homcubes -i -a r2k.map --log r2k_homa.log

Start time: Sun Aug 10 11:15:30 2003

HOMCUBES, ver. 3.04, 07/05/03. 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 the domain of the map from 'r2k.map'... 122178 cubes read.
50000 bit fields allocated (0 MB) to speed up full-dimensional reduction.
Reading the map on X from 'r2k.map' for careful reduction... Done.
Verifying if the image of X is contained in Y... Passed.
Reducing cubes from X [acyclic]... 121365 removed, 813 left.
Reading the map on X from 'r2k.map'... Done.
Computing the image of the map... and of the inclusion... 12909 cubes.
Reducing full-dim cubes from Y... 108866 removed, 13312 left.
Transforming X into a set of cells... 813 cells created.
Transforming Y into a set of cells... 13312 cells created.
Collapsing faces in X... 14670 removed, 3757 left.
Note: The dimension of X decreased from 3 to 2.
Creating the map F on cells in X... 140098 cubes added.
50000 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... 23187 cells added.
Adding boundaries of cells in Y... 132403 cells added.
Computing the image of F... 14828 cells.
Collapsing Y towards F(X)... 108286 cells removed, 37429 left.
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: 157720 of dim 3, 11415 of dim 6.
Time used so far: 351 sec (5.9 min) out of 895 sec (14.9 min).
Computing the homology of the graph of F over the ring of integers...
Reducing D_2: 0 + 178 reductions made. 
Reducing D_1: 104 + 11310 reductions made. 
H_0 = Z
H_1 = Z
H_2 = Z
Computing the homology of Y over the ring of integers...
Reducing D_3: 1 + 11 reductions made. 
Reducing D_2: 6765 + 2137 reductions made. 
Reducing D_1: 6061 + 3738 reductions made. 
H_0 = Z
H_1 = Z
H_2 = Z
The map induced in homology is as follows:
Dim 0:	f (x1) = y1
Dim 1:	f (x1) = -y1
Dim 2:	f (x1) = 0
The map induced in homology by the inclusion:
Dim 0:	i (x1) = y1
Dim 1:	i (x1) = -y1
Dim 2:	i (x1) = -y1
The inverse of the map induced by the inclusion:
Dim 0:	I (y1) = x1
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:	F (x1) = x1
Dim 1:	F (x1) = x1
Dim 2:	F (x1) = 0
Total time used: 389 sec (6.5 min) out of 989 sec (16.5 min).