// Data for the Table 3:

Magma V2.21-2     Thu Mar 19 2015 00:11:06 on luna     [Seed = 912876851]
Type ? for help.  Type <Ctrl>-D to quit.

Loading file "2primary_Ss.txt"

//GCD 

> [GCD({rzb[3][1][i] : rzb in RZB}) : i in [1..5]];
[ 1, 1, 1, 2, 8 ]
> [GCD({rzb[3][2][i] : rzb in RZB}) : i in [1..5]];
[ 1, 1, 1, 4, 16 ]
> [GCD({rzb[3][3][i] : rzb in RZB}) : i in [1..4]];
[ 2, 4, 16, 64 ]
> [GCD({rzb[3][4][i] : rzb in RZB}) : i in [1..3]];
[ 16, 64, 256 ]
> [GCD({rzb[3][5][i] : rzb in RZB}) : i in [1..2]];
[ 128, 512 ]
> [GCD({rzb[3][6][i] : rzb in RZB}) : i in [1..1]];
[ 2048 ]

// Min

> [Min({rzb[3][1][i] : rzb in RZB}) : i in [1..5]];
[ 1, 1, 1, 2, 8 ]
> [Min({rzb[3][2][i] : rzb in RZB}) : i in [1..5]];
[ 1, 1, 1, 4, 16 ]
> [Min({rzb[3][3][i] : rzb in RZB}) : i in [1..4]];
[ 2, 4, 16, 64 ]
> [Min({rzb[3][4][i] : rzb in RZB}) : i in [1..3]];
[ 16, 64, 256 ]
> [Min({rzb[3][5][i] : rzb in RZB}) : i in [1..2]];
[ 256, 1024 ]
> [Min({rzb[3][6][i] : rzb in RZB}) : i in [1..1]];
[ 4096 ]

// Some computations: 

> [Sort(Setseq({rzb[3][1][i] : rzb in RZB})) : i in [1..5]];
[
    [ 1, 3 ],
    [ 1, 2, 3, 4, 6, 12 ],
    [ 1, 2, 4, 8, 12, 16, 24, 48 ],
    [ 2, 4, 8, 16, 32, 48, 64, 96, 192 ],
    [ 8, 16, 32, 64, 128, 192, 256, 384, 768 ]
]
> [Sort(Setseq({rzb[3][2][i] : rzb in RZB})) : i in [1..5]];
[
    [ 1, 2, 3, 6 ],
    [ 1, 2, 4, 6, 8, 12, 24 ],
    [ 1, 2, 4, 8, 16, 24, 32, 48, 96 ],
    [ 4, 8, 16, 32, 64, 96, 128, 192, 384 ],
    [ 16, 32, 64, 128, 256, 384, 512, 768, 1536 ]
]
> [Sort(Setseq({rzb[3][3][i] : rzb in RZB})) : i in [1..4]];
[
    [ 2, 4, 6, 8, 12, 16, 24, 32, 48, 96 ],
    [ 4, 8, 16, 24, 32, 48, 64, 96, 128, 192, 384 ],
    [ 16, 32, 64, 96, 128, 192, 256, 384, 512, 768, 1536 ],
    [ 64, 128, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144 ]
]
> [Sort(Setseq({rzb[3][4][i] : rzb in RZB})) : i in [1..3]];
[
    [ 16, 32, 64, 96, 128, 192, 256, 384, 768, 1536 ],
    [ 64, 128, 256, 384, 512, 768, 1024, 1536, 3072, 6144 ],
    [ 256, 512, 1024, 1536, 2048, 3072, 4096, 6144, 12288, 24576 ]
]
> [Sort(Setseq({rzb[3][5][i] : rzb in RZB})) : i in [1..2]];
[
    [ 256, 384, 512, 1024, 1536, 2048, 3072, 4096, 6144, 12288, 24576 ],
    [ 1024, 1536, 2048, 4096, 6144, 8192, 12288, 16384, 24576, 49152, 98304 ]
]
> [Sort(Setseq({rzb[3][6][i] : rzb in RZB})) : i in [1..1]];
[
    [ 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 196608, 393216 ]
]



// Some more computations:

