   29 32 1 0 14 9 16 2 0 0 9 7
368
                                                   60 1 0 0 29 30 1 0 0 9 11 2
369
                                                   0 14 9 7 19 1 0 14 29 33 1 0
370
                                                   14 9 18 1 0 0 29 31 1 0 0 9
371
                                                   13)))))
372
           '|lookupComplete|)) 
373

374
(SETF (|dbTemplate| (|constructorDB| '|AlgebraicallyClosedField&|))
375
        #(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Symbol|) (0 . |new|)
376
          (|SparseUnivariatePolynomial| $) (4 . |zeroOf|) |ACF-;zeroOf;Sup$;1|
377
          (10 . |rootOf|) |ACF-;rootOf;Sup$;2| (|List| $) (16 . |zerosOf|)
378
          |ACF-;zerosOf;SupL;3| (22 . |rootsOf|) |ACF-;rootsOf;SupL;4|
379
          |ACF-;rootsOf;SupSL;5| |ACF-;zerosOf;SupSL;6| (|Polynomial| 6)
380
          (|List| 7) (28 . |variables|) (|Boolean|) (33 . |empty?|)
381
          (|SparseUnivariatePolynomial| 6) (38 . |univariate|) (43 . |first|)
382
          (|Polynomial| $) |ACF-;zeroOf;P$;8| |ACF-;rootOf;P$;9|
383
          |ACF-;zerosOf;PL;10| |ACF-;rootsOf;PL;11| (|NonNegativeInteger|)
384
          (48 . |degree|) (53 . |zero?|) (58 . |Zero|) (62 . |Zero|)
385
          (66 . |Zero|) (70 . |coefficient|) (76 . |zero?|)
386
          (81 . |leadingCoefficient|) (86 . =) (92 . |One|) (96 . |One|)
387
          (|PositiveInteger|) (100 . |One|) (104 . **) (110 . *) (116 . *)
388
          (122 . -) (128 . |sqrt|) (133 . /) (139 . |reductum|)
389
          (|Union| 6 '#1="failed") (144 . |retractIfCan|) (149 . -) (|Integer|)
390
          (154 . |nthRoot|) |ACF-;zeroOf;SupS$;12| (160 . |new|) (165 . |one?|)
391
          (170 . |One|) (174 . |monomial|)
392
          (|NumberTheoreticPolynomialFunctions| 26) (180 . |cyclotomic|)
393
          (186 . -) (192 . **) (198 . |zero?|) (203 . |quo|) (|List| 6)
394
          (209 . |concat|) (215 . |empty|) (|PolynomialDecomposition| 26 6)
395
          (|List| 26) (219 . |decompose|) (224 . |#|) (229 . >) (235 . |last|)
396
          (|Union| 26 '"failed") (240 . |leftFactor|) (246 . |coerce|)
397
          (251 . -) (257 . |append|) (263 . |nil|) (267 . |ground?|)
398
          (272 . |not|) (277 . |elt|) (|Union| $ '#1#) (283 . |exquo|)
399
          (289 . |reverse!|))) 
400

401
(SETF (|dbLookupFunction| (|constructorDB| '|AlgebraicallyClosedField&|))
402
        '|lookupComplete|) 
403

404
(SETF (|dbConstructorForm| (|constructorDB| '|AlgebraicallyClosedField&|))
405
        '(|AlgebraicallyClosedField&| S)) 
406

407
(SETF (|dbConstructorKind| (|constructorDB| '|AlgebraicallyClosedField&|))
408
        '|package|) 
409

410
(SETF (|dbConstructorModemap| (|constructorDB| '|AlgebraicallyClosedField&|))
411
        '(((|AlgebraicallyClosedField&| |#1|)
412
           (CATEGORY |package|
413
            (SIGNATURE |zerosOf|
414
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
415
            (SIGNATURE |zerosOf|
416
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|)))
417
            (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|)))
418
            (SIGNATURE |zeroOf|
419
             (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
420
            (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|)))
421
            (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|)))
422
            (SIGNATURE |rootsOf|
423
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
424
            (SIGNATURE |rootsOf|
425
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|)))
426
            (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|)))
427
            (SIGNATURE |rootOf|
428
             (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
429
            (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|)))
430
            (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|))))
431
           (|AlgebraicallyClosedField|))
432
          (T |AlgebraicallyClosedField&|))) 
433

434
(SETF (|dbDualSignature| (|constructorDB| '|AlgebraicallyClosedField&|))
435
        '(NIL T)) 
436

437
(SETF (|dbSourceFile| (|constructorDB| '|AlgebraicallyClosedField&|))
438
        '"algfunc.spad") 
439

440
(SETF (|dbOperations| (|constructorDB| '|AlgebraicallyClosedField&|))
441
        '((|zerosOf| (((|List| $) (|Polynomial| $)) 32 T ELT)
442
           (((|List| $) (|SparseUnivariatePolynomial| $)) 16 T ELT)
443
           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 20 T ELT))
444
          (|zeroOf| (($ (|Polynomial| $)) 30 T ELT)
445
           (($ (|SparseUnivariatePolynomial| $)) 11 T ELT)
446
           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 60 T ELT))
447
          (|rootsOf| (((|List| $) (|Polynomial| $)) 33 T ELT)
448
           (((|List| $) (|SparseUnivariatePolynomial| $)) 18 T ELT)
449
           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 19 T ELT))
450
          (|rootOf| (($ (|Polynomial| $)) 31 T ELT)
451
           (($ (|SparseUnivariatePolynomial| $)) 13 T ELT)
452
           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL T ELT)))) 
453

454
(SETF (|dbOperationTable| (|constructorDB| '|AlgebraicallyClosedField&|))
455
        #(|zerosOf| 294 |zeroOf| 310 |rootsOf| 326 |rootOf| 342)) 
456

457
(SETF (|dbCapsuleDefinitions| (|constructorDB| '|AlgebraicallyClosedField&|))
458
        '((|ACF-;zeroOf;SupS$;12|
459
           ($ (|SparseUnivariatePolynomial| $) (|Symbol|)))
460
          (|ACF-;rootsOf;PL;11| ((|List| $) (|Polynomial| $)))
461
          (|ACF-;zerosOf;PL;10| ((|List| $) (|Polynomial| $)))
462
          (|ACF-;rootOf;P$;9| ($ (|Polynomial| $)))
463
          (|ACF-;zeroOf;P$;8| ($ (|Polynomial| $)))
464
          (|ACF-;zerosOf;SupSL;6|
465
           ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))
466
          (|ACF-;rootsOf;SupSL;5|
467
           ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))
468
          (|ACF-;rootsOf;SupL;4| ((|List| $) (|SparseUnivariatePolynomial| $)))
469
          (|ACF-;zerosOf;SupL;3| ((|List| $) (|SparseUnivariatePolynomial| $)))
470
          (|ACF-;rootOf;Sup$;2| ($ (|SparseUnivariatePolynomial| $)))
471
          (|ACF-;zeroOf;Sup$;1| ($ (|SparseUnivariatePolynomial| $))))) 
472

473
(SETF (|dbAbbreviation| (|constructorDB| '|AlgebraicallyClosedField&|)) 'ACF-) 
474

475
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