# a1 is the list of IDs of lattices of rank 1. # b2 (resp. b11) is the list of GAP IDs (Crystcat IDs) of # indecomposable (resp. decomposable) lattices # of rank 2. # c3 (resp. c21, c111) is the list of GAP IDs (Crystcat IDs) of # indecomposable (resp. decomposable with rank 2+1, 1+1+1) # lattices of rank 3. # d4 (resp. d31, d22, d211, d1111) is the list of GAP IDs (Crystcat IDs) of # indecomposable (resp. decomposable with rank 3+1, 2+2, 2+1+1, 1+1+1+1) # lattices of rank 4. # For GAP ID (Crystcat ID), see http://www.ams.org/books/memo/1176/ (Chapter 3). a1:= [ [ 1, 1, 1, 1 ], [ 1, 1, 2, 1 ] ]; b2:= [ [ 2, 2, 1, 2 ], [ 2, 2, 2, 2 ], [ 2, 3, 1, 1 ], [ 2, 3, 2, 1 ], [ 2, 4, 1, 1 ], [ 2, 4, 2, 1 ], [ 2, 4, 2, 2 ], [ 2, 4, 3, 1 ], [ 2, 4, 4, 1 ] ]; b11:= [ [ 2, 1, 1, 1 ], [ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 1 ] ]; c3:= [ [ 3, 3, 1, 3 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 3, 2, 5 ], [ 3, 3, 3, 3 ], [ 3, 3, 3, 4 ], [ 3, 4, 1, 2 ], [ 3, 4, 2, 2 ], [ 3, 4, 3, 2 ], [ 3, 4, 4, 2 ], [ 3, 4, 5, 2 ], [ 3, 4, 6, 3 ], [ 3, 4, 6, 4 ], [ 3, 4, 7, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 3, 5, 3, 1 ], [ 3, 5, 4, 1 ], [ 3, 5, 5, 1 ], [ 3, 7, 1, 1 ], [ 3, 7, 1, 2 ], [ 3, 7, 1, 3 ], [ 3, 7, 2, 1 ], [ 3, 7, 2, 2 ], [ 3, 7, 2, 3 ], [ 3, 7, 3, 1 ], [ 3, 7, 3, 2 ], [ 3, 7, 3, 3 ], [ 3, 7, 4, 1 ], [ 3, 7, 4, 2 ], [ 3, 7, 4, 3 ], [ 3, 7, 5, 1 ], [ 3, 7, 5, 2 ], [ 3, 7, 5, 3 ] ]; c21:= [ [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 2, 3, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 3, 2, 3 ], [ 3, 3, 3, 2 ], [ 3, 4, 1, 1 ], [ 3, 4, 2, 1 ], [ 3, 4, 3, 1 ], [ 3, 4, 4, 1 ], [ 3, 4, 5, 1 ], [ 3, 4, 6, 1 ], [ 3, 4, 6, 2 ], [ 3, 4, 7, 1 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 3, 5, 3, 2 ], [ 3, 5, 3, 3 ], [ 3, 5, 4, 2 ], [ 3, 5, 4, 3 ], [ 3, 5, 5, 2 ], [ 3, 5, 5, 3 ], [ 3, 6, 1, 1 ], [ 3, 6, 2, 1 ], [ 3, 6, 3, 1 ], [ 3, 6, 4, 1 ], [ 3, 6, 5, 1 ], [ 3, 6, 6, 1 ], [ 3, 6, 6, 2 ], [ 3, 6, 7, 1 ] ]; c111:= [ [ 3, 1, 1, 1 ], [ 3, 1, 2, 1 ], [ 3, 2, 1, 1 ], [ 3, 2, 2, 1 ], [ 3, 2, 3, 1 ], [ 3, 3, 1, 1 ], [ 