id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
17896,Polred during exactification takes too long,gagern,,"The following example comes from comment:27:ticket:16964 via comment:2:ticket:17886, with syntax for `z` discussed in ticket:17895.
{{{
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()
}}}
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.
Perhaps we can drop the polred calls in qqbar?",defect,closed,major,sage-duplicate/invalid/wontfix,number fields,duplicate,qqbar polred performance,,,,,N/A,,,,,