# p4m (p4mm)
#
http://en.wikipedia.org/wiki/Wallpaper_group#Group_p4m
M := [ [1,2,4], [1,3,4], [2,4,5], [3,4,7], [4,5,6], [4,6,7] ];
c1 := (2,8)(3,7)(4,6);
c2 := (1,5)(2,4)(6,8);
cd := (1,3)(4,8)(5,7);
C1 := Group( c1 );
C2 := Group( c2 );
CD := Group( cd );
V4 := Group( c1, c2 );
D8 := Group( c1, cd );
iso := rec( 1 := V4, 2 := C1, 3 := C2, 5 := D8, 6 := CD, 7 := D8 );
mu := [];
dim := 3;
# 1: 6 x 69 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 69 x 494 matrix with rank 61 and kernel dimension 8. Time: 0.004 sec.
# 3: 494 x 3919 matrix with rank 427 and kernel dimension 67. Time: 0.104 sec.
# 4: 3919 x 32180 matrix with rank 3483 and kernel dimension 436. Time: 6.893 sec.
# 5: 32180 x 261445 matrix with rank 28685 and kernel dimension 3495. Time: 459.921 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 3)
# Cohomology dimension at degree 2: GF(2)^(1 x 6)
# Cohomology dimension at degree 3: GF(2)^(1 x 9)
# Cohomology dimension at degree 4: GF(2)^(1 x 12)
#----------------->>>> Z/4Z^(1 x 1)
#----------------->>>> Z/4Z/< 2 > ^ 3
#----------------->>>> Z/4Z/< 2 > ^ 6
#----------------->>>> Z/4Z/< 2 > ^ 7 + Z/4Z^(1 x 2)
#---------------------------------------------------------------------------
#matrix sizes:
# [ 6, 95, 1066, 14357, 207788, 3072567 ]
#factors:
# [ 15.8333, 11.2211, 13.4681, 14.4729, 14.7870 ]
#cohomology over Z:
#------------------>>>> Z^(1 x 1)
#------------------>>>> 0
#------------------>>>> Z/< 2 > + Z/< 2 > + Z/< 2 >
# 1: 6 x 95 matrix with rank 5 and kernel dimension 1. Time: 0.000 sec.
# 2: 95 x 1066 matrix with rank 87 and kernel dimension 8. Time: 0.004 sec.
# 3: 1066 x 14357 matrix with rank 973 and kernel dimension 93. Time: 0.580 sec.
# 4: 14357 x 207788 matrix with rank 13375 and kernel dimension 982. Time: 114.411 sec.
# 5: 207788 x 3072567 matrix with rank 194401 and kernel dimension 13387. Time: 17064.879 sec.
# Cohomology dimension at degree 0: GF(2)^(1 x 1)
# Cohomology dimension at degree 1: GF(2)^(1 x 3)
# Cohomology dimension at degree 2: GF(2)^(1 x 6)
# Cohomology dimension at degree 3: GF(2)^(1 x 9)
# Cohomology dimension at degree 4: GF(2)^(1 x 12)
#cohomology over Z/4Z:
#--------->>>> Z/4Z^(1 x 1)
#--------->>>> Z/4Z/< ZmodnZObj(2,4) >^(3)
#--------->>>> Z/4Z/< ZmodnZObj(2,4) >^(5) + Z/4Z^(1 x 1)
#--------->>>> Z/4Z/< ZmodnZObj(2,4) >^(7) + Z/4Z^(1 x 2)