3, 3, 2, 1 ], [ 3, 3, 3, 1 ] ]; d4:= [ [ 4, 5, 1, 1 ], [ 4, 5, 1, 7 ], [ 4, 5, 1, 11 ], [ 4, 5, 1, 12 ], [ 4, 5, 1, 13 ], [ 4, 5, 2, 1 ], [ 4, 5, 2, 5 ], [ 4, 5, 2, 8 ], [ 4, 5, 2, 9 ], [ 4, 6, 1, 6 ], [ 4, 6, 1, 10 ], [ 4, 6, 1, 11 ], [ 4, 6, 1, 12 ], [ 4, 6, 2, 6 ], [ 4, 6, 2, 10 ], [ 4, 6, 2, 11 ], [ 4, 6, 2, 12 ], [ 4, 6, 3, 4 ], [ 4, 6, 3, 7 ], [ 4, 6, 3, 8 ], [ 4, 12, 1, 1 ], [ 4, 12, 1, 6 ], [ 4, 12, 1, 7 ], [ 4, 12, 2, 1 ], [ 4, 12, 2, 5 ], [ 4, 12, 2, 6 ], [ 4, 12, 3, 1 ], [ 4, 12, 3, 10 ], [ 4, 12, 3, 11 ], [ 4, 12, 3, 12 ], [ 4, 12, 3, 13 ], [ 4, 12, 4, 1 ], [ 4, 12, 4, 10 ], [ 4, 12, 4, 11 ], [ 4, 12, 4, 12 ], [ 4, 12, 4, 13 ], [ 4, 12, 5, 1 ], [ 4, 12, 5, 8 ], [ 4, 12, 5, 9 ], [ 4, 12, 5, 10 ], [ 4, 12, 5, 11 ], [ 4, 13, 1, 5 ], [ 4, 13, 1, 6 ], [ 4, 13, 2, 5 ], [ 4, 13, 2, 6 ], [ 4, 13, 3, 5 ], [ 4, 13, 3, 6 ], [ 4, 13, 4, 5 ], [ 4, 13, 4, 6 ], [ 4, 13, 5, 4 ], [ 4, 13, 5, 5 ], [ 4, 13, 6, 5 ], [ 4, 13, 6, 6 ], [ 4, 13, 7, 9 ], [ 4, 13, 7, 10 ], [ 4, 13, 7, 11 ], [ 4, 13, 7, 12 ], [ 4, 13, 8, 5 ], [ 4, 13, 8, 6 ], [ 4, 13, 9, 4 ], [ 4, 13, 9, 5 ], [ 4, 13, 10, 4 ], [ 4, 13, 10, 5 ], [ 4, 14, 1, 2 ], [ 4, 14, 2, 2 ], [ 4, 14, 3, 3 ], [ 4, 14, 3, 4 ], [ 4, 14, 4, 2 ], [ 4, 14, 5, 2 ], [ 4, 14, 6, 2 ], [ 4, 14, 7, 2 ], [ 4, 14, 8, 2 ], [ 4, 14, 9, 2 ], [ 4, 14, 10, 2 ], [ 4, 16, 1, 3 ], [ 4, 18, 1, 1 ], [ 4, 18, 1, 3 ], [ 4, 18, 2, 1 ], [ 4, 18, 2, 4 ], [ 4, 18, 2, 5 ], [ 4, 18, 3, 1 ], [ 4, 18, 3, 5 ], [ 4, 18, 3, 6 ], [ 4, 18, 3, 7 ], [ 4, 18, 4, 1 ], [ 4, 18, 4, 4 ], [ 4, 18, 4, 5 ], [ 4, 18, 5, 1 ], [ 4, 18, 5, 5 ], [ 4, 18, 5, 6 ], [ 4, 18, 5, 7 ], [ 4, 19, 1, 2 ], [ 4, 19, 2, 2 ], [ 4, 19, 3, 2 ], [ 4, 19, 4, 3 ], [ 4, 19, 4, 4 ], [ 4, 19, 5, 2 ], [ 4, 19, 6, 2 ], [ 4, 21, 1, 1 ], [ 4, 21, 2, 1 ], [ 4, 21, 3, 1 ], [ 4, 21, 3, 2 ], [ 4, 21, 4, 1 ], [ 4, 22, 1, 1 ], [ 4, 22, 2, 1 ], [ 4, 22, 3, 1 ], [ 4, 22, 4, 1 ], [ 4, 22, 5, 1 ], [ 4, 22, 5, 2 ], [ 4, 22, 6, 1 ], [ 4, 22, 7, 1 ], [ 4, 22, 8, 1 ], [ 4, 22, 9, 1 ], [ 4, 22, 10, 1 ], [ 4, 22, 11, 1 ], [ 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3 ], [ 4, 29, 4, 4 ], [ 