Example V2-6 : This is a case where we have one ramification of degree2 2x2 (mu=1,d=1,r=2). 

 

> A := rtable(1 .. 2, 1 .. 2, [[`/`(1, `*`(`^`(x, 5))), `+`(`-`(`/`(1, `*`(x))))], [x, `/`(1, `*`(`^`(x, 5)))]], subtype = Matrix); -1; Exp_parts(A, x, t); 1
 

 

 

 

 

 

 

 

[Matrix(%id = 18446744078322838038), `*`(`^`(`+`(1, lambda), 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, `*`(`^`(t, 5))), x = t] (22.1)