Example 1 (ex. in section 3.6  in paper)  

 

> read
 

> A := `/`(`*`(rtable(1 .. 4, 1 .. 4, [[0, 0, x, 0], [1, `+`(`-`(`*`(`^`(x, 2)))), `*`(`^`(x, 2)), `+`(`-`(`*`(`^`(x, 2))))], [0, 1, `*`(`^`(x, 2)), 0], [`*`(`^`(x, 2)), `*`(`^`(x, 2)), 0, `+`(`-`(`*`(`...
 

> Exp_part(A, x, t)
 

 

 

 

 

 

 

 

 

 

 

[rtable(1 .. 4, 1 .. 4, [[O(`*`(`^`(x, 5))), O(`*`(`^`(x, 4))), O(`*`(`^`(x, 4))), `+`(`-`(`*`(2, `*`(`^`(x, 2)))), O(`*`(`^`(x, 5))))], [O(`*`(`^`(x, 8))), O(`*`(`^`(x, 7))), O(`*`(`^`(x, 7))), O(`*`...
The first few terms of the transformation P in C((x)):
List of subsystem up to conjugaison after a first maximal Decomposition in C((x)):
List of subsystem up to conjugaison after a first maximal Decomposition in C((x)):
[`+`(`/`(1, `*`(`^`(t, 11))), `/`(`+`(`*`(3, `*`(`^`(t, 7))))), `-`(`/`(`+`(`*`(3, `*`(`^`(t, 3))))))), x = `*`(`^`(t, 3))], [rtable(1 .. 1, 1 .. 1, [[`+`(`-`(`/`(1, `*`(`^`(t, 2)))))]], subtype = Mat... (1.1)
 

>
 

> int(subs(t = `*`(`^`(x, `/`(1, 3))), `+`(`/`(1, `*`(`^`(t, 11))), `/`(`+`(`*`(3, `*`(`^`(t, 7))))), `-`(`/`(`+`(`*`(3, `*`(`^`(t, 3)))))))), x)
 

`+`(`-`(`/`(`*`(`/`(3, 8)), `*`(`^`(x, `/`(8, 3))))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(x, `/`(4, 3))))), `-`(`*`(`/`(1, 3), `*`(ln(x))))) (1.2)
 

> w1 := int(`+`(`-`(`/`(1, `*`(`^`(t, 2))))), t)
 

`/`(1, `*`(t)) (1.3)
 

> w2 := `+`(`-`(`*`(3, `*`(`/`(`+`(`*`(8, `*`(`^`(x, `/`(8, 3))))))))), `-`(`/`(`+`(`*`(4, `*`(`^`(x, `/`(4, 3)))))))); 1
 

`+`(`-`(`/`(`*`(`/`(3, 8)), `*`(`^`(x, `/`(8, 3))))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(x, `/`(4, 3)))))) (1.4)