; We can write <code>lob-mult</code> using the standard shift-and-add
; multiplication technique taught in grade school, but it's probably easier
; to just use the equations:
; <blockquote>
;   <i>(0) * (0) = 0</i>
;   <i>(0) * (2a + b) = 0</i>
;   <i>(2a + b) * (0) = 0</i>
;   <i>(2x + 0) * (2y + 0) = 4xy</i>
;   <i>(2x + 1) * (2y + 0) = 4xy+2y </i>
;   <i>(2x + 0) * (2y + 1) = 4xy+2x</i>
;   <i>(2x + 1) * (2y + 1) = 4xy+2(x+y)+1</i>
; </blockquote>
;
(define lob-mult
  (lambda (l1 l2)
    (cond
      [(and (null? l1) (null? l2))
       null]
      [(and (null? l1) (cons? l2))
       null]
      [(and (cons? l1) (null? l2))
       null]
      [(and (cons? l1) (cons? l2))
       (cond
	 [(and (zero? (car l1)) (zero? (car l2)))
	  (lob-mult2 (lob-mult2 (lob-mult (cdr l1) (cdr l2))))]
	 [(and (zero? (car l1)) (one? (car l2)))
	  (lob-add l1
		   (lob-mult2 (lob-mult2 (lob-mult (cdr l1) (cdr l2)))))]
	 [(and (one? (car l1)) (zero? (car l2)))
	  (lob-add l2
		   (lob-mult2 (lob-mult2 (lob-mult (cdr l1) (cdr l2)))))]
	 [(and (one? (car l1)) (one? (car l2)))
	  (lob-add1
	   (lob-add (lob-mult2 (lob-add (cdr l1) (cdr l2)))
		    (lob-mult2 (lob-mult2 (lob-mult (cdr l1) (cdr l2))))))]
	 [else (error "missed a case in lob-mult/case1,1: " l1 l2)])]
      [else (error "missed a case in lob-mult: " l1 l2)])))

;(lob-mult null null)
;(lob-mult null (list 0 1))
;(lob-mult (list 0 1) null)
;(lob-mult (list 1 0 1 1) (list 1))
;(lob-mult (list 1 1) (list 0 0 1))
;(lob-mult (list 0 1) (list 0 1))
;'------
;(lob-mult (list 0 1) (list 1 1))
;(lob-mult (list 1 1) (list 0 1))
;(lob-mult (list 1 0 1) (list 1 1))
;(lob-mult (list 1 0 1 1) (list 0 1))