Example V2-5 :  This is a case where we have one simple exponential part and a ramification of degree2 3x3 (mu=1,d=1,r=1)+(mu=1,d=1,r=2). 

 

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

 

 

 

 

 

 

 

[Matrix(%id = 18446744078322837430), `*`(`+`(lambda, 9), `*`(`^`(`+`(lambda, 2), 2)))]
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)):
A multiple of the ramification of each sub system:
We do elementary tranformations and apply the ramification when necessary.
[`+`(`/`(1, `*`(`^`(t, 11))), `/`(1, `*`(`^`(t, 8))), `/`(`*`(`/`(1, 2)), `*`(`^`(t, 7))), `/`(`*`(`/`(1, 2)), `*`(`^`(t, 6))), `/`(`*`(`/`(1, 2)), `*`(`^`(t, 4))), `/`(`*`(`/`(3, 8)), `*`(`^`(t, 3)))... (21.1)