Computational Homology Project

homcubes -i r2k.map --log r2k_hom.log

Start time: Sun Aug 10 11:10:14 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.
Reducing full-dim cubes from X... 121365 removed, 813 left.
Reading the map on X from 'r2k.map'... Done.
Verifying if the image of X is contained in Y... Passed.
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... 14694 removed, 3733 left.
Note: The dimension of X decreased from 3 to 2.
Creating the map F on cells in X... 140604 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... 22085 cells added.
Adding boundaries of cells in Y... 132403 cells added.
Computing the image of F... 14549 cells.
Collapsing Y towards F(X)... 108310 cells removed, 37405 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: 127013 of dim 3, 10921 of dim 6.
Time used so far: 113 sec (1.9 min) out of 279 sec (4.7 min).
Computing the homology of the graph of F over the ring of integers...
Reducing D_2: 0 + 121 reductions made. 
Reducing D_1: 75 + 10845 reductions made. 
H_0 = Z
H_1 = Z
H_2 = Z
Computing the homology of Y over the ring of integers...
Reducing D_3: 0 + 7 reductions made. 
Reducing D_2: 6412 + 2506 reductions made. 
Reducing D_1: 5991 + 3785 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: 128 sec (2.1 min) out of 316 sec (5.3 min).