1# pmg 2 3# http://en.wikipedia.org/wiki/Wallpaper_group#Group_pmg 4 5M := [ [1,2,4], [1,2,5], [1,4,5], [2,3,6], [2,3,9], [2,4,9], [2,5,6], [3,9,10], [4,5,8], [4,7,8], [4,7,9], [5,6,8], [6,8,10], [7,8,9], [8,9,10] ]; 6G := Group( (1,2) ); 7iso := rec( 1 := G, 7 := G, 3 := G, 6 := G, 10 := G ); 8mu:=[ 9[ [4], [1,4], [1,2,4], [1,4,5], x -> (1,2) ], 10[ [4], [1,4], [1,4,5], [1,2,4], x -> (1,2) ], 11[ [4], [4,7], [4,7,8], [4,7,9], x -> (1,2) ], 12[ [4], [4,7], [4,7,9], [4,7,8], x -> (1,2) ], 13]; 14 15dim := 4; 16 17#matrix sizes: 18# [ 16, 139, 546, 2321, 11276, 56251 ] 19#factors: 20# [ 8.6875, 3.92806, 4.25092, 4.85825 ] 21 22# 1: 15 x 134 matrix with rank 14 and kernel dimension 1. Time: 0.000 sec. 23# 2: 134 x 583 matrix with rank 117 and kernel dimension 17. Time: 0.004 sec. 24# 3: 583 x 2934 matrix with rank 462 and kernel dimension 121. Time: 0.152 sec. 25# 4: 2934 x 17126 matrix with rank 2468 and kernel dimension 466. Time: 3.145 sec. 26# 5: 17126 x 104729 matrix with rank 14654 and kernel dimension 2472. Time: 114.119 sec. 27# 6: 104729 x 658093 matrix with rank 90071 and kernel dimension 14658. Time: 4647.566 sec. 28# Cohomology dimension at degree 0: GF(2)^(1 x 1) 29# Cohomology dimension at degree 1: GF(2)^(1 x 3) 30# Cohomology dimension at degree 2: GF(2)^(1 x 4) 31# Cohomology dimension at degree 3: GF(2)^(1 x 4) 32# Cohomology dimension at degree 4: GF(2)^(1 x 4) 33# Cohomology dimension at degree 5: GF(2)^(1 x 4) 34 35# Z 36# 0 37# 3 38# 1 39# 3 40# 1 41 42