If the monodromy group is full symmetric and the degree is large, then the default settings have a good chance of generating the whole group. However, you will need to use a bigger graph than the default settings to fully generate imprimitive groups, as in the following example of a Euclidean distance degree calculation.
i1 : setRandomSeed 100; |
i2 : declareVariable \ {t_1,t_2,u_0,u_1,u_2,u_3}; |
i3 : paramMatrix = gateMatrix{{u_0,u_1,u_2,u_3}}; |
i4 : varMatrix = gateMatrix{{t_1,t_2}}; |
i5 : phi = transpose gateMatrix{{t_1^3, t_1^2*t_2, t_1*t_2^2, t_2^3}}; |
i6 : loss = sum for i from 0 to 3 list (u_i - phi_(i,0))^2; |
i7 : dLoss = diff(varMatrix, gateMatrix{{loss}}); |
i8 : G = gateSystem(paramMatrix,varMatrix,transpose dLoss); |
i9 : monodromyGroup(G,"msOptions" => {NumberOfEdges=>10}) o9 = {{7, 1, 9, 0, 12, 17, 2, 3, 4, 8, 10, 15, 6, 11, 14, 13, 5, 16, 19, 20, ------------------------------------------------------------------------ 18}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ------------------------------------------------------------------------ 19, 20}, {3, 1, 6, 19, 0, 2, 13, 8, 9, 16, 10, 12, 4, 15, 14, 20, 17, ------------------------------------------------------------------------ 18, 11, 5, 7}, {1, 6, 3, 19, 16, 2, 0, 8, 15, 13, 9, 12, 17, 10, 4, 20, ------------------------------------------------------------------------ 14, 18, 11, 5, 7}, {13, 10, 5, 15, 4, 12, 6, 2, 7, 9, 14, 8, 11, 16, 1, ------------------------------------------------------------------------ 17, 0, 3, 19, 20, 18}, {0, 1, 6, 20, 7, 15, 11, 17, 9, 5, 10, 3, 4, 13, ------------------------------------------------------------------------ 14, 18, 16, 19, 2, 8, 12}, {7, 10, 8, 13, 6, 20, 9, 18, 12, 4, 14, 19, ------------------------------------------------------------------------ 2, 11, 1, 16, 5, 0, 3, 15, 17}, {6, 10, 12, 13, 11, 20, 5, 18, 2, 7, 14, ------------------------------------------------------------------------ 19, 8, 9, 1, 16, 4, 0, 3, 15, 17}, {13, 10, 8, 15, 6, 7, 9, 11, 12, 4, ------------------------------------------------------------------------ 14, 5, 2, 16, 1, 17, 0, 3, 19, 20, 18}, {16, 1, 3, 19, 9, 2, 4, 8, 15, ------------------------------------------------------------------------ 6, 10, 12, 17, 0, 14, 20, 13, 18, 11, 5, 7}, {0, 1, 2, 20, 4, 7, 6, 11, ------------------------------------------------------------------------ 8, 9, 10, 5, 12, 13, 14, 18, 16, 19, 15, 17, 3}, {1, 6, 3, 19, 16, 2, 0, ------------------------------------------------------------------------ 8, 15, 13, 9, 12, 17, 10, 4, 20, 14, 18, 11, 5, 7}, {3, 6, 1, 19, 16, 2, ------------------------------------------------------------------------ 0, 8, 10, 13, 9, 12, 14, 15, 4, 20, 17, 18, 11, 5, 7}, {0, 1, 2, 3, 4, ------------------------------------------------------------------------ 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, {0, 1, 15, ------------------------------------------------------------------------ 20, 4, 8, 6, 12, 17, 9, 10, 2, 3, 13, 14, 18, 16, 19, 5, 7, 11}, {0, 9, ------------------------------------------------------------------------ 15, 20, 10, 8, 14, 12, 17, 1, 4, 2, 3, 13, 6, 18, 16, 19, 5, 7, 11}, ------------------------------------------------------------------------ {13, 10, 19, 2, 6, 5, 9, 7, 20, 4, 14, 11, 18, 16, 1, 8, 0, 12, 17, 3, ------------------------------------------------------------------------ 15}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ------------------------------------------------------------------------ 19, 20}, {3, 1, 2, 19, 4, 16, 6, 0, 8, 9, 10, 13, 12, 15, 14, 20, 17, ------------------------------------------------------------------------ 18, 11, 5, 7}, {0, 1, 2, 20, 4, 7, 6, 11, 8, 9, 10, 5, 12, 13, 14, 18, ------------------------------------------------------------------------ 16, 19, 15, 17, 3}, {1, 6, 3, 19, 16, 2, 0, 8, 15, 13, 9, 12, 17, 10, 4, ------------------------------------------------------------------------ 20, 14, 18, 11, 5, 7}, {10, 9, 15, 20, 0, 8, 13, 12, 17, 16, 4, 2, 3, ------------------------------------------------------------------------ 14, 6, 18, 1, 19, 5, 7, 11}, {10, 9, 15, 20, 0, 8, 13, 12, 17, 16, 4, 2, ------------------------------------------------------------------------ 3, 14, 6, 18, 1, 19, 5, 7, 11}, {13, 1, 19, 2, 6, 5, 9, 7, 20, 4, 10, ------------------------------------------------------------------------ 11, 18, 16, 14, 8, 0, 12, 17, 3, 15}, {13, 10, 8, 15, 6, 7, 9, 11, 12, ------------------------------------------------------------------------ 4, 14, 5, 2, 16, 1, 17, 0, 3, 19, 20, 18}, {0, 1, 2, 20, 4, 7, 6, 11, 8, ------------------------------------------------------------------------ 