#18373: special resultants ``composed_op``
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Reporter: pernici | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.7
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pernici/ticket/18373 | add79ac36e8eac6ae522e94b03f2ec9e776d8ee8
Dependencies: | Stopgaps:
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Changes (by pernici):
* commit: => add79ac36e8eac6ae522e94b03f2ec9e776d8ee8
Old description:
> Added ``composed_op``, using the algorithm in
> A. Bostan, P. Flajolet, B. Salvy and E. Schost,
> "Fast Computation of special resultants",
> Journal of Symbolic Computation 41 (2006), 1-29
New description:
added ``composed_op``, using the algorithm in
A. Bostan, P. Flajolet, B. Salvy and E. Schost,
"Fast Computation of special resultants",
Journal of Symbolic Computation 41 (2006), 1-29
These special resultants are useful to compute the minimal polynomials,
see #18242
For instance
{{{
sage: p1 = minpoly(cos(pi/43))
sage: p2 = minpoly(cos(pi/47))
sage: time r1 = p1.composed_op(p2, '+')
Wall time: 108 ms
sage: time r2 = p1.composed_op(p2, '+', algorithm="resultant")
Wall time: 52.3 s
sage: r1 == r2.monic()
True
sage: r1.is_irreducible()
True
sage: r1.degree()
483
}}}
so `r1` is the minimal polynomial of `cos(pi/43) + cos(pi/47)`
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Ticket URL: <http://trac.sagemath.org/ticket/18373#comment:2>
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