;;; EXAMPLES OF TESTING CODE (IN MIT SCHEME)
;;; FROM CHAPTER 2 OF STRUCTURE AND INTERPRETATION OF COMPUTER PROGRAMS


;;;SECTION 2.4.1

;; Ben's rectangular

(define z1 (make-from-real-imag 1 1))
;Value: z1

(real-part z1)
;Value: 1
(imag-part z1)
;Value: 1
(magnitude z1)
;Value: 1.4142135623730951
(angle z1)
;Value: .7853981633974483
(* 4 (angle z1))
;Value: 3.141592653589793
(define z2 (make-from-mag-ang 1.4142135623730951 .7853981633974483))
;Value: z2

(real-part z2)
;Value: 1.
(imag-part z2)
;Value: 1.

z1
;Value 10: (1 . 1)

z2
;Value 14: (1. . 1.)

(add-complex z1 z2)
;Value 16: (2. . 2.)

(sub-complex z1 z2)
;Value 17: (0. . 0.)


;; Alyssa's polar

(define z1 (make-from-real-imag 1 1))
;Value: z1

(real-part z1)
;Value: 1.

(imag-part z1)
;Value: 1.

(magnitude z1)
;Value: 1.4142135623730951

(angle z1)
;Value: .7853981633974483

(* 4 (angle z1))
;Value: 3.141592653589793

(define z2 (make-from-mag-ang 1.4142135623730951 .7853981633974483))
;Value: z2

(real-part z2)
;Value: 1.

(imag-part z2)
;Value: 1.

z1
;Value 12: (1.4142135623730951 . .7853981633974483)

z2
;Value 13: (1.4142135623730951 . .7853981633974483)

(mul-complex z1 z2)
;Value 18: (2.0000000000000004 . 1.5707963267948966)

(div-complex z1 z2)
;Value 19: (1. . 0.)

;;;SECTION 2.4.2

(define z1 (make-from-real-imag 1 1))
;Value: z1

z1
;Value 20: (rectangular 1 . 1)
(real-part z1)
;Value: 1
(imag-part z1)
;Value: 1
(magnitude z1)
;Value: 1.4142135623730951
(angle z1)
;Value: .7853981633974483

(define z2 (make-from-mag-ang 1.4142135623730951 .7853981633974483))
;Value: z2

z2
;Value 22: (polar 1.4142135623730951 . .7853981633974483)

(magnitude z2)
;Value: 1.4142135623730951
(angle z2)
;Value: .7853981633974483
(real-part z2)
;Value: 1.
(imag-part z2)
;Value: 1.

z1
;Value 20: (rectangular 1 . 1)
z2
;Value 22: (polar 1.4142135623730951 . .7853981633974483)

(add-complex z1 z2)
;Value 23: (rectangular 2. . 2.)
(sub-complex z1 z2)
;Value 24: (rectangular 0. . 0.)
(mul-complex z1 z2)
;Value 25: (polar 2.0000000000000004 . 1.5707963267948966)
(div-complex z1 z2)
;Value 26: (polar 1. . 0.)

;;;SECTION 2.5.2

(define z1 (make-complex-from-real-imag 1 1))

;; Before coercion mechanism

(add z1 (make-scheme-number 3))
;Value 1: (complex rectangular 4 . 1)

(add (make-scheme-number 3) z1)
;No method for the given types (add (scheme-number complex))


;; With coercion mechanism

(add z1 (make-scheme-number 3))
;Value 6: (complex rectangular 4 . 1)

(add (make-scheme-number 3) z1)
;Value 7: (complex rectangular 4 . 1)

;;;SECTION 2.5.3

(define a (make-polynomial 'x '((5 1) (4 2) (2 3) (1 -2) (0 -5))))

a
;Value 3: (polynomial x (5 1) (4 2) (2 3) (1 -2) (0 -5))

(add a a)
;Value 4: (polynomial x (5 2) (4 4) (2 6) (1 -4) (0 -10))

(define b (make-polynomial 'x '((100 1) (2 2) (0 1))))

b
;Value 5: (polynomial x (100 1) (2 2) (0 1))

(mul b b)
;Value 6: (polynomial x (200 1) (102 4) (100 2) (4 4) (2 4) (0 1))