> -------------------------------------------------- ;; Loading the Kenzo program. -------------------------------------------------- > -------------------------------------------------- (LOAD-CFILES) -------------------------------------------------- > -------------------------------------------------- ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\classes.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\macros.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\various.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\combinations.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\chain-complexes.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\chcm-elementary-op.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\effective-homology.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\homology-groups.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\searching-homology.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\cones.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\tensor-products.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\coalgebras.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\cobar.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\algebras.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\bar.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\simplicial-sets.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\simplicial-mrphs.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\delta.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\special-smsts.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\suspensions.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\disk-pasting.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\cartesian-products.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\eilenberg-zilber.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\kan.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\simplicial-groups.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\fibrations.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\loop-spaces.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\ls-twisted-products.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\lp-space-efhm.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\classifying-spaces.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\k-pi-n.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\serre.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\cs-twisted-products.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\cl-space-efhm.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\whitehead.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\smith.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\koszul.fasl ; Fast loading C:\Docume~1\Francis\AA\Kenzo\Gift\groebner.fasl --- done ---NIL -------------------------------------------------- > -------------------------------------------------- ;; Kenzo expression of the ideal: ;; | xy-tz y3-x2z x3-ty2 tx2-z t2x-y t3z-y2 t2y2-xz t3y-x2 t5-x | ;; = the Groebner basis of ;; ideal{x-t^5, y-t^7, z-t^11} / (t, x, y, z) & DegRevLex -------------------------------------------------- > -------------------------------------------------- (SETF IDEAL (LIST (CMBN 0 1 '(5 0 0 0) -1 '(0 1 0 0)) ;; t5 - x (CMBN 0 1 '(3 0 1 0) -1 '(0 2 0 0)) ;; t3y - x2 (CMBN 0 1 '(2 0 2 0) -1 '(0 1 0 1)) ;; t2y2 - xz (CMBN 0 1 '(3 0 0 1) -1 '(0 0 2 0)) ;; t3z - y2 (CMBN 0 1 '(2 1 0 0) -1 '(0 0 1 0)) ;; t2x - y (CMBN 0 1 '(1 2 0 0) -1 '(0 0 0 1)) ;; tx2 - z (CMBN 0 1 '(0 3 0 0) -1 '(1 0 2 0)) ;; x3 - ty2 (CMBN 0 1 '(0 0 3 0) -1 '(0 2 0 1)) ;; y3 - x2z (CMBN 0 1 '(0 1 1 0) -1 '(1 0 0 1))));; xy - tz -------------------------------------------------- > -------------------------------------------------- ( ----------------------------------------------------------------------{CMBN 0} <1 * (5 0 0 0)> <-1 * (0 1 0 0)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (3 0 1 0)> <-1 * (0 2 0 0)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (2 0 2 0)> <-1 * (0 1 0 1)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (3 0 0 1)> <-1 * (0 0 2 0)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (2 1 0 0)> <-1 * (0 0 1 0)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (1 2 0 0)> <-1 * (0 0 0 1)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (0 3 0 0)> <-1 * (1 0 2 0)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (0 0 3 0)> <-1 * (0 2 0 1)> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 0} <1 * (0 1 1 0)> <-1 * (1 0 0 1)> ------------------------------------------------------------------------------ ) -------------------------------------------------- > -------------------------------------------------- ;; The corresponding Koszul complex. -------------------------------------------------- > -------------------------------------------------- (SETF K (K-COMPLEX/GI 4 IDEAL)) -------------------------------------------------- > -------------------------------------------------- [K5 Chain-Complex] -------------------------------------------------- > -------------------------------------------------- ;; Computing the effective homology of