> 
--------------------------------------------------<Comment>
;; Loading the Kenzo program.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(LOAD-CFILES)
--------------------------------------------------
> 
--------------------------------------------------<Result>
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classes.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\macros.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\various.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\combinations.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chain-complexes.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chcm-elementary-op.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\effective-homology.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\homology-groups.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\searching-homology.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cones.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\tensor-products.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\coalgebras.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cobar.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\algebras.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\bar.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-sets.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-mrphs.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\delta.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\special-smsts.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\suspensions.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\disk-pasting.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cartesian-products.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\eilenberg-zilber.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\kan.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-groups.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\fibrations.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\loop-spaces.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\ls-twisted-products.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\lp-space-efhm.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classifying-spaces.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\k-pi-n.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\serre.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cs-twisted-products.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cl-space-efhm.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\whitehead.fasl
; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\smith.fasl
--- done ---
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Constructing the 3-sphere.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF S3 (SPHERE 3))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K1 Simplicial-Set]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_3(S^3) = ?
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(HOMOLOGY S3 3)
--------------------------------------------------
> 
--------------------------------------------------<Result>

Computing boundary-matrix in dimension 3.
Rank of the source-module : 1.


;; Clock -> 2006-08-25, 17h 45m 20s.
Computing the boundary of the generator 1 (dimension 3) :
S3 
End of computing.


Computing boundary-matrix in dimension 4.
Rank of the source-module : 0.




Homology in dimension 3 :


Component Z


---done---

;; Clock -> 2006-08-25, 17h 45m 20s.

NIL
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_3(S^3) = Z.
;;
;; Fundamental cohomology class.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FCC3 (CHML-CLSS S3 3))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K9 Cohomology-Class on K1 of degree 3]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Associated fibration K(Z,2) -> X_4 -> S^3
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FBR3 (Z-WHITEHEAD S3 FCC3))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K20 Fibration K1 -> K15]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Corresponding total space X_4.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF X4 (FIBRATION-TOTAL FBR3))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K23 Simplicial-Set]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_4(X_4) = ?
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(HOMOLOGY X4 4)
--------------------------------------------------
> 
--------------------------------------------------<Result>

Computing boundary-matrix in dimension 4.
Rank of the source-module : 1.


;; Clock -> 2006-08-25, 17h 45m 25s.
Computing the boundary of the generator 1 (dimension 4) :
<TnPr * <<Abar[2 S1][2 S1]>>> 
End of computing.


Computing boundary-matrix in dimension 5.
Rank of the source-module : 1.


;; Clock -> 2006-08-25, 17h 45m 25s.
Computing the boundary of the generator 1 (dimension 5) :
<TnPr S3 <<Abar[2 S1]>>> 
End of computing.




Homology in dimension 4 :


Component Z/2Z


---done---

;; Clock -> 2006-08-25, 17h 45m 25s.

NIL
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_4(S^4) = Z/2Z.
;;
;; Fundamental cohomology class.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FCC4 (CHML-CLSS X4 4))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K227 Cohomology-Class on K211 of degree 4]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Associated fibration K(Z/2Z, 3) -> X_5 -> X_4
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FBR4 (Z2-WHITEHEAD X4 FCC4))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K246 Fibration K23 -> K239]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Corresponding total space X_5.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF X5 (FIBRATION-TOTAL FBR4))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K249 Simplicial-Set]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_5(X_5) = ?
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(HOMOLOGY X5 5)
--------------------------------------------------
> 
--------------------------------------------------<Result>

Computing boundary-matrix in dimension 5.
Rank of the source-module : 4.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 1 (dimension 5) :
<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 2 (dimension 5) :
<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 3 (dimension 5) :
<TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 4 (dimension 5) :
<TnPr <TnPr S3 <<Abar[2 S1]>>> <<Abar>>> 
End of computing.


