#16964: MPolynomialIdeal_singular_repr.variety: sage.libs.pari.gen.PariError:
not
enough precomputed primes
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Reporter: gagern | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: algebraic geometry | Resolution:
Keywords: variety qqbar cmp singular | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by gagern):
Here is a reproducing example which at least demonstrates that comparisons
take ''way'' longer than they should:
{{{
sage: r = QQ[x](69721504*x^8 + 251777664*x^6 + 329532012*x^4 +
184429548*x^2 + 37344321).roots(QQbar, False)
sage: r
[-0.0221204634374360? - 1.090991904211621?*I,
-0.0221204634374360? + 1.090991904211621?*I,
-0.8088604911480535?*I,
-0.7598602580415435?*I,
0.7598602580415435?*I,
0.8088604911480535?*I,
0.0221204634374360? - 1.090991904211621?*I,
0.0221204634374360? + 1.090991904211621?*I]
sage: [r[0], r[1]].sort()
}}}
This is because the comparison of the real parts takes like forever. Which
in turn is because the computation of its minimal polynomial takes
forever.
Looking at the set of all zeros, I can see that there are 4 clearly
distinct real parts, and each comes with a pair of conjugate solutions
since the polynomial has real coefficients. This is enough to conclude
that if the intervals for two real parts overlap, then they must be equal
and I don't have to do an exact computation for this. Should we try to
implement some of this reasoning as a special case for
`AlgebraicNumber.__cmp__`, for the case where the descriptor is exact and
the minpoly is the same?
--
Ticket URL: <http://trac.sagemath.org/ticket/16964#comment:3>
Sage <http://www.sagemath.org>
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