;;; (C) 2009
;;; Unicamp
;;; Instituto de Computacao
;;; Prof. Joao Meidanis
;;; MC336 B
;;; Prova 29/09/2009 - Lisp

;;; (1) SUPERINV

(defun superinv (l)
  (superinv-aux l ())
  )

(defun superinv-aux (l result)
  (cond
   ((null l) result)
   ((atom (car l)) (superinv-aux (cdr l) (cons (car l) result)))
   (t (superinv-aux (cdr l) (cons (superinv (car l)) result)))
   )
  )

;;; (2) UNIQUE

(defun unique (l)
  (cond
   ((null l) ())
   ((member (car l) (cdr l)) (unique (cdr l)))
   (t (cons (car l) (unique (cdr l))))
   )
  )

;;; (3) POLY

;;; versao direta

(defun poly (coef x)
  (poly-aux coef x (1- (length coef)))
  )

(defun poly-aux (coef x n)
  (if (null coef)
      0
    (+ (* (car coef) (expt x n))
       (poly-aux (cdr coef) x (1- n)))
    )
  )

;;; versao reversa

(defun poly (coef x)
  (poly-aux (reverse coef) x)
  )

(defun poly-aux (coef x)
  (if (null coef)
      0
    (+ (car coef) (* x (poly (cdr coef) x)))
    )
  )

;;; (4) PROD-TENS  (alguns terao reconhecido o nome "produto tensorial"

(defun prod-tens (l1 l2)
  (if (null l1)
      ()
    (cons (mult-line (car l1) l2)
	  (poly-tens (cdr l1) l2))
    )
  )

(defun mult-line (c line)
  (if (null line)
      ()
    (cons (* c (car line))
	  (mult-line c (cdr line))
	  )
    )
  )