Banproblem

2024-05-14, 23:18 #1

Medlem

Reg: Apr 2024

Inlägg: 597

Låt g1, g2, g3 utgöra generatorer för automorfigruppen för en kod C (|Aut(C)| = 288), med fyra banrepresentanter enligt följande:

g1 = (16, 19)(17, 20)(18, 21)
g2 = (1, 3, 2)(4, 6, 5)(7, 15, 8, 13, 9, 14)(10, 12, 11)(17, 18)(20, 21)
g3 = (2, 3)(4, 10, 13)(5, 12, 14, 6, 11, 15)(8, 9)(16, 18, 17)(19, 21, 20)

rep = [[1, 4, 7, 11, 14, 18, 21], [1, 4, 7, 11, 15, 16, 20], [1, 5, 8, 11, 14, 16, 20], [1, 5, 8, 12, 15, 16, 19]]

Beräkna banan av mängden.

Citera

2024-06-08, 05:05 #2

Bannlyst

Hm… det här ska man nog inte göra för hand. Vad är tillämpningen?

Med Gap (eller Magma) kan man dock enkelt plocka fram resultatet. Givet är:

Kod:

g1 := (16, 19)(17, 20)(18, 21);
g2 := (1, 3, 2)(4, 6, 5)(7, 15, 8, 13, 9, 14)(10, 12, 11)(17, 18)(20, 21);
g3 := (2, 3)(4, 10, 13)(5, 12, 14, 6, 11, 15)(8, 9)(16, 18, 17)(19, 21, 20);

rep := [[1, 4, 7, 11, 14, 18, 21], [1, 4, 7, 11, 15, 16, 20], [1, 5, 8, 11, 14, 16, 20], [1, 5, 8, 12, 15, 16, 19]];

Sätt nu:

Kod:

g := Group(g1, g2, g3);

samt beräkna

Kod:

Orbit(g, rep, OnSetsSets);

Man får en lång radda utdata, men kvar blir efter filtrering 180 unika vektorer:

Kod:

