homcubes -i -a 6dim_f.map 6dim_x.cub 6dim_a.cub 6dim_y.cub 6dim_b.cub --log 6d-a.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. Reading the map on X from '6dim_f.map' for careful reduction... Done. Verifying if the image of X\A is contained in Y... Passed. Verifying if the image of A is contained in B... Passed. Expanding A in X... 2801 moved to A, 846 left in X\A, 3333 added to B. Restricting A to the neighbors of X\A... 4066 cubes removed, 2316 left in A. Reducing cubes from (X,A) [acyclic]... 2885 removed, 277 left. Reading the map on X\A from '6dim_f.map'... Done. Reading the map on A from '6dim_f.map'... Done. Computing the image of the map... and of the inclusion... 7186 cubes. Expanding B in Y... 102 cubes moved to B, 212 left in Y\B. Restricting B to the neighbors of Y\B... 18134 cubes removed, 7391 left in A. Reducing full-dim cubes from (Y,B)... 410 removed, 7193 left. Transforming X\A into a set of cells... 105 cells created. Transforming A into a set of cells... 172 cells created. Transforming Y\B into a set of cells... 173 cells created. Transforming B into a set of cells... 7020 cells created. Collapsing faces in X and A... 42596 removed, 6869 left. There are 61564 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... 570314 cubes added. Creating the map F on cells in A... 3058759 cubes added. 103705 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... 216943 cells added. Adding boundaries of cells in Y and B... 14272 cells added. Forgetting 71132 cells from B. Computing the image of F... 1842 cells. Collapsing Y towards F(X)... 10538 cells removed, 3907 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: 94978 of dim 6, 52709 of dim 12. Time used so far: 25187 sec (7.0 hours) out of 39566 sec (11.0 hours). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 264 + 62514 reductions made. Reducing D_1: 29627 + 13214 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: 774 + 564 reductions made. Reducing D_2: 395 + 133 reductions made. Reducing D_1: 14 + 0 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) = y3 f (x2) = -y14 f (x3) = -y2 f (x4) = -y9 f (x5) = y12 f (x6) = y6 f (x7) = -y9 f (x8) = y1 + y15 - y16 f (x9) = -y9 f (x10) = y17 f (x11) = y4 + y10 f (x12) = y13 - y15 f (x13) = y5 f (x14) = y8 f (x15) = 0 f (x16) = y7 + y10 + y18 f (x17) = y11 f (x18) = 0 The map induced in homology by the inclusion: Dim 0: 0 Dim 1: i (x1) = y1 Dim 2: i (x1) = y11 i (x2) = -y5 i (x3) = -y3 i (x4) = -y4 - y7 i (x5) = -y15 i (x6) = y14 i (x7) = -y7 - y18 i (x8) = -y8 i (x9) = -y4 i (x10) = y2 i (x11) = y9 i (x12) = y13 i (x13) = y12 i (x14) = y17 i (x15) = y1 + y13 i (x16) = y6 i (x17) = y10 i (x18) = y16 The inverse of the map induced by the inclusion: Dim 0: 0 Dim 1: I (y1) = x1 Dim 2: I (y1) = -x12 + x15 I (y2) = x10 I (y3) = -x3 I (y4) = -x9 I (y5) = -x2 I (y6) = x16 I (y7) = x4 - x9 I (y8) = -x8 I (y9) = x11 I (y10) = x17 I (y11) = x1 I (y12) = x13 I (y13) = x12 I (y14) = x6 I (y15) = -x5 I (y16) = x18 I (y17) = x14 I (y18) = -x4 + x7 - x9 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) = -x3 F (x2) = -x6 F (x3) = -x10 F (x4) = -x11 F (x5) = x13 F (x6) = x16 F (x7) = -x11 F (x8) = -x5 - x12 + x15 - x18 F (x9) = -x11 F (x10) = x14 F (x11) = -x9 + x17 F (x12) = x5 + x12 F (x13) = -x2 F (x14) = -x8 F (x15) = 0 F (x16) = -x7 + x17 F (x17) = x1 F (x18) = 0 Total time used: 25201 sec (7.0 hours) out of 39580 sec (11.0 hours).