Example V2-4 : This is a case where we have 3 different exponential parts (mu=1, d=1, r=1)+(mu=1, d=1, r=1)+(mu=1, d=1, r=1). 

 

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

 

 

 

 

 

 

 

[Matrix(%id = 18446744078322836670), `*`(`+`(lambda, 253), `*`(`+`(lambda, `-`(286)), `*`(`+`(lambda, 274))))]
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)):
A multiple of the ramification of each sub system:
We do elementary tranformations and apply the ramification when necessary.
[`+`(`/`(1, `*`(`^`(t, 5))), `-`(`/`(1, `*`(`^`(t, 3)))), `-`(`/`(1, `*`(t)))), x = t], [`+`(`/`(1, `*`(`^`(t, 5))), `/`(`*`(`/`(1, 2)), `*`(`^`(t, 4))), `/`(`*`(`/`(9, 8)), `*`(`^`(t, 3))), `/`(`*`(`... (20.1)