[1, 4, 7, 11, 14, 18, 21],
[1, 4, 7, 11, 15, 16, 20],
[1, 4, 7, 11, 15, 17, 19],
[1, 4, 7, 12, 14, 16, 20],
[1, 4, 7, 12, 14, 17, 19],
[1, 4, 7, 12, 15, 18, 21],
[1, 4, 8, 10, 14, 16, 19],
[1, 4, 8, 10, 15, 17, 21],
[1, 4, 8, 10, 15, 18, 20],
[1, 4, 8, 11, 13, 17, 20],
[1, 4, 8, 12, 13, 16, 21],
[1, 4, 8, 12, 13, 18, 19],
[1, 4, 9, 10, 14, 17, 21],
[1, 4, 9, 10, 14, 18, 20],
[1, 4, 9, 10, 15, 16, 19],
[1, 4, 9, 11, 13, 16, 21],
[1, 4, 9, 11, 13, 18, 19],
[1, 4, 9, 12, 13, 17, 20],
[1, 5, 7, 10, 14, 17, 20],
[1, 5, 7, 10, 15, 16, 21],
[1, 5, 7, 10, 15, 18, 19],
[1, 5, 7, 11, 13, 16, 19],
[1, 5, 7, 12, 13, 17, 21],
[1, 5, 7, 12, 13, 18, 20],
[1, 5, 8, 10, 13, 18, 21],
[1, 5, 8, 11, 14, 16, 20],
[1, 5, 8, 11, 14, 16, 21],
[1, 5, 8, 11, 14, 17, 19],
[1, 5, 8, 11, 14, 17, 21],
[1, 5, 8, 11, 14, 18, 19],
[1, 5, 8, 11, 14, 18, 20],
[1, 5, 8, 12, 15, 16, 19],
[1, 5, 8, 12, 15, 17, 20],
[1, 5, 9, 10, 13, 16, 20],
[1, 5, 9, 10, 13, 17, 19],
[1, 5, 9, 11, 15, 17, 20],
[1, 5, 9, 11, 15, 18, 21],
[1, 5, 9, 12, 14, 16, 19],
[1, 5, 9, 12, 14, 18, 21],
[1, 6, 7, 10, 14, 16, 21],
[1, 6, 7, 10, 14, 18, 19],
[1, 6, 7, 10, 15, 17, 20],
[1, 6, 7, 11, 13, 17, 21],
[1, 6, 7, 11, 13, 18, 20],
[1, 6, 7, 12, 13, 16, 19],
[1, 6, 8, 10, 13, 16, 20],
[1, 6, 8, 10, 13, 17, 19],
[1, 6, 8, 11, 15, 16, 19],
[1, 6, 8, 11, 15, 18, 21],
[1, 6, 8, 12, 14, 17, 20],
[1, 6, 8, 12, 14, 18, 21],
[1, 6, 9, 10, 13, 18, 21],
[1, 6, 9, 11, 14, 16, 19],
[1, 6, 9, 11, 14, 17, 20],
[1, 6, 9, 12, 15, 16, 20],
[1, 6, 9, 12, 15, 16, 21],
[1, 6, 9, 12, 15, 17, 19],
[1, 6, 9, 12, 15, 17, 21],
[1, 6, 9, 12, 15, 18, 19],
[1, 6, 9, 12, 15, 18, 20],
[2, 4, 7, 10, 13, 16, 20],
[2, 4, 7, 10, 13, 16, 21],
[2, 4, 7, 10, 13, 17, 19],
[2, 4, 7, 10, 13, 17, 21],
[2, 4, 7, 10, 13, 18, 19],
[2, 4, 7, 10, 13, 18, 20],
[2, 4, 7, 11, 14, 18, 21],
[2, 4, 7, 12, 15, 16, 19],
[2, 4, 7, 12, 15, 17, 20],
[2, 4, 8, 10, 14, 16, 19],
[2, 4, 8, 11, 13, 17, 20],
[2, 4, 8, 11, 15, 16, 21],
[2, 4, 8, 11, 15, 18, 19],
[2, 4, 8, 12, 14, 17, 21],
[2, 4, 8, 12, 14, 18, 20],
[2, 4, 9, 10, 15, 17, 20],
[2, 4, 9, 10, 15, 18, 21],
[2, 4, 9, 11, 14, 16, 20],
[2, 4, 9, 11, 14, 17, 19],
[2, 4, 9, 12, 13, 16, 19],
[2, 4, 9, 12, 13, 18, 21],
[2, 5, 7, 10, 14, 17, 20],
[2, 5, 7, 11, 13, 16, 19],
[2, 5, 7, 11, 15, 17, 21],
[2, 5, 7, 11, 15, 18, 20],
[2, 5, 7, 12, 14, 16, 21],
[2, 5, 7, 12, 14, 18, 19],
[2, 5, 8, 10, 13, 18, 21],
[2, 5, 8, 10, 15, 16, 20],
[2, 5, 8, 10, 15, 17, 19],
[2, 5, 8, 12, 13, 16, 20],
