Example V2-3 :  This is a case where we have one simple exponential part and 2 conjugated 3x3 (mu=1, d=1, r=1)+(mu=1, d=2, r=1). 

 

> A := rtable(1 .. 3, 1 .. 3, [[`/`(1, `*`(`^`(x, 4))), `/`(1, `*`(`^`(x, 3))), `/`(1, `*`(`^`(x, 2)))], [`/`(1, `*`(`^`(x, 3))), `/`(1, `*`(`^`(x, 5))), `/`(1, `*`(`^`(x, 4)))], [`/`(1, `*`(`^`(x, 5)))...
 

 

 

 

 

 

 

 

[Matrix(%id = 18446744078322836062), `*`(`+`(lambda, 8), `*`(`+`(`*`(`^`(lambda, 2)), `*`(20, `*`(lambda)), 80)))]
The first few terms in the transformation P in Q((x)):
List of subsystems after a first Decomposition in Q((x)):
List of subsystems after a first Decomposition in Q((x)):
List of subsystems after a first Decomposition 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, `*`(`^`(t, 4))), `-`(`/`(`*`(2), `*`(t)))), x = t], [`+`(`/`(`*`(RootOf(`+`(`*`(`^`(_Z, 2)), `-`(_Z), `-`(1)))), `*`(`^`(t, 5))), `-`(`/`(`*`(`/`(1, 5), `*`(RootOf(`+`(`*`(`^`(_Z, 2)), `-`...
[`+`(`/`(1, `*`(`^`(t, 4))), `-`(`/`(`*`(2), `*`(t)))), x = t], [`+`(`/`(`*`(RootOf(`+`(`*`(`^`(_Z, 2)), `-`(_Z), `-`(1)))), `*`(`^`(t, 5))), `-`(`/`(`*`(`/`(1, 5), `*`(RootOf(`+`(`*`(`^`(_Z, 2)), `-`...		 (19.1)