> Sort(Setseq({rzb[3][1] : rzb in RZB}));
[
    [ 1, 1, 1, 2, 8 ],
    [ 1, 1, 1, 4, 16 ],
    [ 1, 1, 2, 4, 8 ],
    [ 1, 1, 2, 4, 16 ],
    [ 1, 1, 2, 8, 32 ],
    [ 1, 1, 4, 8, 16 ],
    [ 1, 1, 4, 8, 32 ],
    [ 1, 1, 4, 16, 64 ],
    [ 1, 2, 2, 2, 8 ],
    [ 1, 2, 2, 4, 8 ],
    [ 1, 2, 2, 4, 16 ],
    [ 1, 2, 2, 8, 16 ],
    [ 1, 2, 2, 8, 32 ],
    [ 1, 2, 4, 8, 16 ],
    [ 1, 2, 4, 8, 32 ],
    [ 1, 2, 4, 16, 64 ],
    [ 1, 2, 8, 16, 64 ],
    [ 1, 2, 8, 32, 128 ],
    [ 1, 4, 4, 16, 64 ],
    [ 1, 4, 8, 16, 64 ],
    [ 1, 4, 8, 32, 128 ],
    [ 1, 4, 16, 32, 128 ],
    [ 1, 4, 16, 64, 256 ],
    [ 3, 3, 12, 48, 192 ],
    [ 3, 6, 24, 96, 384 ],
    [ 3, 12, 48, 192, 768 ]
]
> Sort(Setseq({rzb[3][2] : rzb in RZB}));
[
    [ 1, 1, 1, 4, 16 ],
    [ 1, 1, 2, 4, 16 ],
    [ 1, 1, 2, 8, 32 ],
    [ 1, 1, 4, 16, 64 ],
    [ 1, 2, 2, 4, 16 ],
    [ 1, 2, 2, 8, 32 ],
    [ 1, 2, 4, 8, 32 ],
    [ 1, 2, 4, 16, 64 ],
    [ 1, 2, 8, 32, 128 ],
    [ 1, 4, 8, 32, 128 ],
    [ 1, 4, 16, 64, 256 ],
    [ 2, 2, 2, 4, 16 ],
    [ 2, 2, 2, 8, 32 ],
    [ 2, 2, 4, 8, 16 ],
    [ 2, 2, 4, 8, 32 ],
    [ 2, 2, 4, 16, 64 ],
    [ 2, 2, 8, 32, 128 ],
    [ 2, 4, 4, 4, 16 ],
    [ 2, 4, 4, 8, 16 ],
    [ 2, 4, 4, 8, 32 ],
    [ 2, 4, 4, 16, 64 ],
    [ 2, 4, 8, 16, 32 ],
    [ 2, 4, 8, 16, 64 ],
    [ 2, 4, 8, 32, 128 ],
    [ 2, 4, 16, 32, 128 ],
    [ 2, 4, 16, 64, 256 ],
    [ 2, 8, 16, 32, 128 ],
    [ 2, 8, 16, 64, 256 ],
    [ 2, 8, 32, 128, 512 ],
    [ 3, 12, 48, 192, 768 ],
    [ 6, 6, 24, 96, 384 ],
    [ 6, 12, 48, 192, 768 ],
    [ 6, 24, 96, 384, 1536 ]
]
>  Sort(Setseq({rzb[3][3] : rzb in RZB}));
[
    [ 2, 4, 16, 64 ],
    [ 2, 8, 32, 128 ],
    [ 4, 4, 16, 64 ],
    [ 4, 8, 16, 64 ],
    [ 4, 8, 32, 128 ],
    [ 4, 16, 64, 256 ],
    [ 6, 24, 96, 384 ],
    [ 8, 8, 16, 64 ],
    [ 8, 8, 32, 128 ],
    [ 8, 16, 32, 64 ],
    [ 8, 16, 32, 128 ],
    [ 8, 16, 64, 256 ],
    [ 8, 32, 128, 512 ],
    [ 12, 48, 192, 768 ],
    [ 16, 16, 16, 64 ],
    [ 16, 16, 32, 64 ],
    [ 16, 16, 32, 128 ],
    [ 16, 16, 64, 256 ],
    [ 16, 32, 64, 128 ],
    [ 16, 32, 64, 256 ],
    [ 16, 32, 128, 512 ],
    [ 16, 64, 256, 1024 ],
    [ 24, 96, 384, 1536 ],
    [ 32, 128, 512, 2048 ],
    [ 48, 192, 768, 3072 ],
    [ 96, 384, 1536, 6144 ]
]

> Sort(Setseq({rzb[3][4] : rzb in RZB}));
[
    [ 16, 64, 256 ],
    [ 32, 64, 256 ],
    [ 32, 128, 512 ],
    [ 64, 64, 256 ],
    [ 64, 128, 256 ],
    [ 64, 128, 512 ],
    [ 64, 256, 1024 ],
    [ 96, 384, 1536 ],
    [ 128, 256, 512 ],
    [ 128, 256, 1024 ],
    [ 128, 512, 2048 ],
    [ 192, 768, 3072 ],
    [ 256, 1024, 4096 ],
    [ 384, 1536, 6144 ],
    [ 768, 3072, 12288 ],
    [ 1536, 6144, 24576 ]
]
> Sort(Setseq({rzb[3][5] : rzb in RZB}));
[
    [ 256, 1024 ],
    [ 384, 1536 ],
    [ 512, 1024 ],
    [ 512, 2048 ],
    [ 1024, 2048 ],
    [ 1024, 4096 ],
    [ 1536, 6144 ],
    [ 2048, 8192 ],
    [ 3072, 12288 ],
    [ 4096, 16384 ],
    [ 6144, 24576 ],
    [ 12288, 49152 ],
    [ 24576, 98304 ]
]
> Sort(Setseq({rzb[3][6] : rzb in RZB}));
[
    [ 4096 ],
    [ 6144 ],
    [ 8192 ],
    [ 12288 ],
    [ 16384 ],
    [ 24576 ],
    [ 32768 ],
    [ 49152 ],
    [ 65536 ],
    [ 98304 ],
    [ 196608 ],
    [ 393216 ]
]
>