# p3m1
#
http://en.wikipedia.org/wiki/Wallpaper_group#Group_p3m1
M := [ [1,2,4], [1,3,4], [2,4,5], [3,4,7], [4,5,6], [4,6,7] ];
S3 := Group( (1,2,3), (1,2) );
iso := rec( 1 := S3, 5 := S3, 7 := S3,
2 := Group( (1,2) ), 3 := Group( (1,3) ), 6 := Group( (2,3) ) );
mu := [];
dim := 3;
# 1: 6 x 63 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 63 x 362 matrix with rank 57 and kernel dimension 6. Time: 0.000 sec.
# 3: 362 x 2133 matrix with rank 303 and kernel dimension 59. Time: 0.088 sec.
# 4: 2133 x 12780 matrix with rank 1828 and kernel dimension 305. Time: 1.716 sec.
# 5: 12780 x 75031 matrix with rank 10950 and kernel dimension 1830. Time: 66.120 sec.
# 6: 75031 x 431286 matrix with rank 64079 and kernel dimension 10952. Time: 2016.518 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 1)
# Cohomology dimension at degree 2: GF(2)^(1 x 2)
# Cohomology dimension at degree 3: GF(2)^(1 x 2)
# Cohomology dimension at degree 4: GF(2)^(1 x 2)
# Cohomology dimension at degree 5: GF(2)^(1 x 2)
# 1: 6 x 63 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 63 x 362 matrix with rank 58 and kernel dimension 5. Time: 0.020 sec.
# 3: 362 x 2133 matrix with rank 304 and kernel dimension 58. Time: 1.240 sec.
# 4: 2133 x 12780 matrix with rank 1826 and kernel dimension 307. Time: 92.274 sec.
# 5: 12780 x 75031 matrix with rank 10951 and kernel dimension 1829. Time: 25313.330 sec.
# Cohomology dimension at degree 0: GF(3)^(1 x 1)
# Cohomology dimension at degree 1: GF(3)^(1 x 0)
# Cohomology dimension at degree 2: GF(3)^(1 x 0)
# Cohomology dimension at degree 3: GF(3)^(1 x 3)
# Cohomology dimension at degree 4: GF(3)^(1 x 3)
#-------------------------------------------------------------------------------
-------------
#matrix sizes
# [ <A homalg internal 6 by 87 matrix>,
# <A homalg internal 87 by 794 matrix>,
# <A homalg internal 794 by 8157 matrix>,
# <A homalg internal 8157 by 88332 matrix> ]
#factors
# [ 14.5, 9.12644, 10.2733, 10.829 ]
#cohomology over Z:
#--------->>>> Z^(1 x 1)
#--------->>>> 0
#--------->>>> Z/< 2 >
#cohomology over GF(5):
#------>>>> GF(5)^(1 x 1)
#------>>>> 0
#------>>>> 0
# 1: 6 x 87 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 87 x 794 matrix with rank 81 and kernel dimension 6. Time: 0.000 sec.
# 3: 794 x 8157 matrix with rank 711 and kernel dimension 83. Time: 0.236 sec.
# 4: 8157 x 88332 matrix with rank 7444 and kernel dimension 713. Time: 27.446 sec.
# 5: 88332 x 967759 matrix with rank 80886 and kernel dimension 7446. Time: 2786.274 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 1)
# Cohomology dimension at degree 2: GF(2)^(1 x 2)
# Cohomology dimension at degree 3: GF(2)^(1 x 2)
# Cohomology dimension at degree 4: GF(2)^(1 x 2)
#cohomology over GF(3):
# 1: 6 x 87 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 87 x 794 matrix with rank 82 and kernel dimension 5. Time: 0.032 sec.
# 3: 794 x 8157 matrix with rank 712 and kernel dimension 82. Time: 24.981 sec.
# 4: 8157 x 88332 matrix with rank 7442 and kernel dimension 715. Time: 5485.735 sec.
# Cohomology dimension at degree 0: GF(3)^(1 x 1)
# Cohomology dimension at degree 1: GF(3)^(1 x 0)
# Cohomology dimension at degree 2: GF(3)^(1 x 0)
# Cohomology dimension at degree 3: GF(3)^(1 x 3)
