Example V2-8 : This is a case where we have one ramification of degree3 3x3 (mu=1,d=1,r=3). 

 

> read
 

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

 

 

 

 

 

 

 

[Matrix(%id = 18446744078322838950), `*`(`^`(`+`(lambda, `-`(6)), 3))]
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, 11))), `/`(`*`(`/`(1, 3)), `*`(`^`(t, 7))), `-`(`/`(`*`(4), `*`(`^`(t, 15))))), x = `*`(`^`(t, 3))] (24.1)
 

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