# p6m (p6mm)
#
http://en.wikipedia.org/wiki/Wallpaper_group#Group_p6m
M:=[ [1,2,4], [1,3,4], [2,4,5], [3,4,7], [4,5,6], [4,6,7] ];
C2n := Group( (1,4)(2,3)(5,6) ); #north
C2e := Group( (2,6)(3,5) ); #east
C2sw := Group( (1,3)(4,6) ); #southwest
D12 := Group( (1,4)(2,3)(5,6), (1,3)(4,6) ); #north and southwest
D6 := Group( (2,6)(3,5), (1,3)(4,6) ); #east and southwest
V4 := Group( (1,4)(2,3)(5,6), (2,6)(3,5) ); #north and east
iso := rec( 1 := D12, 2 := C2sw, 3 := C2n , 5 := D6, 6 := C2e, 7 := V4 );
mu := [];
dim := 3;
# 1: 6 x 75 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 75 x 690 matrix with rank 68 and kernel dimension 7. Time: 0.000 sec.
# 3: 690 x 7913 matrix with rank 618 and kernel dimension 72. Time: 0.232 sec.
# 4: 7913 x 98044 matrix with rank 7289 and kernel dimension 624. Time: 42.559 sec.
# 5: 98044 x 1227699 matrix with rank 90747 and kernel dimension 7297. Time: 7575.654 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 2)
# Cohomology dimension at degree 2: GF(2)^(1 x 4)
# Cohomology dimension at degree 3: GF(2)^(1 x 6)
# Cohomology dimension at degree 4: GF(2)^(1 x 8)
# 1: 6 x 75 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 75 x 690 matrix with rank 70 and kernel dimension 5. Time: 0.016 sec.
# 3: 690 x 7913 matrix with rank 620 and kernel dimension 70. Time: 163.226 sec.
# 4: 7913 x 98044 matrix with rank 7291 and kernel dimension 622. Time: 209241.009 sec. (60h)
# 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 2)
#--------------------------------------------------------------------------
#matrix sizes
# [ 6, 103, 1466, 27853, 594252 ]
#factor
# [ 17.1667, 14.233, 18.9993, 21.3353 ]
#----------------------------------------------->>>> Z^(1 x 1)
#----------------------------------------------->>>> 0
#----------------------------------------------->>>> Z/< 2 > + Z/< 2 >
########## p = 0 ##########
#cohomology over Z:
#---------------------------
#at cohomology degree: 0
#Z^(1 x 1)
#---------------------------
#at cohomology degree: 1
#0
#---------------------------
#at cohomology degree: 2
#Z/< 2 > + Z/< 2 >
#-------------------------
#homology over Z:
#-------------------------
#at homology degree: 0
#Z^(1 x 1)
#-------------------------
#at homology degree: 1
#Z/< 2 > + Z/< 2 >
#-------------------------
#at homology degree: 2
#Z/< 2 > + Z/< 2 >
#-------------------------
########## p = 2 ##########
#cohomology over GF(2):
# 1: 6 x 103 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 103 x 1466 matrix with rank 96 and kernel dimension 7. Time: 0.004 sec.
# 3: 1466 x 27853 matrix with rank 1366 and kernel dimension 100. Time: 3.224 sec.
# 4: 27853 x 594252 matrix with rank 26481 and kernel dimension 1372. Time: 494.547 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 2)
# Cohomology dimension at degree 2: GF(2)^(1 x 4)
# Cohomology dimension at degree 3: GF(2)^(1 x 6)
########## p = 3 ##########
#cohomology over GF(3):