K. -------------------------------------------------- > -------------------------------------------------- (SETF EFHM (EFHM K)) -------------------------------------------------- > -------------------------------------------------- [K716 Equivalence K5 <= K699 => K713] -------------------------------------------------- > -------------------------------------------------- ;; Homology in degree 2. -------------------------------------------------- > -------------------------------------------------- (HOMOLOGY K 2) -------------------------------------------------- > -------------------------------------------------- Computing boundary-matrix in dimension 2. Rank of the source-module : 16. ;; Clock -> 2006-04-24, 14h 27m 7s. Computing the boundary of the generator 1 (dimension 2) : >>>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 7s. Computing the boundary of the generator 2 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 8s. Computing the boundary of the generator 3 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 8s. Computing the boundary of the generator 4 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 8s. Computing the boundary of the generator 5 (dimension 2) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 9s. Computing the boundary of the generator 6 (dimension 2) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 9s. Computing the boundary of the generator 7 (dimension 2) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 9s. Computing the boundary of the generator 8 (dimension 2) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 10s. Computing the boundary of the generator 9 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 10s. Computing the boundary of the generator 10 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 10s. Computing the boundary of the generator 11 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 11s. Computing the boundary of the generator 12 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 11s. Computing the boundary of the generator 13 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 11s. Computing the boundary of the generator 14 (dimension 2) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 12s. Computing the boundary of the generator 15 (dimension 2) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 12s. Computing the boundary of the generator 16 (dimension 2) : >>> End of computing. Computing boundary-matrix in dimension 3. Rank of the source-module : 10. ;; Clock -> 2006-04-24, 14h 27m 12s. Computing the boundary of the generator 1 (dimension 3) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 13s. Computing the boundary of the generator 2 (dimension 3) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 13s. Computing the boundary of the generator 3 (dimension 3) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 14s. Computing the boundary of the generator 4 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 14s. Computing the boundary of the generator 5 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 14s. Computing the boundary of the generator 6 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 15s. Computing the boundary of the generator 7 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 15s. Computing the boundary of the generator 8 (dimension 3) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 16s. Computing the boundary of the generator 9 (dimension 3) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 27m 16s. Computing the boundary of the generator 10 (dimension 3) : >>> End of computing. Homology in dimension 2 : Component Z Component Z Component Z ---done--- ;; Clock -> 2006-04-24, 14h 27m 17s. NIL -------------------------------------------------- > -------------------------------------------------- ;; Tor^A_2(A/I, k) = k^3 -------------------------------------------------- > -------------------------------------------------- ;; Important: much more than the homology group is computed. ;; The complete homological nature of K ;; is canonically related to the homological nature ;; of the effective component. ;; ;; Extracting this effective component. -------------------------------------------------- > -------------------------------------------------- (SETF EK (RBCC EFHM)) -------------------------------------------------- > -------------------------------------------------- [K713 Chain-Complex] -------------------------------------------------- > -------------------------------------------------- ;; This complex is effective. ;; Basis in degree 2. -------------------------------------------------- > -------------------------------------------------- (DOLIST (ITEM (BASIS EK 2) NIL) (PRINT ITEM)) -------------------------------------------------- > -------------------------------------------------- >>>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>> >>>>>> >>>>> >>>>> >>>> >>>> >>>> >>>> >>>> >>> >>> >>> NIL -------------------------------------------------- > -------------------------------------------------- ;; The Koszul complex is NOT effective. -------------------------------------------------- > -------------------------------------------------- (BASIS