; http://people.math.gatech.edu/~mbaker/pdf/cipolla2011.pdf
; this value is mutable because of variable rg.
(let ((ff (fileVal "finiteField"))(J (fileVal "Jacobi"))
      (rg (((fileVal "RC4") "froth") 'rbi)))
(lambda (p) (let ((rx (rg (- p 1)))(Fp (ff p))) (lambda (a)
(let ((jt (J a p)))
    (if (< jt 0) 'none (if (= jt 0) 0 
    (let ((m+ (Fp 'm+)) (m- (Fp 'm-)) (m* (Fp 'm*)) (fops (Fp 'fops)))
    (let y () (let* ((t (+ 1 (rx)))(w2 (m+ (m* t t) (m- a))))
      (if (= (J w2 p) 1) (y)
      (vector-ref (((fops (list->vector (list (m- w2) 0 1))) 'fexpt)
         (list->vector (list t 1)) (arithmetic-shift (+ p 1) -1)) 0))))))))))))

; (t 49 103) ; produces a complex vector!!
; t = 96, w2 = 0, final field val = (7, 51)
; The real part is right.
(((fileVal "GFsqrt") 17) 2) ; => 11 (11*11=121 = 119+2 = 17*7+2)

(let* ((p ((fileVal "pias") 4000000000000000000000 7))
(rx ((((fileVal "RC4") "foth") 'rbi) (- p 1)))(sqrt ((fileVal "GFsqrt") p)))
  (cons (let w ((i 1000)) (or (zero? i) (and
    (let* ((r (rx)) (y (sqrt (modulo (* r r) p))))
    (or (= y r) (= y (- p r))))
    (w (- i 1)))))
    (let w ((i 10000)(R 0)) (or (and (zero? i) R)
       (and (let* ((r (rx)) (y (sqrt r)))
         (or (and (eq? y 'none) (w (- i 1) R))
             (and (= (modulo (* y y) p) r) (w (- i 1) (+ R 1))))))))))
; => (#t . 4970)