#16651: NumberField to SymbolicRing: rational but still approximate
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Reporter: gagern | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-6.3
Component: number fields | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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I noticed this in comment:18:ticket:14239.
{{{
sage: poly = QQ[x](x^7 - x - 1)
sage: root = sorted(poly.roots(QQbar, False), key=imag)[0]
sage: root
-0.3636235193291805? - 0.9525611952610331?*I
sage: nf = NumberField(poly, "y", embedding=CC(root))
sage: z = SR(nf.gen()); z
-3775/3963*I - 2573/7076
sage: poly(QQbar(z)).is_zero()
False
}}}
The problem here for me as a user is the fact that when I see rational
numbers in some expression, I expect them to be accurate. But the
conversion to SR here uses `solve(to_poly_solve=True)`, which according to
its documentation may yield approximate solutions. I'm still surprised
that these approximate solutions may take the form of elements from ℚ[I].
I guess some code further down the line might get confused as well, since
these conversions look as if they were exact.
--
Ticket URL: <http://trac.sagemath.org/ticket/16651>
Sage <http://www.sagemath.org>
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