homcubes -i 6dim_f.map 6dim_x.cub 6dim_a.cub 6dim_y.cub 6dim_b.cub --log 6dim.log Start time: Wed Sep 3 07:32:21 2003 HOMCUBES, ver. 3.04, 05/09/03. Copyright (C) 1997-2003 by Pawel Pilarczyk. This is free software. No warranty. Consult 'license.txt' for details. [Tech info: cube 4, qcell 8, chain 12, addr 4, coord 2, intgr 2. PBase Ok.] Reading cubes to X from '6dim_x.cub'... 10330 cubes read. Reading cubes to A from '6dim_a.cub'... 6683 cubes read. Computing X\A... 6683 cubes removed from X, 3647 left. Restricting A to the neighbors of X\A... 3102 cubes removed, 3581 left in A. Reading cubes to Y from '6dim_y.cub'... 25737 cubes read. Reading cubes to B from '6dim_b.cub'... 22090 cubes read. Computing Y\B... 22090 cubes removed from Y, 3647 left. Verifying if X\A is contained in Y... Passed. Verifying if A is contained in B... Passed. 103705 bit fields allocated (9 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from (X,A)... 6529 removed, 699 left. Reading the map on X\A from '6dim_f.map' for extended reduction... Done. Verifying if the image of X\A is contained in Y... Passed. Expanding A in X... 273 moved to A, 135 left in X\A, 2222 added to B. Restricting A to the neighbors of X\A... 301 cubes removed, 263 left in A. Reducing full-dim cubes from (X,A)... 66 removed, 332 left. Reading the map on X\A from '6dim_f.map'... Done. Reading the map on A from '6dim_f.map'... Done. Verifying if the image of A is contained in B... Passed. Computing the image of the map... and of the inclusion... 7588 cubes. Expanding B in Y... 1091 cubes moved to B, 334 left in Y\B. Restricting B to the neighbors of Y\B... 17716 cubes removed, 7687 left in A. Reducing full-dim cubes from (Y,B)... 411 removed, 7610 left. Transforming X\A into a set of cells... 135 cells created. Transforming A into a set of cells... 197 cells created. Transforming Y\B into a set of cells... 283 cells created. Transforming B into a set of cells... 7327 cells created. Collapsing faces in X and A... 39978 removed, 8949 left. There are 66766 faces of dimension up to 2 left in A. Note: The dimension of X decreased from 6 to 2. Creating the map F on cells in X... 681894 cubes added. Creating the map F on cells in A... 3122160 cubes added. 17208 bit fields were used. Creating a cell map for F... Done. Note: It has been verified successfully that the map is acyclic. Creating the graph of F... 225649 cells added. Adding boundaries of cells in Y and B... 26456 cells added. Forgetting 73164 cells from B. Computing the image of F... 2922 cells. Collapsing Y towards F(X)... 19892 cells removed, 6847 left. Note: The dimension of Y decreased from 6 to 3. Creating the chain complex of the graph of F... Done. Creating the chain complex of Y... Done. Creating the chain map of the projection... Done. Creating the chain map of the inclusion... Done. Vertices used: 88447 of dim 6, 56637 of dim 12. Time used so far: 11473 sec (3.2 hours) out of 24268 sec (6.7 hours). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 171 + 64840 reductions made. Reducing D_1: 30873 + 13271 reductions made. H_0 = 0 H_1 = Z H_2 = Z^18 Computing the homology of Y over the ring of integers... Reducing D_3: 1155 + 979 reductions made. Reducing D_2: 867 + 269 reductions made. Reducing D_1: 42 + 1 reductions made. H_0 = 0 H_1 = Z H_2 = Z^18 Maximal homology level considered for the map is 2. The map induced in homology is as follows: Dim 0: 0 Dim 1: f (x1) = 0 Dim 2: f (x1) = y6 + y11 f (x2) = -y4 f (x3) = -y2 f (x4) = -y11 - y15 f (x5) = 0 f (x6) = -y12 f (x7) = y10 - y14 f (x8) = -y10 - y16 - y17 f (x9) = -y7 f (x10) = y18 f (x11) = y1 f (x12) = 0 f (x13) = -y3 f (x14) = y13 f (x15) = y9 f (x16) = -y8 f (x17) = -y12 f (x18) = 0 The map induced in homology by the inclusion: Dim 0: 0 Dim 1: i (x1) = -y1 Dim 2: i (x1) = y2 i (x2) = -y8 i (x3) = -y4 i (x4) = -y12 i (x5) = -y14 - y16 i (x6) = -y6 i (x7) = y9 i (x8) = -y14 + -2 * y16 i (x9) = -y10 i (x10) = y11 i (x11) = y18 i (x12) = y17 i (x13) = -y1 i (x14) = y3 i (x15) = y13 i (x16) = -y7 i (x17) = y5 - y15 i (x18) = y5 The inverse of the map induced by the inclusion: Dim 0: 0 Dim 1: I (y1) = -x1 Dim 2: I (y1) = -x13 I (y2) = x1 I (y3) = x14 I (y4) = -x3 I (y5) = x2 + x18 I (y6) = -x6 I (y7) = -x16 I (y8) = -x2 I (y9) = x7 I (y10) = -x9 I (y11) = x10 I (y12) = -x4 I (y13) = x15 I (y14) = -2 * x5 - x8 I (y15) = -x17 + x18 I (y16) = x5 I (y17) = x12 I (y18) = x11 The composition of F and the inverse of the map induced by the inclusion: Dim 0: 0 Dim 1: F (x1) = 0 Dim 2: F (x1) = -x6 + x10 F (x2) = x3 F (x3) = -x1 F (x4) = -x10 + x17 - x18 F (x5) = 0 F (x6) = x4 F (x7) = 2 * x5 + x8 - x9 F (x8) = -x5 + x9 - x12 F (x9) = x16 F (x10) = x11 F (x11) = -x13 F (x12) = 0 F (x13) = -x14 F (x14) = x15 F (x15) = x7 F (x16) = x2 F (x17) = x4 F (x18) = 0 Total time used: 11488 sec (3.2 hours) out of 24298 sec (6.7 hours).