K 2) -------------------------------------------------- > -------------------------------------------------- Error: The object [K5 Chain-Complex] is locally-effective. > -------------------------------------------------- ;; But any homological information about this complex ;; can be reached through the effective component. ;; ;; Typical example: Finding a representant for ;; a HOMOLOGY CLASS. ;; ;; Finding representants in the effective component. -------------------------------------------------- > -------------------------------------------------- (SETF H2EKR (HOMOLOGY-GEN EK 2)) -------------------------------------------------- > -------------------------------------------------- Computing boundary-matrix in dimension 2. Rank of the source-module : 16. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 1 (dimension 2) : >>>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 2 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 3 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 4 (dimension 2) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 5 (dimension 2) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 6s. Computing the boundary of the generator 6 (dimension 2) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 7 (dimension 2) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 8 (dimension 2) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 9 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 10 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 11 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 12 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 7s. Computing the boundary of the generator 13 (dimension 2) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 14 (dimension 2) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 15 (dimension 2) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 16 (dimension 2) : >>> End of computing. Computing boundary-matrix in dimension 3. Rank of the source-module : 10. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 1 (dimension 3) : >>>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 2 (dimension 3) : >>>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 3 (dimension 3) : >>>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 8s. Computing the boundary of the generator 4 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 5 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 6 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 7 (dimension 3) : >>>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 8 (dimension 3) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 9 (dimension 3) : >>> End of computing. ;; Clock -> 2006-04-24, 14h 28m 9s. Computing the boundary of the generator 10 (dimension 3) : >>> End of computing. Homology in dimension 2 : Component Z Component Z Component Z ( ----------------------------------------------------------------------{CMBN 2} <1 * >>>>>>>> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 2} <1 * >>>>>>>> <-1 * >>>> ------------------------------------------------------------------------------ ----------------------------------------------------------------------{CMBN 2} <1 * >>>>>> <-1 * >>>> ------------------------------------------------------------------------------ ) -------------------------------------------------- > -------------------------------------------------- ;; Three generators are produced. ;; The first one. -------------------------------------------------- > -------------------------------------------------- (SETF RIGHT-G (FIRST H2EKR)) -------------------------------------------------- > -------------------------------------------------- ----------------------------------------------------------------------{CMBN 2} <1 * >>>>>>>> ------------------------------------------------------------------------------ -------------------------------------------------- > -------------------------------------------------- ;; Finding the middle corresponding generator. -------------------------------------------------- > -------------------------------------------------- (SETF MIDDLE-G (RG EFHM RIGHT-G)) -------------------------------------------------- > -------------------------------------------------- ----------------------------------------------------------------------{CMBN 2} <1 * >>>>>>>>> <-1 * >>>>>>>>> <1 * >>>>>>>>> <1 * >>>>>>>>> <-1 * >>>>>>>> <1 * >>>>>>>> <1 * >>>>>> ------------------------------------------------------------------------------ -------------------------------------------------- > -------------------------------------------------- ;; It's a complicated mixture of cones and Koszul expressions. ;; ;; The image in the Koszul complex. -------------------------------------------------- > -------------------------------------------------- (SETF KOSZUL-G (LF EFHM MIDDLE-G)) -------------------------------------------------- > -------------------------------------------------- ----------------------------------------------------------------------{CMBN 2} <1 * ((1 1 0 0) (0 1 1 0))> <-1 * ((2 0 0 0) (0 1 0 1))> <1 * ((0 0 0 0) (0 0 1 1))> ------------------------------------------------------------------------------ -------------------------------------------------- > -------------------------------------------------- ;; = tx dx.dy - t^2 dx.dz + dy.dz ;; ;; Verifying it's a cycle. -------------------------------------------------- > -------------------------------------------------- (? K KOSZUL-G) -------------------------------------------------- > -------------------------------------------------- ----------------------------------------------------------------------{CMBN 1} ------------------------------------------------------------------------------ -------------------------------------------------- > -------------------------------------------------- ;; But this cycle is definitively not a boundary !!! -------------------------------------------------- > -------------------------------------------------- ;; How many chain-complexes in our environment? -------------------------------------------------- > -------------------------------------------------- (COUNT-IF #'(LAMBDA (ITEM) (TYPEP ITEM 'CHAIN-COMPLEX)) *K-LIST*) -------------------------------------------------- > -------------------------------------------------- 67 -------------------------------------------------- > -------------------------------------------------- ;; How many chain-complex morphisms? -------------------------------------------------- > -------------------------------------------------- (COUNT-IF #'(LAMBDA (ITEM) (TYPEP ITEM 'MORPHISM)) *K-LIST*) -------------------------------------------------- > -------------------------------------------------- 547 -------------------------------------------------- > -------------------------------------------------- ;; How many Koszul complexes? -------------------------------------------------- > -------------------------------------------------- (COUNT-IF #'(LAMBDA (ITEM) (MEMBER (FIRST (DFNT ITEM)) '(K-COMPLEX/GI K-COMPLEX/I K-COMPLEX))) *K-LIST*) -------------------------------------------------- > -------------------------------------------------- 18 -------------------------------------------------- > -------------------------------------------------- ;; How many cones? -------------------------------------------------- > -------------------------------------------------- (COUNT 'CONE *K-LIST* :KEY #'(LAMBDA (ITEM) (FIRST (DFNT ITEM)))) -------------------------------------------------- > -------------------------------------------------- 44 -------------------------------------------------- > -------------------------------------------------- ;; Examining the morphisms which have been called ;; more than 10,000 times. -------------------------------------------------- > -------------------------------------------------- (DOLIST (ITEM *K-LIST*) (WHEN (AND (TYPEP ITEM 'MORPHISM) (< 10000 (???-CLNM ITEM))) (FORMAT T " ~7D = ~A~%" (???-CLNM ITEM) ITEM))) -------------------------------------------------- > -------------------------------------------------- 14664 = [K558 Morphism (degree 0): K517 -> K534] 17256 = [K557 Morphism (degree 0): K534 -> K517] 24836 = [K553 Morphism (degree 1): K534 -> K534] 24836 = [K552 Morphism (degree 2): K1 -> K1] 27228 = [K546 Morphism (degree 1): K1 -> K1] 31920 = [K544 Morphism (degree 0): K534 -> K534] 14664 = [K537 Morphism (degree 0): K517 -> K534] 17256 = [K536 Morphism (degree 0): K534 -> K517] 14664 = [K533 Morphism (degree 0): K517 -> K1] 17256 = [K532 Morphism (degree 0): K1 -> K517] 14664 = [K531 Morphism (degree 0): K1 -> K1] 31008 = [K530 Morphism (degree 0): K1 -> K1] 10231 = [K368 Morphism (degree 0): K66 -> K346] 12105 = [K361 Morphism (degree 1): K316 -> K316] 10231 = [K355 Morphism (degree 1): K316 -> K274] 10231 = [K352 Morphism (degree 0): K84 -> K346] 10336 = [K342 Morphism (degree 0): K316 -> K274] 10336 = [K341 Morphism (degree 0): K316 -> K78] 17773 = [K335 Morphism (degree 0): K51 -> K316] 18745 = [K334 Morphism (degree 0): K316 -> K51] 29878 = [K330 Morphism (degree 1): K316 -> K316] 29878 = [K329 Morphism (degree 2): K239 -> K239] 35546 = [K323 Morphism (degree 1): K239 -> K239] 17773 = [K321 Morphism (degree 0): K306 -> K316] 18745 = [K320 Morphism (degree 0): K316 -> K306] 36176 = [K313 Morphism (degree 0): K239 -> K239] 36176 = [K312 Morphism (degree 0): K239 -> K90] 17773 = [K309 Morphism (degree 0): K51 -> K306] 18745 = [K308 Morphism (degree 0): K306 -> K51] 17773 = [K305 Morphism (degree 0): K51 -> K90] 18745 = [K304 Morphism (degree 0): K90 -> K51] 17773 = [K303 Morphism (degree 0): K90 -> K90] 36176 = [K302 Morphism (degree 0): K90 -> K90] 20567 = [K296 Morphism (degree 0): K78 -> K274] 13963 = [K291 Morphism (degree 1): K274 -> K274] 13963 = [K290 Morphism (degree 2): K239 -> K207] 43841 = [K289 Morphism (degree 1): K239 -> K239] 20567 = [K283 Morphism (degree 1): K239 -> K207] 20567 = [K280 Morphism (degree 0): K99 -> K274] 20672 = [K270 Morphism (degree 0): K239 -> K207] 20672 = [K269 Morphism (degree 0): K239 -> K92] 92289 = [K263 Morphism (degree 0): K90 -> K239] 94557 = [K262 Morphism (degree 0): K239 -> K90] 160184 = [K258 Morphism (degree 1): K239 -> K239] 160184 = [K257 Morphism (degree 2): K1 -> K1] 23764 = [K253 Morphism (degree 0): K239 -> K247] 23764 = [K252 