(in-package :kenzo-test)

(in-suite :kenzo)

#|
(test cs-hat-u-t
      (cat:cat-init)
      (let* ((c (cat:cs-hat-u-t (cat:k-z-1)))
	     (abar (random-abar 8 4))
	     (abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	     (gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3) 0 '())
					 2 '(4 5))
			     abar-degr abar)))
	(cat:? c (+ 5 abar-degr) gnrt)
	(is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr) gnrt))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (print (cat:? c (+ 6 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 6 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6)) abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 11)
	      (print (cat:? c (+ 4 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 4 abar-degr)
						   gnrt)))))))))
|#

#|
(test cs-hat-t-u
      (cat:cat-init)
      (dotimes (i 5) (print (random-abar 8 4)))
      (let* ((c (cat:cs-hat-t-u (cat:k-z-1)))
	     (abar (random-abar 8 4))
	     (abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	     (gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3) 0 '())
					 2 '(4 5))
			     abar-degr abar)))
	(cat:? c (+ 5 abar-degr) gnrt)
	(is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr) gnrt))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (print (cat:? c (+ 6 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 6 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 11)
	      (print (cat:? c (+ 4 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 4 abar-degr)
						   gnrt)))))))))
|#

#|
(test cs-left-hmeq-hat
      (cat:cat-init)
      (let ((c (cat:cs-left-hmeq-hat (cat:k-z-1)))
	    abar-degr
	    gnrt)
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (print (cat:? c (+ 6 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 6 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (print (cat:? c (+ 5 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 5 abar-degr)
						   gnrt)))))))
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 11)
	      (print (cat:? c (+ 4 abar-degr) gnrt))
	      (is (cat:cmbn-zero-p (cat:? c (cat:? c (+ 4 abar-degr)
						   gnrt)))))))))
|#


(test cs-pre-left-hmeq-left-reduction-intr-f
      (cat:cs-pre-left-hmeq-left-reduction-intr-f
       (cat:cmbn 6 100 (cat:tnpr 4 (cat:tnpr 2 'a 2 'b) 2 'c)
		 10  (cat:tnpr 6 (cat:tnpr 2 'a 4 'b) 0 'c)
		 50  (cat:tnpr 6 (cat:tnpr 6 'a 0 'b) 0 'c)
		 1   (cat:tnpr 6 (cat:tnpr 6 'aa 0 'b) 0 'c))))


(test cs-pre-left-hmeq-left-reduction-intr-g
      (let ((g (cat:cs-pre-left-hmeq-left-reduction-intr-g '())))
	(funcall g (cat:cmbn 3 14 (cat:gbar 3 0 'a 1 'b 0 '())))))


#|
(test cs-pre-left-hmeq-left-reduction
      (cat:cat-init)
      (let ((rdct (cat:cs-pre-left-hmeq-left-reduction (cat:k-z-1)))
	    abar-degr
	    gnrt
	    gbar)
	(cat:pre-check-rdct rdct)
	(setf cat:*tc* (cat:cmbn 0 1
				 (cat:tnpr 0 (cat:tnpr 0
						       cat:+null-gbar+ 0 '())
					   0 cat:+null-abar+))
	      cat:*bc* (cat:cmbn 0 1 cat:+null-gbar+))
	(check-rdct)
	(setf cat:*tc* (cat:cmbn 1 1
				 (cat:tnpr 1 (cat:tnpr 0
						       cat:+null-gbar+ 1 '(13))
					   0 cat:+null-abar+)))
	(check-rdct)
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (setf gbar (cat:gbar 2 0 '(1) 0 '()))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn 2 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (setf gbar (cat:gbar 3 0 '(1 2) 1 '() 0 '()))
	    (unless (>= abar-degr 8)
	      (setf cat:*tc* (cat:cmbn (+ 6 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn 3 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6))
				 abar-degr abar))
	    (setf gbar (cat:gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn 4 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (setf gbar (cat:gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9)
				 0 '()))
	    (unless (>= abar-degr 10)
	      (setf cat:*tc* (cat:cmbn (+ 4 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn 5 1 gbar))
	      (check-rdct))))))
|#

#|
(test cs-left-hmeq-left-reduction
      (cat:cat-init)
      (let ((rdct (cat:cs-left-hmeq-left-reduction (cat:k-z-1)))
	    abar-degr gnrt gbar)
	(cat:pre-check-rdct rdct)
	(setf cat:*tc* (cat:cmbn 0 1 (cat:tnpr 0
					       (cat:tnpr 0 cat:+null-gbar+
							 0 '()) 0
							 cat:+null-abar+))
	      cat:*bc* (cat:cmbn 0 1 cat:+null-gbar+))
	(check-rdct)
	(setf cat:*tc* (cat:cmbn 1 1 (cat:tnpr 1
					       (cat:tnpr 0 cat:+null-gbar+
							 1 '(13)) 0
							 cat:+null-abar+)))
	(check-rdct)
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (setf gbar (cat:gbar 2 0 '(1) 0 '()))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn 2 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (setf gbar (cat:gbar 3 0 '(1 2) 1 '() 0 '()))
	    (unless (>= abar-degr 8)
	      (setf cat:*tc* (cat:cmbn (+ 6 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn 3 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6))
				 abar-degr abar))
	    (setf gbar (cat:gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn 4 1 gbar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (setf gbar (cat:gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9)
				 0 '()))
	    (unless (>= abar-degr 10)
	      (setf cat:*tc* (cat:cmbn (+ 4 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn 5 1 gbar))
	      (check-rdct))))))
|#

