#16222: Faster exactification using numeric minpoly
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Reporter: gagern | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Martin von Gagern | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gagern/ticket/16222 | 8597313c855ce7a413cfcabead498059d2cfcbf6
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Hello,
Did you try using the magic `algdep` from pari? It perform (very quickly)
some LLL to find the polynomial with smallest coefficient for which `x` is
almost a root. With your example
{{{
sage: a = (443/96*I*sqrt(443)*sqrt(3) + 833939/1728)^(1/3)
sage: b = sqrt(144*a + 9205/a + 1176)/12
sage: c = QQbar(b)
sage: gp.algdep(c.n(prec=150).real(), 6)
16*x^6 - 392*x^4 + 133*x^2 + 900
}}}
The advantage is that it would potentially speed up non symbolic cases.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16222#comment:6>
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