# Revision history [back]

Thanks for reporting this issue.

Doing things in a slightly different order works well:

sage: R.<s> = PolynomialRing(CC)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2.00000000000000*s + 6.00000000000000)/(3.00000000000000*s^2 + 13.0000000000000*s + 10.0000000000000)
sage: L.partial_fraction_decomposition()
(0,
[0.571428571428571/(s + 1.00000000000000),
0.0952380952380953/(s + 3.33333333333333)])


Note that in this case where all coefficients are integer, one could work with exact algebraic numbers:

sage: R.<s> = PolynomialRing(QQbar)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2*s + 6)/(3*s^2 + 13*s + 10)
sage: L.partial_fraction_decomposition()
(0, [0.571428571428572?/(s + 1), 2/21/(s + 10/3)])


Thanks for reporting this issue.

Doing things in a slightly different order works well:

sage: R.<s> = PolynomialRing(CC)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2.00000000000000*s + 6.00000000000000)/(3.00000000000000*s^2 + 13.0000000000000*s + 10.0000000000000)
sage: L.partial_fraction_decomposition()
(0,
[0.571428571428571/(s + 1.00000000000000),
0.0952380952380953/(s + 3.33333333333333)])


Note that in this case where all coefficients are integer, one could work with exact algebraic numbers:

sage: R.<s> = PolynomialRing(QQbar)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2*s + 6)/(3*s^2 + 13*s + 10)
sage: L.partial_fraction_decomposition()
(0, [0.571428571428572?/(s + 1), 2/21/(s + 10/3)])


In this case one can even work over the rationals.

sage: R.<s> = PolynomialRing(QQ)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2*s + 6)/(3*s^2 + 13*s + 10)
sage: L.partial_fraction_decomposition()
(0, [4/7/(s + 1), 2/21/(s + 10/3)])


Thanks for reporting this issue.

Doing things in a slightly different order works well:

sage: R.<s> = PolynomialRing(CC)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2.00000000000000*s + 6.00000000000000)/(3.00000000000000*s^2 + 13.0000000000000*s + 10.0000000000000)
sage: L.partial_fraction_decomposition()
(0,
[0.571428571428571/(s + 1.00000000000000),
0.0952380952380953/(s + 3.33333333333333)])


Note that in this case where all coefficients are integer, one could work with exact algebraic numbers:

sage: R.<s> = PolynomialRing(QQbar)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2*s + 6)/(3*s^2 + 13*s + 10)
sage: L.partial_fraction_decomposition()
(0, [0.571428571428572?/(s + 1), 2/21/(s + 10/3)])


In this case one can even work over the rationals.

sage: R.<s> = PolynomialRing(QQ)
sage: F = R.fraction_field()
sage: L = 2*(s + 3)/(3*s^2 + 13*s + 10)
sage: L
(2*s + 6)/(3*s^2 + 13*s + 10)
sage: f = L.partial_fraction_decomposition()
sage: f
(0, [4/7/(s + 1), 2/21/(s + 10/3)])


Then you can take Laplace transform of each partial fraction:

sage: a, b = f
sage: a
0
sage: b
[4/7/(s + 1), 2/21/(s + 10/3)]
sage: inverse_laplace(b[1], s, u)
sage: u = SR.var('u')
sage: inverse_laplace(b[0], s, u)
4/7*e^(-u)
sage: inverse_laplace(b[1], s, u)
2/21*e^(-10/3*u)