Sage: Ticket #17896: Polred during exactification takes too long
https://trac.sagemath.org/ticket/17896
<p>
The following example comes from <a class="closed ticket" href="https://trac.sagemath.org/ticket/16964#comment:27" title="Comment 27 for Ticket #16964">comment:27:ticket:16964</a> via <a class="new ticket" href="https://trac.sagemath.org/ticket/17886#comment:2" title="Comment 2 for Ticket #17886">comment:2:ticket:17886</a>, with syntax for <code>z</code> discussed in <a class="closed ticket" href="https://trac.sagemath.org/ticket/17895" title="defect: Computing all roots is faster than computing a single one (closed: fixed)">ticket:17895</a>.
</p>
<pre class="wiki">sage: x,y = polygens(QQ,"x,y")
sage: p1 = x^5 + 6*x^4 - 42*x^3 - 142*x^2 + 467*x + 422
sage: p2 = p1(x=(x-1)^2)
sage: p3 = p2(x=x*y).resultant(p2,x).univariate_polynomial()
sage: p4, = [f[0] for f in p3.factor() if f[0].degree() == 80]
sage: ival = CIF((0.77, 0.78), (-0.08, -0.07))
sage: z, = [r for r in p4.roots(QQbar, False) if r in ival]
sage: %time z.exactify()
</pre><p>
This exactification didn't complete in 6 hours. OK, the polynomial in question has degree 80, so this is quite some work, but nevertheless Mathematica can find a minimal polynomial for just this number in 0.2 seconds. There should be some way we can get at least into the less-than-a-minute range, although I don't know exactly how.
</p>
<p>
Perhaps we can drop the polred calls in qqbar?
</p>
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https://trac.sagemath.org/ticket/17896
Trac 1.1.6gagernSat, 18 Apr 2015 19:37:35 GMTstatus changed
https://trac.sagemath.org/ticket/17896#comment:1
https://trac.sagemath.org/ticket/17896#comment:1
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
</ul>
<p>
This appears to be a duplicate of <a class="closed ticket" href="https://trac.sagemath.org/ticket/15600" title="defect: Skip polredbest() for large extensions in exact computations in QQbar (closed: fixed)">#15600</a>.
</p>
TicketmmezzarobbaSun, 19 Apr 2015 05:50:31 GMTstatus, milestone changed
https://trac.sagemath.org/ticket/17896#comment:2
https://trac.sagemath.org/ticket/17896#comment:2
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
<li><strong>milestone</strong>
changed from <em>sage-6.6</em> to <em>sage-duplicate/invalid/wontfix</em>
</li>
</ul>
TicketvbraunSun, 19 Apr 2015 12:17:10 GMTstatus changed; resolution set
https://trac.sagemath.org/ticket/17896#comment:3
https://trac.sagemath.org/ticket/17896#comment:3
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>closed</em>
</li>
<li><strong>resolution</strong>
set to <em>duplicate</em>
</li>
</ul>
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