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#lang racket
(require "modulo-arithmetic.rkt")
;; 4a^3 + 27b^2 != 0
(define a 2)
(define b 3)
(define (point-in-curve lst)
(define x (car lst))
(define y (cadr lst))
(= (* y y) (+ (* x x x) (* x a) b)))
(define (add p q)
(cond ((not (point-in-curve p))
q)
((not (point-in-curve q))
p)
(else
(define xp (first p))
(define xq (first q))
(define yp (second p))
(define yq (second q))
(let* ((m (if (equal? p q)
(/ (+ (* 3 xp xp) a)
(* 2 yp))
(/ (- yp yq)
(- xp xq))))
(xr (- (* m m) xp xq))
(yr (+ yp (* m (- xr xp)))))
(list xr (- yr))))))
(define (mul n p)
(cond ((= n 0)
(list 0 0))
((= n 1)
p)
(else
(add p (mul (sub1 n) p)))))
(define curve-points (filter point-in-curve
(cartesian-product (range cardinality)
(range cardinality))))
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