Let's consider the following example:
w = x^4 - (1+3*i)*x^3 - (2-4*i)*x^2 + (6-2*i)*x - 4 - 4*i
p = x^4 + (1-3*i)*x^3 - (4-3*i)*x^2 - (4-2*i)*x + 2*i
solve(w, x)
w.roots()
When using solve, all complex roots are found. When using roots, only two of them. Why?
As you can see with the documentation of the roots() method, (which you can get by typing w.roots?), " Not all roots are guaranteed to be found.". But you can also set a ring option to tell that the symbolic expression should be considered as a polynomial over the given ring, and find roots which belong to that ring. You can get all root by chosing the albebraic numbers for the ring:
sage: w.roots(ring=QQbar)
[(-1 + 1*I, 1), (2*I, 1), (1 - 1*I, 1), (1 + 1*I, 1)]
Or numerically, with the complex double field:
sage: w.roots(ring=CDF)
[(-1.0000000000000002 + 1.0000000000000004*I, 1),
(-1.473610092985238e-15 + 2.000000000000001*I, 1),
(1.0000000000000004 - 0.9999999999999997*I, 1),
(1.0000000000000018 + 1.0000000000000038*I, 1)]
Asked: 2015-12-07 19:44:44 +0200
Seen: 6,407 times
Last updated: Dec 07 '15
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