[2, 5, 8, 12, 13, 17, 19],
[2, 5, 8, 12, 15, 18, 21],
[2, 5, 9, 10, 14, 16, 21],
[2, 5, 9, 10, 14, 18, 19],
[2, 5, 9, 11, 13, 17, 21],
[2, 5, 9, 11, 13, 18, 20],
[2, 5, 9, 11, 15, 16, 19],
[2, 5, 9, 12, 14, 17, 20],
[2, 6, 7, 10, 15, 16, 19],
[2, 6, 7, 10, 15, 18, 21],
[2, 6, 7, 11, 14, 16, 20],
[2, 6, 7, 11, 14, 17, 19],
[2, 6, 7, 12, 13, 17, 20],
[2, 6, 7, 12, 13, 18, 21],
[2, 6, 8, 10, 14, 17, 21],
[2, 6, 8, 10, 14, 18, 20],
[2, 6, 8, 11, 13, 16, 21],
[2, 6, 8, 11, 13, 18, 19],
[2, 6, 8, 11, 15, 17, 20],
[2, 6, 8, 12, 14, 16, 19],
[2, 6, 9, 10, 13, 16, 19],
[2, 6, 9, 10, 13, 17, 20],
[2, 6, 9, 11, 14, 18, 21],
[2, 6, 9, 12, 15, 16, 20],
[2, 6, 9, 12, 15, 16, 21],
[2, 6, 9, 12, 15, 17, 19],
[2, 6, 9, 12, 15, 17, 21],
[2, 6, 9, 12, 15, 18, 19],
[2, 6, 9, 12, 15, 18, 20],
[3, 4, 7, 10, 13, 16, 20],
[3, 4, 7, 10, 13, 16, 21],
[3, 4, 7, 10, 13, 17, 19],
[3, 4, 7, 10, 13, 17, 21],
[3, 4, 7, 10, 13, 18, 19],
[3, 4, 7, 10, 13, 18, 20],
[3, 4, 7, 11, 14, 16, 19],
[3, 4, 7, 11, 14, 17, 20],
[3, 4, 7, 12, 15, 18, 21],
[3, 4, 8, 10, 14, 17, 20],
[3, 4, 8, 10, 14, 18, 21],
[3, 4, 8, 11, 13, 16, 19],
[3, 4, 8, 11, 13, 18, 21],
[3, 4, 8, 12, 15, 16, 20],
[3, 4, 8, 12, 15, 17, 19],
[3, 4, 9, 10, 15, 16, 19],
[3, 4, 9, 11, 15, 17, 21],
[3, 4, 9, 11, 15, 18, 20],
[3, 4, 9, 12, 13, 17, 20],
[3, 4, 9, 12, 14, 16, 21],
[3, 4, 9, 12, 14, 18, 19],
[3, 5, 7, 10, 14, 16, 19],
[3, 5, 7, 10, 14, 18, 21],
[3, 5, 7, 11, 13, 17, 20],
[3, 5, 7, 11, 13, 18, 21],
[3, 5, 7, 12, 15, 16, 20],
[3, 5, 7, 12, 15, 17, 19],
[3, 5, 8, 10, 13, 16, 19],
[3, 5, 8, 10, 13, 17, 20],
[3, 5, 8, 11, 14, 16, 20],
[3, 5, 8, 11, 14, 16, 21],
[3, 5, 8, 11, 14, 17, 19],
[3, 5, 8, 11, 14, 17, 21],
[3, 5, 8, 11, 14, 18, 19],
[3, 5, 8, 11, 14, 18, 20],
[3, 5, 8, 12, 15, 18, 21],
[3, 5, 9, 10, 15, 17, 21],
[3, 5, 9, 10, 15, 18, 20],
[3, 5, 9, 11, 15, 16, 19],
[3, 5, 9, 12, 13, 16, 21],
[3, 5, 9, 12, 13, 18, 19],
[3, 5, 9, 12, 14, 17, 20],
[3, 6, 7, 10, 15, 17, 20],
[3, 6, 7, 11, 15, 16, 21],
[3, 6, 7, 11, 15, 18, 19],
[3, 6, 7, 12, 13, 16, 19],
[3, 6, 7, 12, 14, 17, 21],
[3, 6, 7, 12, 14, 18, 20],
[3, 6, 8, 10, 15, 16, 21],
[3, 6, 8, 10, 15, 18, 19],
[3, 6, 8, 11, 15, 17, 20],
[3, 6, 8, 12, 13, 17, 21],
[3, 6, 8, 12, 13, 18, 20],
[3, 6, 8, 12, 14, 16, 19],
[3, 6, 9, 10, 13, 18, 21],
[3, 6, 9, 10, 14, 16, 20],
[3, 6, 9, 10, 14, 17, 19],
[3, 6, 9, 11, 13, 16, 20],
[3, 6, 9, 11, 13, 17, 19],
[3, 6, 9, 11, 14, 18, 21]

Citera

Banproblem

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