Computational Homology Project

homcubes -R -i rep3d_f.map rep3d_x.cub rep3d_a.cub rep3d_y.cub rep3d_b.cub --log v3-r.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.
Reading the map on X\A from 'rep3d_f.map'... Done.
Verifying if the image of X\A is contained in Y... Passed.
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... 4042 cubes.
Transforming X\A into a set of cells... 2136 cells created.
Transforming A into a set of cells... 654 cells created.
Transforming Y\B into a set of cells... 2136 cells created.
Transforming B into a set of cells... 2712 cells created.
Collapsing faces in X and A... 10378 removed, 15720 left.
There are 8995 faces of dimension up to 2 left in A.
Note: The dimension of X decreased from 3 to 2.
Creating the map F on cells in X... 156218 cubes added.
Creating the map F on cells in A... 66438 cubes added.
Creating a cell map for F... Done.
Note: It has been verified successfully that the map is acyclic.
Creating the graph of F... 179174 cells added.
Adding boundaries of cubical cells in Y and B... 21516 cubical cells added.
Forgetting 6824 cells from B.
Computing the image of F... 21015 cells.
Collapsing Y towards F(X)... 708 cells removed, 22944 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: 10436 of dim 3, 44989 of dim 6.
Time used so far: 39.8 sec (0.66 min) out of 152 sec (2.5 min).
Computing the homology of the graph of F over the ring of integers...
Reducing D_2: 163 + 47694 reductions made. 
Reducing D_1: 27432 + 12480 reductions made. 
H_0 = 0
H_1 = Z
H_2 = Z
Computing the homology of Y over the ring of integers...
Reducing D_3: 1785 + 36 reductions made. 
Reducing D_2: 2581 + 3456 reductions made. 
Reducing D_1: 2185 + 878 reductions made. 
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: 125 sec (2.1 min) out of 343 sec (5.7 min).