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MonodromySolver :: monodromyGroup

monodromyGroup -- compute the group of permutations implicitly defined by a homotopy graph

Synopsis

Description

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 = {{3, 4, 2, 6, 7, 5, 0, 1, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
     ------------------------------------------------------------------------
     20}, {4, 2, 6, 7, 5, 0, 1, 8, 3, 15, 10, 16, 12, 17, 14, 9, 11, 13, 18,
     ------------------------------------------------------------------------
     19, 20}, {5, 1, 6, 8, 4, 0, 2, 7, 3, 9, 10, 11, 12, 13, 14, 15, 16, 17,
     ------------------------------------------------------------------------
     18, 19, 20}, {4, 2, 6, 7, 5, 0, 1, 8, 3, 15, 10, 16, 12, 17, 14, 9, 11,
     ------------------------------------------------------------------------
     13, 18, 19, 20}, {9, 4, 10, 11, 7, 12, 13, 1, 14, 3, 2, 6, 5, 0, 8, 15,
     ------------------------------------------------------------------------
     16, 17, 19, 20, 18}, {3, 4, 2, 6, 7, 5, 0, 1, 8, 9, 10, 11, 12, 13, 14,
     ------------------------------------------------------------------------
     15, 16, 17, 18, 19, 20}, {3, 4, 2, 6, 7, 5, 0, 1, 8, 9, 10, 11, 12, 13,
     ------------------------------------------------------------------------
     14, 15, 16, 17, 18, 19, 20}, {9, 4, 18, 11, 7, 19, 13, 1, 20, 3, 10, 6,
     ------------------------------------------------------------------------
     12, 0, 14, 15, 16, 17, 5, 8, 2}, {3, 4, 2, 6, 7, 5, 0, 1, 8, 9, 10, 11,
     ------------------------------------------------------------------------
     12, 13, 14, 15, 16, 17, 18, 19, 20}}

o9 : List

Caveat

This is still somewhat experimental.

Ways to use monodromyGroup :

For the programmer

The object monodromyGroup is a method function with options.