Example V2-10: (mu=1,d=2,r=2) 

 

> A := rtable(1 .. 4, 1 .. 4, [[`/`(1, `*`(`^`(x, 5))), `+`(`/`(`*`(`/`(1, 3)), `*`(`^`(x, 8)))), `/`(1, `*`(`^`(x, 3))), `+`(`/`(`*`(`/`(1, 3)), `*`(`^`(x, 6))))], [`+`(`/`(`*`(`/`(1, 3)), `*`(`^`(x, 7...
 

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[Matrix(%id = 18446744078322840310), `*`(`^`(`+`(`*`(`^`(lambda, 2)), `-`(`*`(4, `*`(lambda))), `-`(16)), 2))]
The first few terms in the transformation P in Q((x)):
List of subsystems after a first Decomposition in Q((x)):
A multiple of the ramification of each sub system:
We do elementary tranformations and apply the ramification when necessary.
[`+`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`(4))))), `*`(`^`(t, 15))), `/`(`*`(`/`(3, 8), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`...
[`+`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`(4))))), `*`(`^`(t, 15))), `/`(`*`(`/`(3, 8), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`...
[`+`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`(4))))), `*`(`^`(t, 15))), `/`(`*`(`/`(3, 8), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`...
[`+`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`(4))))), `*`(`^`(t, 15))), `/`(`*`(`/`(3, 8), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`...
[`+`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`(4))))), `*`(`^`(t, 15))), `/`(`*`(`/`(3, 8), `*`(RootOf(`+`(`*`(9, `*`(`^`(_Z, 2))), `-`(`*`(6, `*`(_Z))), `-`...		 (26.1)