9, 10, 5, 12, 13, 14, 18, 16, 19, 15, 17, 3}, {16, 6, 3, 19, 1, 2, 10, ------------------------------------------------------------------------ 8, 15, 14, 9, 12, 17, 0, 4, 20, 13, 18, 11, 5, 7}, {13, 10, 5, 15, 4, ------------------------------------------------------------------------ 12, 6, 2, 7, 9, 14, 8, 11, 16, 1, 17, 0, 3, 18, 19, 20}, {0, 1, 6, 20, ------------------------------------------------------------------------ 7, 2, 11, 8, 9, 5, 10, 12, 4, 13, 14, 18, 16, 19, 15, 17, 3}, {0, 1, 6, ------------------------------------------------------------------------ 3, 7, 2, 11, 8, 9, 5, 10, 12, 4, 13, 14, 15, 16, 17, 18, 19, 20}, {6, ------------------------------------------------------------------------ 10, 7, 13, 2, 20, 8, 18, 11, 12, 14, 19, 5, 9, 1, 16, 4, 0, 3, 15, 17}, ------------------------------------------------------------------------ {13, 10, 8, 15, 6, 7, 9, 11, 12, 4, 14, 5, 2, 16, 1, 17, 0, 3, 19, 20, ------------------------------------------------------------------------ 18}, {13, 10, 8, 15, 6, 7, 9, 11, 12, 4, 14, 5, 2, 16, 1, 17, 0, 3, 19, ------------------------------------------------------------------------ 20, 18}, {16, 6, 3, 19, 10, 2, 14, 8, 15, 1, 9, 12, 17, 0, 4, 20, 13, ------------------------------------------------------------------------ 18, 11, 5, 7}, {19, 14, 4, 16, 2, 3, 8, 15, 6, 12, 1, 17, 9, 20, 10, 0, ------------------------------------------------------------------------ 18, 13, 11, 5, 7}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ------------------------------------------------------------------------ 15, 16, 17, 19, 20, 18}, {10, 9, 15, 20, 0, 8, 13, 12, 17, 16, 4, 2, 3, ------------------------------------------------------------------------ 14, 6, 18, 1, 19, 5, 7, 11}, {11, 10, 8, 13, 6, 20, 9, 18, 12, 4, 14, ------------------------------------------------------------------------ 19, 2, 5, 1, 16, 7, 0, 3, 15, 17}, {10, 9, 7, 0, 12, 17, 2, 3, 11, 8, 4, ------------------------------------------------------------------------ 15, 5, 14, 6, 13, 1, 16, 19, 20, 18}, {13, 10, 8, 15, 6, 7, 9, 11, 12, ------------------------------------------------------------------------ 4, 14, 5, 2, 16, 1, 17, 0, 3, 19, 20, 18}, {16, 6, 3, 19, 10, 2, 14, 8, ------------------------------------------------------------------------ 15, 1, 9, 12, 17, 0, 4, 20, 13, 18, 11, 5, 7}, {16, 14, 4, 19, 2, 3, 8, ------------------------------------------------------------------------ 15, 6, 12, 1, 17, 9, 0, 10, 20, 13, 18, 11, 5, 7}, {13, 10, 8, 15, 4, 7, ------------------------------------------------------------------------ 6, 11, 12, 9, 14, 5, 2, 16, 1, 17, 0, 3, 19, 20, 18}, {13, 10, 5, 15, 4, ------------------------------------------------------------------------ 12, 6, 2, 7, 9, 14, 8, 11, 16, 1, 17, 0, 3, 19, 20, 18}, {10, 9, 15, 20, ------------------------------------------------------------------------ 0, 8, 13, 12, 17, 16, 4, 2, 3, 14, 6, 18, 1, 19, 5, 7, 11}, {10, 0, 5, ------------------------------------------------------------------------ 2, 6, 19, 9, 20, 7, 4, 13, 18, 11, 14, 16, 8, 1, 12, 17, 3, 15}, {11, ------------------------------------------------------------------------ 10, 12, 13, 6, 20, 9, 18, 2, 4, 14, 19, 8, 5, 1, 16, 7, 0, 3, 15, 17}, ------------------------------------------------------------------------ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ------------------------------------------------------------------------ 20}, {0, 1, 2, 20, 4, 7, 6, 11, 8, 9, 10, 5, 12, 13, 14, 18, 16, 19, 15, ------------------------------------------------------------------------ 17, 3}, {1, 6, 3, 19, 16, 2, 0, 8, 15, 13, 9, 12, 17, 10, 4, 20, 14, 18, ------------------------------------------------------------------------ 11, 5, 7}, {15, 9, 0, 7, 10, 8, 14, 12, 13, 1, 4, 2, 16, 17, 6, 11, 3, ------------------------------------------------------------------------ 5, 19, 20, 18}, {15, 1, 0, 7, 4, 8, 6, 12, 13, 9, 10, 2, 16, 17, 14, 11, ------------------------------------------------------------------------ 3, 5, 19, 20, 18}, {3, 1, 6, 5, 16, 2, 0, 8, 9, 13, 10, 12, 4, 15, 14, ------------------------------------------------------------------------ 7, 17, 11, 18, 19, 20}, {6, 10, 12, 13, 11, 20, 5, 18, 2, 7, 14, 19, 8, ------------------------------------------------------------------------ 9, 1, 16, 4, 0, 3, 15, 17}, {13, 10, 19, 2, 6, 5, 9, 7, 20, 4, 14, 11, ------------------------------------------------------------------------ 18, 16, 1, 8, 0, 12, 17, 3, 15}} o9 : List |
This is still somewhat experimental.
The object monodromyGroup is a method function with options.