roots() returns no real solutions for cubic function

Anonymous

Hi there

I have a pretty complicated third-order polynomial which I use Sage to solve. However, somehow roots() only returns imaginary solutions. This should not be possible as a cubic function always has at least one root, so naturally I'm puzzled by this.

I could't seem to include all my code (formatting gets messed up). First I checked that the equation really is a polynomial in m:

print dldm.degree(m)

Outputs 3, so that's OK. Next, I obtain the roots, which I have printed below:

-0.000119434160296805 + 2.27373675443232e-12*I
-5395.14738658974 - 7.95807864051312e-13*I
2560.33896686341 - 1.36424205265939e-12*I

As you can see, they're all imaginary, which should not be possible. The imaginary part is very small on all the solutions. My guess is that Sage uses some numerical approximations to obtain the solutions which is why it seemingly violates mathematics. But what do you think? Thanks!

Comments

Perhaps using more precision can help p.roots(ring=RealField(300)) p.roots(ring=ComplexField(300))

achrzesz ( 12 years ago )

add a comment

sage: R.<x> = QQ[] sage: (x^3-8).roots() [(2, 1)] sage: (x^3-2).roots() # one real root but not rational [] sage: (x^3-2).roots(ring=CDF) [(1.25992104989, 1), (-0.629960524947 - 1.09112363597*I, 1), (-0.629960524947 + 1.09112363597*I, 1)] sage: R.<x> = CDF[] sage: (x^3-8).roots() [(2.0, 1), (-1.0 - 1.73205080757*I, 1), (-1.0 + 1.73205080757*I, 1)] sage: (x^3-2).roots() [(1.25992104989, 1), (-0.629960524947 - 1.09112363597*I, 1), (-0.629960524947 + 1.09112363597*I, 1)]

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

roots() returns no real solutions for cubic function

Comments

1 Answer

Your Answer

Question Tools

Stats

Related questions

roots() returns no real solutions for cubic function savecancel

Comments

1 Answer