Cohomology-Class on K1 of degree -1] 183948 = [K251 Morphism (degree 1): K1 -> K1] 186846 = [K249 Morphism (degree 0): K239 -> K239] 92289 = [K242 Morphism (degree 0): K90 -> K239] 94557 = [K241 Morphism (degree 0): K239 -> K90] 92289 = [K238 Morphism (degree 0): K90 -> K1] 94557 = [K237 Morphism (degree 0): K1 -> K90] 92289 = [K236 Morphism (degree 0): K1 -> K1] 186048 = [K235 Morphism (degree 0): K1 -> K1] 41239 = [K229 Morphism (degree 0): K92 -> K207] 27979 = [K224 Morphism (degree 1): K207 -> K207] 27979 = [K223 Morphism (degree 2): K172 -> K125] 29989 = [K222 Morphism (degree 1): K172 -> K172] 13260 = [K218 Morphism (degree 0): K207 -> K210] 13260 = [K217 Morphism (degree 1): K172 -> K144] 41239 = [K216 Morphism (degree 1): K172 -> K125] 41239 = [K213 Morphism (degree 0): K114 -> K207] 41344 = [K203 Morphism (degree 0): K172 -> K125] 41344 = [K202 Morphism (degree 0): K172 -> K107] 46197 = [K196 Morphism (degree 0): K105 -> K172] 47169 = [K195 Morphism (degree 0): K172 -> K105] 77780 = [K191 Morphism (degree 1): K172 -> K172] 77780 = [K190 Morphism (degree 2): K1 -> K1] 14404 = [K186 Morphism (degree 0): K172 -> K180] 14404 = [K185 Cohomology-Class on K1 of degree -1] 92184 = [K184 Morphism (degree 1): K1 -> K1] 93366 = [K182 Morphism (degree 0): K172 -> K172] 46197 = [K175 Morphism (degree 0): K105 -> K172] 47169 = [K174 Morphism (degree 0): K172 -> K105] 46197 = [K171 Morphism (degree 0): K105 -> K1] 47169 = [K170 Morphism (degree 0): K1 -> K105] 46197 = [K169 Morphism (degree 0): K1 -> K1] 93024 = [K168 Morphism (degree 0): K1 -> K1] 82583 = [K162 Morphism (degree 0): K107 -> K125] 56011 = [K157 Morphism (degree 1): K125 -> K125] 56011 = [K156 Morphism (degree 2): K1 -> K1] 318811 = [K155 Morphism (degree 1): K1 -> K1] 26572 = [K151 Morphism (degree 0): K125 -> K144] 26572 = [K150 Cohomology-Class on K1 of degree -1] 82583 = [K149 Morphism (degree 1): K1 -> K1] 82802 = [K146 Morphism (degree 0): K125 -> K125] 1348213 = [K138 Morphism (degree 1): K1 -> K1] 18499 = [K137 Morphism (degree 0): K134 -> K1] 202384 = [K136 Cohomology-Class on K1 of degree 0] 789868 = [K131 Morphism (degree 0): K1 -> K1] 82583 = [K128 Morphism (degree 0): K107 -> K125] 82583 = [K123 Morphism (degree 0): K107 -> K1] 82583 = [K121 Morphism (degree 0): K1 -> K1] 82688 = [K120 Morphism (degree 0): K1 -> K1] 41239 = [K117 Morphism (degree 0): K92 -> K114] 41239 = [K112 Morphism (degree 0): K92 -> K107] 41239 = [K110 Morphism (degree 0): K107 -> K105] 41344 = [K109 Morphism (degree 0): K105 -> K107] 41239 = [K108 Morphism (degree -1): K107 -> K107] 20567 = [K102 Morphism (degree 0): K78 -> K99] 20567 = [K97 Morphism (degree 0): K78 -> K92] 20567 = [K95 Morphism (degree 0): K92 -> K90] 20672 = [K94 Morphism (degree 0): K90 -> K92] 20567 = [K93 Morphism (degree -1): K92 -> K92] 17773 = [K91 Morphism (degree -1): K90 -> K90] 10231 = [K87 Morphism (degree 0): K66 -> K84] 10231 = [K83 Morphism (degree 0): K66 -> K78] 10231 = [K81 Morphism (degree 0): K78 -> K51] 10336 = [K80 Morphism (degree 0): K51 -> K78] 10231 = [K79 Morphism (degree -1): K78 -> K78] 340870 = [K2 Morphism (degree -1): K1 -> K1] NIL -------------------------------------------------- > -------------------------------------------------- ;; The same for more than 100,000 times. -------------------------------------------------- > -------------------------------------------------- (DOLIST (ITEM *K-LIST*) (WHEN (AND (TYPEP ITEM 'MORPHISM) (< 100000 (???-CLNM ITEM))) (FORMAT T " ~7D = ~A~%" (???-CLNM ITEM) ITEM))) -------------------------------------------------- > -------------------------------------------------- 160184 = [K258 Morphism (degree 1): K239 -> K239] 160184 = [K257 Morphism (degree 2): K1 -> K1] 183948 = [K251 Morphism (degree 1): K1 -> K1] 186846 = [K249 Morphism (degree 0): K239 -> K239] 186048 = [K235 Morphism (degree 0): K1 -> K1] 318811 = [K155 Morphism (degree 1): K1 -> K1] 1348213 = [K138 Morphism (degree 1): K1 -> K1] 202384 = [K136 Cohomology-Class on K1 of degree 0] 789868 = [K131 Morphism (degree 0): K1 -> K1] 340870 = [K2 Morphism (degree -1): K1 -> K1] NIL -------------------------------------------------- > -------------------------------------------------- ;; Examining the morphism which has so much worked. -------------------------------------------------- > -------------------------------------------------- (K 138) -------------------------------------------------- > -------------------------------------------------- [K138 Morphism (degree 1): K1 -> K1] -------------------------------------------------- > -------------------------------------------------- (DFNT (K 138)) -------------------------------------------------- > -------------------------------------------------- (K-COMPLEX-H 4) -------------------------------------------------- > -------------------------------------------------- ;; It's the homotopy contraction of ;; the initial Koszul complex with four variables: ;; K[t,x,y,z] otimes_t wedge k^4 -------------------------------------------------- > -------------------------------------------------- ;; +-----------+ ;; | | ;; | The END. | ;; | | ;; +-----------+ -------------------------------------------------- >