4, 29, 5, 1 ], [ 4, 29, 5, 2 ], [ 4, 29, 6, 1 ], [ 4, 29, 6, 2 ], [ 4, 29, 6, 3 ], [ 4, 29, 7, 1 ], [ 4, 29, 7, 2 ], [ 4, 29, 7, 3 ], [ 4, 29, 7, 4 ], [ 4, 29, 8, 1 ], [ 4, 29, 8, 2 ], [ 4, 29, 8, 3 ], [ 4, 29, 8, 4 ], [ 4, 29, 9, 1 ], [ 4, 29, 9, 2 ], [ 4, 29, 9, 3 ], [ 4, 30, 1, 1 ], [ 4, 30, 2, 1 ], [ 4, 30, 3, 1 ], [ 4, 30, 4, 1 ], [ 4, 30, 4, 2 ], [ 4, 30, 5, 1 ], [ 4, 30, 6, 1 ], [ 4, 30, 7, 1 ], [ 4, 30, 8, 1 ], [ 4, 30, 9, 1 ], [ 4, 30, 10, 1 ], [ 4, 30, 11, 1 ], [ 4, 30, 12, 1 ], [ 4, 30, 12, 2 ], [ 4, 30, 13, 1 ], [ 4, 31, 1, 1 ], [ 4, 31, 1, 2 ], [ 4, 31, 1, 3 ], [ 4, 31, 1, 4 ], [ 4, 31, 2, 1 ], [ 4, 31, 2, 2 ], [ 4, 31, 3, 1 ], [ 4, 31, 3, 2 ], [ 4, 31, 4, 1 ], [ 4, 31, 4, 2 ], [ 4, 31, 5, 1 ], [ 4, 31, 5, 2 ], [ 4, 31, 6, 1 ], [ 4, 31, 6, 2 ], [ 4, 31, 7, 1 ], [ 4, 31, 7, 2 ], [ 4, 32, 1, 1 ], [ 4, 32, 1, 2 ], [ 4, 32, 2, 1 ], [ 4, 32, 2, 2 ], [ 4, 32, 3, 1 ], [ 4, 32, 3, 2 ], [ 4, 32, 4, 1 ], [ 4, 32, 4, 2 ], [ 4, 32, 5, 1 ], [ 4, 32, 5, 2 ], [ 4, 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[ 4, 33, 12, 1 ], [ 4, 33, 13, 1 ], [ 4, 33, 14, 1 ], [ 4, 33, 14, 2 ], [ 4, 33, 15, 1 ], [ 4, 33, 16, 1 ] ]; d31:= [ [ 4, 4, 1, 4 ], [ 4, 4, 1, 6 ], [ 4, 4, 2, 5 ], [ 4, 4, 2, 7 ], [ 4, 4, 3, 4 ], [ 4, 4, 3, 6 ], [ 4, 4, 4, 4 ], [ 4, 4, 4, 6 ], [ 4, 5, 1, 5 ], [ 4, 5, 1, 6 ], [ 4, 5, 1, 9 ], [ 4, 5, 1, 10 ], [ 4, 5, 2, 4 ], [ 4, 5, 2, 7 ], [ 4, 6, 1, 4 ], [ 4, 6, 1, 5 ], [ 4, 6, 1, 8 ], [ 4, 6, 1, 9 ], [ 4, 6, 2, 4 ], [ 4, 6, 2, 5 ], [ 4, 6, 2, 8 ], [ 4, 6, 2, 9 ], [ 4, 6, 3, 3 ], [ 4, 6, 3, 6 ], [ 4, 7, 1, 2 ], [ 4, 7, 2, 2 ], [ 4, 7, 3, 2 ], [ 4, 7, 4, 3 ], [ 4, 7, 4, 4 ], [ 4, 7, 5, 2 ], [ 4, 7, 6, 2 ], [ 4, 7, 7, 2 ], [ 4, 8, 1, 1 ], [ 4, 8, 2, 1 ], [ 4, 8, 3, 1 ], [ 4, 8, 4, 1 ], [ 4, 8, 5, 1 ], [ 4, 12, 1, 4 ], [ 4, 12, 1, 5 ], [ 4, 12, 2, 4 ], [ 4, 12, 3, 6 ], [ 4, 12, 3, 7 ], [ 4, 12, 3, 8 ], [ 4, 12, 3, 9 ], [ 4, 12, 4, 6 ], [ 4, 12, 4, 7 ], [ 4, 12, 4, 8 ], [ 4, 12, 4, 9 ], [ 4, 12, 5, 6 ], [ 4, 12, 5, 7 ], [ 4, 13, 1, 3 ], [ 4, 13, 1, 4 ], [ 4, 13, 2, 3 ], [ 4, 13, 2, 4 ], 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