;; A Polynomial is a (listof Number)
;; Interpretation: 
;;  - each list is a list of coefficients
;;  - the exponent for each index, i, (starting from 0) of a list of length N
;;    is N-i-1

;; Data examples

"4"
(list 4)

"x + 3"
(list 1 3)

"x^3 + 2x^2 + 3x + 4"
(list 1 2 3 4)


;; der: Polynomial -> Polynomail
;; retuns the derivative of p
(define (der p)
  ;; handles the case were there's a polynomial of at least 1
  (local ((define (der2 p acc)
            (cond
              [(empty? (rest p)) empty]
              [else (cons (* acc (first p))
                          (der2 (rest p) (- acc 1)))])))
    (cond
      [(= (length p) 1) (list 0)]
      [else (der2 p (- (length p) 1))])))



;; Examples
;; d/dx 4 = 0
(equal? (der (list 4)) (list 0)) 
;; d/dx x + 3
(equal? (der (list 1 3)) (list 1))
;; d/x x^3 + 2x^2 + 3x + 4 = 3x^2 + 4x + 3
(equal? (der (list 1 2 3 4)) (list 3 4 3))