# Revision history [back]

Samuel and Emanuel, thanks for teaching me the magic of QQbar and SR! one more question, please. How to do this inverse_laplace of a fraction whose denominator roots may be real (and maybe even complex)? For example,

var('s,u')
R.<s> = PolynomialRing(QQbar)
F = R.fraction_field()
L=3/4*(19*s^2 + 156*s + 284)/(19*s^3 + 174*s^2 + 422*s + 228)
whole,LL=L.partial_fraction_decomposition()
show(LL)


Here I'm stuck with the "decimals?" numbers and

inverse_laplace(L,s,u)


ends again in

TypeError: unable to convert [0.6934316866155686?/(s + 0.7570751092241817?), 0.0477251478733486?/(s + 2.861392366086696?), 0.00884316551108293?/(s + 5.539427261531228?)] to a symbolic expression


on the other hand

SR(L).partial_fraction()


fails to find the real roots, and inverse_laplace fails also. Thanks, F

Samuel and Emanuel, thanks for teaching me the magic of QQbar and SR! one more question, please. How to do this inverse_laplace of a fraction whose denominator roots may be real (and maybe even complex)? For example,

var('s,u')
R.<s> = PolynomialRing(QQbar)
F = R.fraction_field()
L=3/4*(19*s^2 + 156*s + 284)/(19*s^3 + 174*s^2 + 422*s + 228)
whole,LL=L.partial_fraction_decomposition()
show(LL)


Here I'm stuck with the "decimals?" numbers and

inverse_laplace(L,s,u)


ends again in

TypeError: unable to convert [0.6934316866155686?/(s + 0.7570751092241817?), 0.0477251478733486?/(s + 2.861392366086696?), 0.00884316551108293?/(s + 5.539427261531228?)] to a symbolic expression


on the other hand

SR(L).partial_fraction()


fails to find the real roots, and inverse_laplace fails also. Thanks, F

Samuel and Emanuel, thanks for teaching me the magic of QQbar and SR! one more question, please. How to do this inverse_laplace of a fraction whose denominator roots may be real (and maybe even complex)? For example,

var('s,u')
R.<s> = PolynomialRing(QQbar)
F = R.fraction_field()
L=3/4*(19*s^2 + 156*s + 284)/(19*s^3 + 174*s^2 + 422*s + 228)
whole,LL=L.partial_fraction_decomposition()
show(LL)


Here I'm stuck with the "decimals?" numbers and

inverse_laplace(L,s,u)


ends again in

TypeError: unable to convert [0.6934316866155686?/(s + 0.7570751092241817?), 0.0477251478733486?/(s + 2.861392366086696?), 0.00884316551108293?/(s + 5.539427261531228?)] to a symbolic expression


on the other hand

SR(L).partial_fraction()


fails to find the real roots, and inverse_laplace fails also. Thanks, F

The problem is really how to do partial_fractions and then extract the answer, but I added more of the story to make it clear this is a numeric question. For a first answer, I do not need 100 digits precision :)

I have added a new question "inverse_laplace of a fraction whose denominator roots are real (or complex) to relance this with more details