Exponential Part 

ExpPart computes the exponential part of a fundamental matrix of formal solutions.  

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

 

Matrix(%id = 18446744078232069174)
[[x = `*`(`^`(t, 2)), `+`(`-`(`/`(`*`(`/`(2, 3)), `*`(`^`(t, 3)))), `-`(`*`(`/`(9, 2), `*`(ln(t)))), `-`(`/`(`*`(2), `*`(t)))), 1], [x = `*`(`^`(t, 2)), `+`(`-`(`/`(`*`(`/`(1, 2), `*`(RootOf(`+`(`*`(`... (3.1)
 

> A := map(simplify, `/`(`*`(Matrix(4, 4, [4, `*`(`^`(x, 3)), `+`(`-`(`*`(2, `*`(`^`(x, 6))))), `+`(`-`(`*`(`^`(x, 6)))), 0, `+`(`-`(1), `-`(`/`(1, `*`(x)))), `/`(1, `*`(x)), 0, `/`(1, `*`(`^`(x, 7))), ...
A := map(simplify, `/`(`*`(Matrix(4, 4, [4, `*`(`^`(x, 3)), `+`(`-`(`*`(2, `*`(`^`(x, 6))))), `+`(`-`(`*`(`^`(x, 6)))), 0, `+`(`-`(1), `-`(`/`(1, `*`(x)))), `/`(1, `*`(x)), 0, `/`(1, `*`(`^`(x, 7))), ...
 

 

 

Matrix(%id = 18446744078208207918)
[[x = `*`(`^`(t, 3)), `+`(`-`(`/`(`*`(`/`(3, 5)), `*`(`^`(t, 5)))), `/`(`*`(`/`(1, 54)), `*`(`^`(t, 2))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(t, 4)))), `-`(`*`(7, `*`(ln(t)))), `-`(`/`(`*`(`/`(82, 81)), `...
[[x = `*`(`^`(t, 3)), `+`(`-`(`/`(`*`(`/`(3, 5)), `*`(`^`(t, 5)))), `/`(`*`(`/`(1, 54)), `*`(`^`(t, 2))), `-`(`/`(`*`(`/`(1, 4)), `*`(`^`(t, 4)))), `-`(`*`(7, `*`(ln(t)))), `-`(`/`(`*`(`/`(82, 81)), `... (3.2)
 

> A := `/`(`*`(Matrix(2, 2, [`+`(`/`(`*`(2), `*`(z))), `/`(1, `*`(z)), `/`(`*`(`+`(z, `-`(1))), `*`(`^`(z, 2))), 1])), `*`(z)); 1; ExpPart(A, z, y); 1
 

 

Matrix(%id = 18446744078229825286)
[[z = `+`(`-`(`*`(`^`(y, 2)))), `+`(`/`(`*`(`/`(2, 3)), `*`(`^`(y, 3))), `/`(1, `*`(`^`(y, 2))), `*`(`/`(1, 2), `*`(ln(y))), `/`(`*`(2), `*`(y))), 1]] (3.3)
 

> A := `/`(`*`(Matrix(4, 4, [`+`(`-`(`/`(`*`(5), `*`(x)))), `+`(`/`(`*`(5), `*`(x))), `+`(`-`(`/`(1, `*`(`^`(x, 2))))), `+`(`/`(`*`(4), `*`(x))), 0, `/`(`*`(`+`(1, `-`(`*`(4, `*`(x))))), `*`(`^`(x, 2)))...
A := `/`(`*`(Matrix(4, 4, [`+`(`-`(`/`(`*`(5), `*`(x)))), `+`(`/`(`*`(5), `*`(x))), `+`(`-`(`/`(1, `*`(`^`(x, 2))))), `+`(`/`(`*`(4), `*`(x))), 0, `/`(`*`(`+`(1, `-`(`*`(4, `*`(x))))), `*`(`^`(x, 2)))...
 

 

Matrix(%id = 18446744078222219734)
[[x = `*`(RootOf(`+`(`*`(`^`(_Z, 2)), 1)), `*`(`^`(t, 2))), `+`(`/`(`*`(`/`(1, 2)), `*`(`^`(t, 4))), `/`(`*`(`/`(2, 3), `*`(RootOf(`+`(`*`(`^`(_Z, 2)), 1)))), `*`(`^`(t, 3))), `-`(`/`(`*`(`/`(11, 4), ...
[[x = `*`(RootOf(`+`(`*`(`^`(_Z, 2)), 1)), `*`(`^`(t, 2))), `+`(`/`(`*`(`/`(1, 2)), `*`(`^`(t, 4))), `/`(`*`(`/`(2, 3), `*`(RootOf(`+`(`*`(`^`(_Z, 2)), 1)))), `*`(`^`(t, 3))), `-`(`/`(`*`(`/`(11, 4), ...		 (3.4)
 

> A := `/`(`*`(Matrix(6, 6, [0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, `+`(`-`(`/`(1, `*`(`^`(x, 8))))), 0, `/`(1, `*`(`^`(x, 5))), 0, `/`(1, `*`(`^`(x, 2...
A := `/`(`*`(Matrix(6, 6, [0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0, 0, x, `+`(`-`(`/`(1, `*`(`^`(x, 8))))), 0, `/`(1, `*`(`^`(x, 5))), 0, `/`(1, `*`(`^`(x, 2...
 

 

Matrix(%id = 18446744078222447670)
[[x = `+`(`-`(`*`(`^`(t, 2)))), `+`(`/`(`*`(2), `*`(t))), 1], [x = `+`(`*`(`/`(1, 36), `*`(`^`(t, 4)))), `+`(`-`(`/`(`*`(12), `*`(`^`(t, 2)))), `-`(`/`(`*`(12), `*`(t)))), 1]] (3.5)
 

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