Computing boundary-matrix in dimension 6.
Rank of the source-module : 7.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 1 (dimension 6) :
<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 2 (dimension 6) :
<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 3 (dimension 6) :
<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 4 (dimension 6) :
<TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 31s.
Computing the boundary of the generator 5 (dimension 6) :
<TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 32s.
Computing the boundary of the generator 6 (dimension 6) :
<TnPr <TnPr S3 <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 32s.
Computing the boundary of the generator 7 (dimension 6) :
<TnPr <TnPr * <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> 
End of computing.




Homology in dimension 5 :


Component Z/2Z


---done---

;; Clock -> 2006-08-25, 17h 45m 32s.

NIL
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_5(X_5) = Z/2Z.
;;
;; Fundamental cohomology class.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FCC5 (CHML-CLSS X5 5))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K549 Cohomology-Class on K533 of degree 5]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Associated fibration K(Z/2Z,4) -> X_6 -> X_5
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF FBR5 (Z2-WHITEHEAD X5 FCC5))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K557 Fibration K249 -> K550]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; Corresponding total space X_6.
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(SETF X6 (FIBRATION-TOTAL FBR5))
--------------------------------------------------
> 
--------------------------------------------------<Result>
[K560 Simplicial-Set]
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; H_6(X_6) = ?
--------------------------------------------------
> 
--------------------------------------------------<Lisp Statement>
(TIME (HOMOLOGY X6 6))
--------------------------------------------------
> 
--------------------------------------------------<Result>

Computing boundary-matrix in dimension 6.
Rank of the source-module : 10.


;; Clock -> 2006-08-25, 17h 45m 42s.
Computing the boundary of the generator 1 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 42s.
Computing the boundary of the generator 2 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 42s.
Computing the boundary of the generator 3 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 42s.
Computing the boundary of the generator 4 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 42s.
Computing the boundary of the generator 5 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 43s.
Computing the boundary of the generator 6 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 43s.
Computing the boundary of the generator 7 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 43s.
Computing the boundary of the generator 8 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 43s.
Computing the boundary of the generator 9 (dimension 6) :
<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 43s.
Computing the boundary of the generator 10 (dimension 6) :
<TnPr <TnPr <TnPr * <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
End of computing.


Computing boundary-matrix in dimension 7.
Rank of the source-module : 19.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 1 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[5 4]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 2 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[2 1][3 2]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 3 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[3 2][2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 4 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 5 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 6 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 7 (dimension 7) :
<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 8 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[6 5]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 9 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[2 1][4 3]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 44s.
Computing the boundary of the generator 10 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[3 2][3 2]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 45s.
Computing the boundary of the generator 11 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[4 3][2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 45s.
Computing the boundary of the generator 12 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[2 1][2 1][2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 45s.
Computing the boundary of the generator 13 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][4 <<Abar[3 2]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 46s.
Computing the boundary of the generator 14 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[4 <<Abar[3 2]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 47s.
Computing the boundary of the generator 15 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 47s.
Computing the boundary of the generator 16 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 47s.
Computing the boundary of the generator 17 (dimension 7) :
<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 47s.
Computing the boundary of the generator 18 (dimension 7) :
<TnPr <TnPr <TnPr * <<Abar[2 S1][2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
End of computing.


;; Clock -> 2006-08-25, 17h 45m 49s.
Computing the boundary of the generator 19 (dimension 7) :
<TnPr <TnPr <TnPr S3 <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
End of computing.




Homology in dimension 6 :


Component Z/12Z


---done---

;; Clock -> 2006-08-25, 17h 46m 13s.

; cpu time (non-gc) 19,367 msec user, 0 msec system
; cpu time (gc)     11,447 msec user, 0 msec system
; cpu time (total)  30,814 msec user, 0 msec system
; real time  30,815 msec
; space allocation:
;  25,440,099 cons cells, 0 symbols, 328,454,200 other bytes, 6473 static bytesNIL
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;;
;;  Conclusion:
;;
;;  pi_6(S^3) = H_6(X_6) = Z/12Z.
;;
--------------------------------------------------
> 
--------------------------------------------------<Comment>
;; +-----------------+
;; +                 |
;; +     The END     |
;; +                 |
;; +-----------------+
--------------------------------------------------
>