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#lang racket
(provide (struct-out complex) parse eval)
(struct complex (re im) #:transparent)
(define value?
complex?)
(define (comp-plus x y)
(let ((x-re (complex-re x))
(x-im (complex-im x))
(y-re (complex-re y))
(y-im (complex-im y)))
(complex (+ x-re y-re) (+ x-im y-im))))
(define (comp-minus x y)
(let ((x-re (complex-re x))
(x-im (complex-im x))
(y-re (complex-re y))
(y-im (complex-im y)))
(complex (- x-re y-re) (- x-im y-im))))
(define (comp-mult x y)
(let ((x-re (complex-re x))
(x-im (complex-im x))
(y-re (complex-re y))
(y-im (complex-im y)))
(complex (- (* x-re y-re) (* x-im y-im)) (+ (* x-re y-im) (* x-im y-re)))))
(define (comp-mod2 x)
(let ((x-re (complex-re x))
(x-im (complex-im x)))
(complex (+ (* x-re x-re) (* x-im x-im)) 0)))
(define (comp-mod x)
(let ((mod2 (comp-mod2 x))
(x-re (complex-re x)))
(complex (sqrt x-re) 0)))
(define (comp-div x y)
(let* ((mod2 (complex-re (comp-mod2 y)))
(x-re (complex-re x))
(x-im (complex-im x))
(y-re (complex-re y))
(y-im (complex-im y))
(real (+ (* x-re y-re) (* x-im y-im)))
(imag (- (* x-im y-re) (* x-re y-im))))
(complex (/ real mod2) (/ imag mod2))))
;; Ponizej znajduje sie interpreter zwyklych wyrazen arytmetycznych.
;; Zadanie to zmodyfikowac go tak, by dzialal z liczbami zespolonymi.
(struct const (val) #:transparent)
(struct binop (op l r) #:transparent)
(define (imaginary-unit? c)
(eq? c 'i))
(define (op->proc op)
(match op ['+ comp-plus] ['- comp-minus] ['* comp-mult] ['/ comp-div]))
(define (eval e)
(match e
[(const n) n]
[(binop op l r) ((op->proc op) (eval l) (eval r))]))
(define (parse q)
(cond [(number? q) (const (complex q 0))]
[(imaginary-unit? q) (const (complex 0 1))]
[(and (list? q) (eq? (length q) 3) (symbol? (first q)))
(binop (first q) (parse (second q)) (parse (third q)))]))
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