Перемножение двух многочленов

(defun sum-product (w v)
  (loop for a in w sum
        (loop for b in v sum (* a b))))
 
> (sum-product '(1 2 3) '(4 5 6))
90

;; Произведение полиномов
 
(defun poly-prod (p q)
  (let ((pp (mapcar 'cons p (range 0 (length p))))
        (qq (mapcar 'cons q (range 0 (length q)))))
       (simplify (apply 'append (mapcar #'(lambda (x) 
                         (mapcar #'(lambda (y) 
                                    (cons (* (car x) (car y)) (+ (cdr x) (cdr y)))) qq)) pp)))))
 
==> poly-prod
 
;; Упрощение 
 
(defun simplify (p &optional (k 0) (res nil))
 (if (null p) 
  res
  (let ((r nil))
     (mapcar #'(lambda (x) (when (= k (cdr x)) (push (car x) r))) p)
     (simplify (remove-if #'(lambda (x) (= k (cdr x))) p) (+ k 1) (append res (list (apply '+ r)))))))
 
==> simplify
 
(poly-prod '(1 1) '(1 1))
 
==> (1 2 1)
 
(poly-prod '(1 2 1) '(1 1))
 
==> (1 3 3 1)
 
(let ((p1 '(1 1))
      (p2 '(1 1)))
     (dotimes (i 22 p2) (setq p2 (poly-prod p1 p2))))
 
==> (1 23 253 1771 8855 33649 100947 245157 490314 817190 1144066 1352078 1352078 1144066 817190 490314 245157 100947 33649 8855 1771 253 23 1)