Marshall Hampton wrote:
> sage: z = var('z')
> sage: f5 = (z^5-1)^2
> sage: f5.roots()
>
> [(e^(2/5*I*pi), 2),
> (e^(4/5*I*pi), 2),
> (e^(-4/5*I*pi), 1),
> (e^(-2/5*I*pi), 1),
> (1, 2)]
>
> Odd, very odd. I guess one of us should write about this on the
> maxima list.
CVS log claims this bug was fixed recently (between 5.17 & 5.18).
Here's what I get with Maxima from CVS (5.18+).
(%i2) solve ((z^5 - 1)^2 = 0, z);
(%o2) [z = %e^(2*%i*%pi/5),z = %e^(4*%i*%pi/5),
z = %e^-(4*%i*%pi/5),z = %e^-(2*%i*%pi/5),z = 1]
(%i3) multiplicities;
(%o3) [2,2,2,2,2]
Another example which was cited:
(%i5) solve ((z^3 - 1)^3 = 0, z);
(%o5) [z = (sqrt(3)*%i-1)/2,z = -(sqrt(3)*%i+1)/2,z = 1]
(%i6) multiplicities;
(%o6) [3,3,3]
FWIW
Robert Dodier
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