Use definitions of trnxx and matpak, ops and inv.

(define (rank a) (call-with-current-continuation (lambda (cc)
  (let rnk ((a a)) (begin (inv a (lambda (d)
    (rnk (map (lambda (r) (let lx ((r r)(x d)(n 0))
    (if (pair? x) (if (pair? r) (if (zero? (car x))
         (cons (car r) (lx (cdr r)(cdr x)(+ n 1))) (cdr r))
       (cc n)) r))) a)))) (cc (length a)))))))

these cases:
r= (3 ..), x= (0 ..) recurse lx
r= (3 ..), x= (1 ..) omit & return r
r= (3 ..), x= () recurse rnk
r= (),     x= (1) report rank

(rank '((1 0 0)(0 1 0)(0 0 1))) ; 3
(rank '((0 0 1)(1 0 0)(0 1 0))) ; 3
(rank '((0 0 0)(1 0 0)(0 1 0))) ; 2
(rank '((0 1 0)(0 2 1)(0 0 1))) ; 2
(rank '((0 1 0)(0 0 0)(0 0 1))) ; 2
(rank '((0 1 0)(0 0 0)(0 0 0))) ; 1
(rank '((0 0 0)(0 0 0)(0 0 0))) ; 0


(rank
'((2 3    5) ; rank 2
  (5 7.5  8)
  (6 9    4)))

(rank
'((3    5) ; rank 2
 (7.5  8)
 (9    4)))
 
(define (rv m v) (begin (write (list m v)) v))
; version with print statements.
(define (rank a) (call-with-current-continuation (lambda (cc)
  (let rnk ((a a)) (write (list "fuz" a)) (newline)
    (begin (inv a (lambda (d) (write (list "d=" d)) (newline)
    (rnk (rv "mapv" (map (lambda (r) 
      (write (list "jx" d r))
    (rv "lxv" (let lx ((r r)(x d)(n 0)) (write (list "maparg" r x n))
    (if (pair? x) (if (pair? r)
       (if (zero? (car x))
         (cons (car r) (lx (cdr r)(cdr x)(+ n 1))) (cdr r))
       (cc n)) r)))) a))))) (cc (length a)))))))
 
 (define (Rank a) (call-with-current-continuation (lambda (cc)
  (let rnk ((a a)) (begin (inv a (lambda (d)
    (rnk (map (lambda (r) (let lx ((r r)(x d))
    (if (pair? x) (if (pair? r) (if (zero? (car x))
         (cons (car r) (lx (cdr r)(cdr x))) (cdr r))
       (cc a)) r))) a)))) (cc a))))))