Is the following a bug, or  not:

# Sage 7.6 built with clang 3.8 on x86_64 FreeBSD 11.0 (see #22679)
sage: z=(1/2)*(1+RDF(sqrt(3))*CDF.0); z
0.5 + 0.8660254037844386*I
sage: [z.algdep(k) for k in [2..6]]
[x^2 - x + 1, x^3 - x^2 + x, x^3 - x^2 + x, x^5 + x^2, x^5 + x^2]

# Sage 7.6 on x86_64 Linux wth gcc:
sage: z=(1/2)*(1+RDF(sqrt(3))*CDF.0); z
0.5 + 0.8660254037844387*I
sage: [z.algdep(k) for k in [2..6]]
[x^2 - x + 1, x^3 + 1, x^3 + 1, x^3 + 1, x^3 + 1]

Interestingly, clang/FreeBSD does a better job in computing the last 
(approx.) digit, '6' of z. Indeed:
sage: t=(1/2)*(1+I*sqrt(3)); t
1/2*I*sqrt(3) + 1/2
sage: t.n(prec=100)
0.50000000000000000000000000000 + 0.86602540378443864676372317075*I

and so it should indeed round to '6', and not to '7'.

Also I find it funny that factors of the form x^j are not removed by PARI...

Thanks,
Dima






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