It runs a loop to find elements of the Galois group until it find a generating set or die after mx tries.
i1 : l={1,1} o1 = {1, 1} o1 : List |
i2 : m={2,1} o2 = {2, 1} o2 : List |
i3 : (k,n) = (3,7) o3 = (3, 7) o3 : Sequence |
Generate a random set of flags to compute an instance of the problem
i4 : G = createRandomFlagsForSimpleSchubert((k,n),l,m); |
Solve the Schubert problem
i5 : S = solveSimpleSchubert((k,n),l,m,G); |
Check if the Galois group is the symmetric group
i6 : isGaloisFullSymmetric((l,m,k,n), G, S, 5) sh: gap: command not found sh: gap: command not found sh: gap: command not found sh: gap: command not found sh: gap: command not found o6 = (false, {{13, 15, 76, 8, 4, 58, 38, 31, 43, 44, 71, 67, 32, 54, 14, 57, ------------------------------------------------------------------------ 34, 22, 52, 59, 9, 20, 69, 75, 2, 21, 35, 33, 74, 17, 7, 49, 24, 28, 11, ------------------------------------------------------------------------ 55, 37, 25, 68, 63, 40, 66, 27, 73, 5, 51, 6, 45, 50, 30, 61, 36, 41, ------------------------------------------------------------------------ 62, 64, 48, 56, 26, 19, 53, 60, 42, 46, 39, 0, 47, 3, 23, 1, 29, 65, 70, ------------------------------------------------------------------------ 72, 12, 16, 18, 10}, {40, 32, 23, 7, 70, 43, 69, 39, 59, 74, 71, 56, 53, ------------------------------------------------------------------------ 75, 14, 15, 66, 19, 28, 17, 6, 67, 73, 2, 37, 22, 27, 76, 54, 26, 5, 13, ------------------------------------------------------------------------ 21, 8, 0, 44, 24, 46, 38, 58, 34, 9, 61, 41, 45, 20, 29, 10, 30, 49, 31, ------------------------------------------------------------------------ 51, 55, 4, 11, 64, 68, 57, 52, 33, 60, 63, 18, 12, 48, 65, 42, 62, 16, ------------------------------------------------------------------------ 35, 25, 47, 72, 3, 50, 1, 36}, {56, 48, 2, 61, 0, 46, 74, 31, 52, 43, ------------------------------------------------------------------------ 45, 40, 5, 22, 14, 58, 11, 21, 67, 3, 8, 66, 10, 57, 39, 29, 38, 23, 37, ------------------------------------------------------------------------ 49, 30, 28, 55, 24, 42, 4, 7, 16, 64, 59, 60, 9, 12, 1, 13, 17, 35, 47, ------------------------------------------------------------------------ 76, 69, 73, 26, 62, 18, 54, 72, 71, 20, 65, 33, 51, 50, 36, 63, 70, 27, ------------------------------------------------------------------------ 15, 32, 68, 34, 19, 75, 6, 25, 44, 53, 41}, {0, 1, 2, 36, 23, 5, 16, 19, ------------------------------------------------------------------------ 8, 34, 10, 68, 29, 55, 76, 67, 74, 28, 50, 26, 41, 33, 47, 38, 56, 25, ------------------------------------------------------------------------ 32, 27, 37, 57, 46, 18, 22, 59, 9, 20, 64, 72, 58, 31, 14, 11, 42, 40, ------------------------------------------------------------------------ 66, 45, 12, 52, 48, 30, 4, 51, 21, 49, 62, 65, 13, 61, 15, 39, 60, 7, ------------------------------------------------------------------------ 71, 63, 17, 6, 44, 53, 54, 24, 69, 3, 43, 73, 70, 75, 35}, {56, 10, 40, ------------------------------------------------------------------------ 58, 28, 21, 33, 7, 8, 53, 44, 15, 22, 43, 27, 36, 11, 38, 1, 20, 17, 54, ------------------------------------------------------------------------ 62, 4, 52, 59, 63, 75, 6, 29, 50, 31, 30, 24, 34, 2, 3, 25, 35, 26, 18, ------------------------------------------------------------------------ 23, 42, 0, 55, 45, 12, 47, 48, 74, 61, 73, 67, 32, 13, 57, 51, 19, 16, ------------------------------------------------------------------------ 66, 60, 72, 5, 37, 64, 65, 46, 41, 68, 69, 70, 71, 39, 9, 49, 14, 76}}) o6 : Sequence |
one permutation is not enough
i7 : isGaloisFullSymmetric((l,m,k,n), G, S, 1) sh: gap: command not found o7 = (false, {{36, 1, 20, 66, 65, 37, 28, 6, 52, 67, 10, 19, 35, 13, 14, 24, ------------------------------------------------------------------------ 11, 17, 18, 46, 57, 51, 64, 26, 45, 58, 7, 27, 22, 29, 32, 23, 2, 49, ------------------------------------------------------------------------ 73, 76, 56, 54, 38, 59, 4, 9, 42, 43, 44, 71, 55, 47, 5, 62, 3, 0, 16, ------------------------------------------------------------------------ 53, 39, 15, 30, 61, 12, 33, 60, 31, 8, 63, 68, 69, 25, 48, 70, 41, 40, ------------------------------------------------------------------------ 34, 72, 21, 74, 75, 50}}) o7 : Sequence |
This assumes that GAP runs when you type in the terminal gap and that we already know that the Galois group is the full symmetric group, otherwise it will output false after mx repetitions.