Example : Example 3.6 in paper "A new approach for formal reduction of singular linear
differential systems using eigenrings". 

 

> 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, [[`+`(`-`(1), O(`*`(`^`(x, 5)))), O(`*`(`^`(x, 4))), O(`*`(`^`(x, 4))), `+`(`-`(`*`(`^`(x, 2))), O(`*`(`^`(x, 5))))], [O(`*`(`^`(x, 8))), `+`(`-`(1), 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... (6.1)
 

>
 

>
 

> subs(t = `*`(`^`(x, `/`(1, 3))), int(`+`(`/`(`*`(3), `*`(`^`(t, 9))), `/`(1, `*`(`^`(t, 5))), `-`(`/`(1, `*`(t)))), t))
 

`+`(`-`(`/`(`*`(`/`(3, 8)), `*`(`^`(x, `/`(8, 3))))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(x, `/`(4, 3))))), `-`(ln(`*`(`^`(x, `/`(1, 3)))))) (6.2)
 

>
 

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

`/`(1, `*`(t)) (6.3)
 

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

`+`(`-`(`/`(`*`(`/`(3, 8)), `*`(`^`(x, `/`(8, 3))))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(x, `/`(4, 3)))))) (6.4)
 

>