Exponential Part - Multivariate systems 

Computes the Exponential Part of a fundamental matrix of formal solutions of a multivariate  completely integrable Pfaffian system with normal crossings 

 

Function call: 

 

ExpPartPfaff(list of the matrices of the system (with their poles), list of the varibales of the system, list of the new varibales to be used in the notation of the ramifications ); 

 

Output: see ExpPart in miniISODLE 

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

 

 

Matrix(%id = 18446744078284223662)
Matrix(%id = 18446744078284223902)
[[], []] (1.1)
 

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

 

 

Matrix(%id = 18446744078277212510)
Matrix(%id = 18446744078277212630)
[[[x = u, `+`(`-`(`/`(1, `*`(u)))), 2]], [[y = v, `+`(`/`(`*`(3), `*`(`^`(v, 2))), `/`(`*`(2), `*`(v))), 2]]] (1.2)
 

> A := `/`(`*`(Matrix(4, 4, [`*`(2, `+`(`+`(`+`(`*`(2, `*`(x))), `+`(`-`(`*`(2, `*`(x))))), 1, `-`(`*`(2, `*`(x, `*`(y)))))), `*`(x, `*`(y, `*`(`+`(`-`(x), 8, `*`(4, `*`(y)))))), `+`(`*`(4, `*`(`^`(x, 2...
A := `/`(`*`(Matrix(4, 4, [`*`(2, `+`(`+`(`+`(`*`(2, `*`(x))), `+`(`-`(`*`(2, `*`(x))))), 1, `-`(`*`(2, `*`(x, `*`(y)))))), `*`(x, `*`(y, `*`(`+`(`-`(x), 8, `*`(4, `*`(y)))))), `+`(`*`(4, `*`(`^`(x, 2...
A := `/`(`*`(Matrix(4, 4, [`*`(2, `+`(`+`(`+`(`*`(2, `*`(x))), `+`(`-`(`*`(2, `*`(x))))), 1, `-`(`*`(2, `*`(x, `*`(y)))))), `*`(x, `*`(y, `*`(`+`(`-`(x), 8, `*`(4, `*`(y)))))), `+`(`*`(4, `*`(`^`(x, 2...
 

 

 

Matrix(%id = 18446744078269356622)
Matrix(%id = 18446744078269356862)
[[[x = u, `+`(`-`(`/`(1, `*`(`^`(u, 2)))), `-`(`/`(`*`(4), `*`(u)))), 1], [x = u, `+`(`-`(`/`(1, `*`(`^`(u, 2))))), 4]], [[y = v, `+`(`/`(`*`(2), `*`(v))), 1], [y = v, `/`(1, `*`(v)), 2]]] (1.3)