(test cs-pre-left-hmeq-right-reduction-intr-f
      (cat:cs-pre-left-hmeq-right-reduction-intr-f
       (cat:cmbn 4 2 (cat:tnpr 0 (cat:tnpr 0 cat:+null-gbar+ 0 'i)
			       4 (cat:abar 2 'a 2 'b))
		 3 (cat:tnpr 0 (cat:tnpr 0 cat:+null-gbar+ 0 'i)
			     4 (cat:abar 2 'a 2 'c))
		 5 (cat:tnpr 1 (cat:tnpr 0 cat:+null-gbar+ 1 'a)
			     3 (cat:abar 1 'a 2 'b)))))


(test cs-pre-left-hmeq-right-reduction-g
      (let ((g (cat:cs-pre-left-hmeq-right-reduction-intr-g 'i)))
	(funcall g (cat:cmbn 3 2 (cat:abar 1 'a 2 'b)))))

#|
(test cs-pre-left-hmeq-right-reduction
      (cat:cat-init)
      (let ((rdct (cat:cs-pre-left-hmeq-right-reduction (cat:k-z-1)))
	    abar-degr
	    gnrt)
	(cat:pre-check-rdct rdct)
	(setf cat:*tc* (cat:cmbn 0 1 (cat:tnpr 0
					       (cat:tnpr 0 cat:+null-gbar+
							 0 '())
					       0 cat:+null-abar+))
	      cat:*bc* (cat:cmbn 0 1 cat:+null-abar+))
	(check-rdct)
	(setf cat:*tc* (cat:cmbn 1 1 (cat:tnpr 1
					       (cat:tnpr 0 cat:+null-gbar+
							 1 '(13))
					       0 cat:+null-abar+)))
	(check-rdct)
	(dotimes (i 10)
	  (let ((abar (random-abar 8 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 6 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 0 '(3)
							 0 '()) 3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 8)
	      (setf cat:*tc* (cat:cmbn (+ 6 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     3 '(4 5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (setf cat:*tc* (cat:cmbn (+ 4 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))))
|#

#|
(test cs-left-hmeq-right-reduction
      (cat:cat-init)

      (let ((rdct (cat:cs-left-hmeq-right-reduction (cat:k-z-1)))
	    abar-degr
	    gnrt)
	(cat:pre-check-rdct rdct)
	(setf cat:*tc* (cat:cmbn 0 1
				 (cat:tnpr 0 (cat:tnpr 0 cat:+null-gbar+
						       0 '())
					   0 cat:+null-abar+))
	      cat:*bc* (cat:cmbn 0 1 cat:+null-abar+))
	(check-rdct)
	(setf cat:*tc* (cat:cmbn 1 1
				 (cat:tnpr 1 (cat:tnpr 0 cat:+null-gbar+
						       1 '(13))
					   0 cat:+null-abar+)))
	(check-rdct)
	(dotimes (i 10)
	  (let ((abar (random-abar 4 2)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 3 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     1 '(4))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 3 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 3 1)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 8)
	      (setf cat:*tc* (cat:cmbn (+ 4 abar-degr) 1 gnrt)
		    cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 3 1)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 5 (cat:tnpr 3 (cat:gbar 3 0 '(1 2) 1 '()
							 0 '()) 2 '(5 6))
				 abar-degr abar))
	    (unless (>= abar-degr 9)
	      (setf cat:*tc* (cat:cmbn (+ 5 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))
	(dotimes (i 10)
	  (let ((abar (random-abar 6 4)))
	    (setf abar-degr (apply #'+ (mapcar #'car (cat:abar-list abar))))
	    (setf gnrt (cat:tnpr 4 (cat:tnpr 2 (cat:gbar 2 0 '(3) 0 '())
					     2 '(4 5))
				 abar-degr abar))
	    (unless (>= abar-degr 10)
	      (setf cat:*tc* (cat:cmbn (+ 4 abar-degr) 1 gnrt))
	      (setf cat:*bc* (cat:cmbn abar-degr 1 abar))
	      (check-rdct))))))
|#

(test cs-left-hmeq
      (cat:cat-init)
      (let* ((h (cat:cs-left-hmeq (cat:k-z-1)))
	     (abar (cat:abar 2 '(2) 3 '(3 4))))
	(cat:rf h
	    (cat:lg h
		(cat:lf h
		    (cat:rg h 5 abar))))))


(test classifying-space
      (cat:cat-init)
      (let* ((k (cat:k-z-1))
	     (bk (cat:classifying-space k))
	     (obk (cat:loop-space bk)))
	(cat:homology k 0 10)
	(cat:homology bk 0 10)
	(cat:homology obk 0 6)))