homcubes -i -a r2i.map --log r2i_homa.log

Start time: Sun Aug 10 20:51:07 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 'r2i.map'... 840303 cubes read.
50000 bit fields allocated (0 MB) to speed up full-dimensional reduction.
Reading the map on X from 'r2i.map' for careful reduction... Done.
Verifying if the image of X is contained in Y... Passed.
Reducing cubes from X [acyclic]... 832108 removed, 8195 left.
Reading the map on X from 'r2i.map'... Done.
Computing the image of the map... and of the inclusion... 33267 cubes.
Reducing full-dim cubes from Y... 785224 removed, 55079 left.
Transforming X into a set of cells... 8195 cells created.
Transforming Y into a set of cells... 55079 cells created.
Collapsing faces in X... 99652 removed, 51837 left.
Note: The dimension of X decreased from 3 to 2.
Creating the map F on cells in X... 635974 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... 538957 cells added.
Adding boundaries of cells in Y... 658178 cells added.
Computing the image of F... 130195 cells.
Collapsing Y towards F(X)... 379214 cells removed, 334043 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: 943643 of dim 3, 147038 of dim 6.
Time used so far: 33887 sec (9.4 hours) out of 66426 sec (18.5 hours).
Computing the homology of the graph of F over the ring of integers...
Reducing D_2: 344 + 122073 reductions made. 
Reducing D_1: 73587 + 73450 reductions made. 
H_0 = Z
H_1 = Z^4
H_2 = Z^44
Computing the homology of Y over the ring of integers...
Reducing D_3: 1474 + 3160 reductions made. 
Reducing D_2: 24797 + 58438 reductions made. 
Reducing D_1: 48041 + 31087 reductions made. 
H_0 = Z
H_1 = Z^4
H_2 = Z^44
The map induced in homology is as follows:
Dim 0:	f (x1) = y1
Dim 1:	f (x1) = y4
	f (x2) = 0
	f (x3) = 0
	f (x4) = 0
Dim 2:	f (x1) = 0
	f (x2) = 0
	f (x3) = 0
	f (x4) = 0
	f (x5) = 0
	f (x6) = 0
	f (x7) = 0
	f (x8) = 0
	f (x9) = 0
	f (x10) = 0
	f (x11) = 0
	f (x12) = 0
	f (x13) = 0
	f (x14) = 0
	f (x15) = 0
	f (x16) = 0
	f (x17) = 0
	f (x18) = 0
	f (x19) = 0
	f (x20) = 0
	f (x21) = 0
	f (x22) = 0
	f (x23) = 0
	f (x24) = 0
	f (x25) = 0
	f (x26) = 0
	f (x27) = 0
	f (x28) = 0
	f (x29) = 0
	f (x30) = 0
	f (x31) = 0
	f (x32) = 0
	f (x33) = 0
	f (x34) = 0
	f (x35) = 0
	f (x36) = 0
	f (x37) = 0
	f (x38) = 0
	f (x39) = 0
	f (x40) = 0
	f (x41) = 0
	f (x42) = 0
	f (x43) = 0
	f (x44) = 0
The map induced in homology by the inclusion:
Dim 0:	i (x1) = y1
Dim 1:	i (x1) = y4
	i (x2) = -y1
	i (x3) = y2
	i (x4) = y3
Dim 2:	i (x1) = -y33
	i (x2) = y28
	i (x3) = -y17
	i (x4) = y5
	i (x5) = -y31
	i (x6) = -y43
	i (x7) = -y2
	i (x8) = -y6
	i (x9) = -y37
	i (x10) = -y4
	i (x11) = y42
	i (x12) = y24
	i (x13) = y23
	i (x14) = y8
	i (x15) = y38
	i (x16) = -y13
	i (x17) = y41
	i (x18) = y16
	i (x19) = y3
	i (x20) = y19
	i (x21) = -y36
	i (x22) = y27
	i (x23) = y18
	i (x24) = -y30
	i (x25) = y21
	i (x26) = y1
	i (x27) = y39
	i (x28) = -y25
	i (x29) = y29
	i (x30) = y22
	i (x31) = y15
	i (x32) = y20
	i (x33) = y12
	i (x34) = y7
	i (x35) = -y10
	i (x36) = -y34
	i (x37) = -y44
	i (x38) = -y35
	i (x39) = y9
	i (x40) = -y26
	i (x41) = -y14
	i (x42) = y11
	i (x43) = y40
	i (x44) = y32
The inverse of the map induced by the inclusion:
Dim 0:	I (y1) = x1
Dim 1:	I (y1) = -x2
	I (y2) = x3
	I (y3) = x4
	I (y4) = x1
Dim 2:	I (y1) = x26
	I (y2) = -x7
	I (y3) = x19
	I (y4) = -x10
	I (y5) = x4
	I (y6) = -x8
	I (y7) = x34
	I (y8) = x14
	I (y9) = x39
	I (y10) = -x35
	I (y11) = x42
	I (y12) = x33
	I (y13) = -x16
	I (y14) = -x41
	I (y15) = x31
	I (y16) = x18
	I (y17) = -x3
	I (y18) = x23
	I (y19) = x20
	I (y20) = x32
	I (y21) = x25
	I (y22) = x30
	I (y23) = x13
	I (y24) = x12
	I (y25) = -x28
	I (y26) = -x40
	I (y27) = x22
	I (y28) = x2
	I (y29) = x29
	I (y30) = -x24
	I (y31) = -x5
	I (y32) = x44
	I (y33) = -x1
	I (y34) = -x36
	I (y35) = -x38
	I (y36) = -x21
	I (y37) = -x9
	I (y38) = x15
	I (y39) = x27
	I (y40) = x43
	I (y41) = x17
	I (y42) = x11
	I (y43) = -x6
	I (y44) = -x37
The composition of F and the inverse of the map induced by the inclusion:
Dim 0:	F (x1) = x1
Dim 1:	F (x1) = x1
	F (x2) = 0
	F (x3) = 0
	F (x4) = 0
Dim 2:	F (x1) = 0
	F (x2) = 0
	F (x3) = 0
	F (x4) = 0
	F (x5) = 0
	F (x6) = 0
	F (x7) = 0
	F (x8) = 0
	F (x9) = 0
	F (x10) = 0
	F (x11) = 0
	F (x12) = 0
	F (x13) = 0
	F (x14) = 0
	F (x15) = 0
	F (x16) = 0
	F (x17) = 0
	F (x18) = 0
	F (x19) = 0
	F (x20) = 0
	F (x21) = 0
	F (x22) = 0
	F (x23) = 0
	F (x24) = 0
	F (x25) = 0
	F (x26) = 0
	F (x27) = 0
	F (x28) = 0
	F (x29) = 0
	F (x30) = 0
	F (x31) = 0
	F (x32) = 0
	F (x33) = 0
	F (x34) = 0
	F (x35) = 0
	F (x36) = 0
	F (x37) = 0
	F (x38) = 0
	F (x39) = 0
	F (x40) = 0
	F (x41) = 0
	F (x42) = 0
	F (x43) = 0
	F (x44) = 0
Total time used: 34445 sec (9.6 hours) out of 67593 sec (18.8 hours).