homcubes -i r2i.map --log r2i_hom.log

Start time: Sun Aug 10 12:20:38 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.
Reducing full-dim cubes from X... 832533 removed, 7770 left.
Reading the map on X from 'r2i.map'... Done.
Verifying if the image of X is contained in Y... Passed.
Computing the image of the map... and of the inclusion... 32140 cubes.
Reducing full-dim cubes from Y... 786991 removed, 53312 left.
Transforming X into a set of cells... 7770 cells created.
Transforming Y into a set of cells... 53312 cells created.
Collapsing faces in X... 91794 removed, 52755 left.
Note: The dimension of X decreased from 3 to 2.
Creating the map F on cells in X... 639131 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... 554267 cells added.
Adding boundaries of cells in Y... 668315 cells added.
Computing the image of F... 130519 cells.
Collapsing Y towards F(X)... 367240 cells removed, 354387 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: 846091 of dim 3, 149752 of dim 6.
Time used so far: 14013 sec (3.9 hours) out of 29100 sec (8.1 hours).
Computing the homology of the graph of F over the ring of integers...
Reducing D_2: 325 + 127033 reductions made. 
Reducing D_1: 76976 + 72775 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: 1441 + 3431 reductions made. 
Reducing D_2: 24679 + 64516 reductions made. 
Reducing D_1: 50204 + 32898 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) = y29
	i (x2) = y8
	i (x3) = y14
	i (x4) = -y34
	i (x5) = -y30
	i (x6) = y23
	i (x7) = y6
	i (x8) = -y21
	i (x9) = -y15
	i (x10) = -y1
	i (x11) = -y43
	i (x12) = y41
	i (x13) = -y11
	i (x14) = -y2
	i (x15) = -y40
	i (x16) = -y32
	i (x17) = y10
	i (x18) = y16
	i (x19) = -y7
	i (x20) = -y35
	i (x21) = y17
	i (x22) = y20
	i (x23) = -y13
	i (x24) = y26
	i (x25) = y9
	i (x26) = y37
	i (x27) = -y38
	i (x28) = y44
	i (x29) = y28
	i (x30) = -y4
	i (x31) = -y5
	i (x32) = -y3
	i (x33) = -y39
	i (x34) = y18
	i (x35) = -y12
	i (x36) = y24
	i (x37) = -y33
	i (x38) = y22
	i (x39) = y42
	i (x40) = -y31
	i (x41) = -y19
	i (x42) = -y36
	i (x43) = -y25
	i (x44) = y27
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) = -x10
	I (y2) = -x14
	I (y3) = -x32
	I (y4) = -x30
	I (y5) = -x31
	I (y6) = x7
	I (y7) = -x19
	I (y8) = x2
	I (y9) = x25
	I (y10) = x17
	I (y11) = -x13
	I (y12) = -x35
	I (y13) = -x23
	I (y14) = x3
	I (y15) = -x9
	I (y16) = x18
	I (y17) = x21
	I (y18) = x34
	I (y19) = -x41
	I (y20) = x22
	I (y21) = -x8
	I (y22) = x38
	I (y23) = x6
	I (y24) = x36
	I (y25) = -x43
	I (y26) = x24
	I (y27) = x44
	I (y28) = x29
	I (y29) = x1
	I (y30) = -x5
	I (y31) = -x40
	I (y32) = -x16
	I (y33) = -x37
	I (y34) = -x4
	I (y35) = -x20
	I (y36) = -x42
	I (y37) = x26
	I (y38) = -x27
	I (y39) = -x33
	I (y40) = -x15
	I (y41) = x12
	I (y42) = x39
	I (y43) = -x11
	I (y44) = x28
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: 14725 sec (4.1 hours) out of 30617 sec (8.5 hours).