Computational Homology Project

homcubes -C -i rep3d_f.map rep3d_x.cub rep3d_a.cub rep3d_y.cub rep3d_b.cub --log v3-c.log --quiet

Start time: Sun Sep  7 09:35:18 2003

HOMCUBES, ver. 3.04, 09/05/03. 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 'rep3d_x.cub'... 2136 cubes read.
Reading cubes to A  from 'rep3d_a.cub'... 1016 cubes read.
Computing X\A... 0 cubes removed from X, 2136 left.
Restricting A to the neighbors of X\A... 362 cubes removed, 654 left in A.
Reading cubes to Y  from 'rep3d_y.cub'... 2136 cubes read.
Reading cubes to B  from 'rep3d_b.cub'... 2712 cubes read.
Computing Y\B... 0 cubes removed from Y, 2136 left.
Verifying if X\A is contained in Y... Passed.
Verifying if A is contained in B... Passed.
50000 bit fields allocated (0 MB) to speed up 3-dimensional reduction.
Reducing full-dim cubes from (X,A)... 180 removed, 2610 left.
Reading the map on X\A from 'rep3d_f.map' for extended reduction... Done.
Verifying if the image of X\A is contained in Y... Passed.
Expanding A in X... 1491 moved to A, 645 left in X\A, 1798 added to B.
Restricting A to the neighbors of X\A... 1316 cubes removed, 649 left in A.
Reducing full-dim cubes from (X,A)... 160 removed, 1134 left.
Reading the map on X\A from 'rep3d_f.map'... Done.
Reading the map on A from 'rep3d_f.map'... Done.
Verifying if the image of A is contained in B... Passed.
Verifying if the image of A is disjoint from Y\B... Passed.
Computing the image of the map... and of the inclusion... 1978 cubes.
Expanding B in Y... 22 cubes moved to B, 316 left in Y\B.
Restricting B to the neighbors of Y\B... 2870 cubes removed, 1662 left in A.
Reducing full-dim cubes from (Y,B)... 0 removed, 1978 left.
Transforming X\A into a set of cells... 645 cells created.
Transforming A into a set of cells... 489 cells created.
Transforming Y\B into a set of cells... 316 cells created.
Transforming B into a set of cells... 1662 cells created.
Adding boundaries of cubical cells in X and A... 18402 cubical cells added.
Creating the map F on cells in X... 93540 cubes added.
Creating the map F on cells in A... 66585 cubes added.
237 bit fields for dimension 3 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... 102384 cells added.
Adding boundaries of cubical cells in Y and B... 1580 cubical cells added.
Forgetting 4636 cells from B.
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: 7179 of dim 3, 20328 of dim 6.
Time used so far: 34.3 sec (0.57 min) out of 138 sec (2.3 min).
Computing the homology of the graph of F over the ring of integers...
Reducing D_3: 9596 + 94 reductions made. 
Reducing D_2: 16814 + 9939 reductions made. 
Reducing D_1: 9903 + 2425 reductions made. 
H_0 = 0
H_1 = Z
H_2 = Z
Computing the homology of Y over the ring of integers...
Reducing D_3: 312 + 4 reductions made. 
Reducing D_2: 280 + 351 reductions made. 
Reducing D_1: 
H_0 = 0
H_1 = Z
H_2 = Z
The map induced in homology is as follows:
Dim 0:	0
Dim 1:	f (x1) = -y1
Dim 2:	f (x1) = -y1
The map induced in homology by the inclusion:
Dim 0:	0
Dim 1:	i (x1) = -y1
Dim 2:	i (x1) = -y1
The inverse of the map induced by the inclusion:
Dim 0:	0
Dim 1:	I (y1) = -x1
Dim 2:	I (y1) = -x1
The composition of F and the inverse of the map induced by the inclusion:
Dim 0:	0
Dim 1:	F (x1) = x1
Dim 2:	F (x1) = x1
Total time used: 38.5 sec (0.64 min) out of 155 sec (2.6 min).