#18356: special resultants ``composed_sum`` and ``composed_product``
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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/18356 | 3806e8403764abf4d391161f836f0ec422201cc5
Dependencies: | Stopgaps:
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Changes (by pernici):
* commit: => 3806e8403764abf4d391161f836f0ec422201cc5
Comment:
For polynomials of degree less than 6, the "resultant" algorithm is
faster.
The "BFSS" algorithm becomes progressively faster, as shown in this
benchmark
{{{sage: K.<x> = QQ[]
sage: n = 2
sage: q = (x^4 + 3*x + 2)^n
sage: p1 = q*(q + 1)
sage: p2 = (q + 2)*(q + 3)
sage: %time r1 = p1.composed_sum(p2, "resultant", "+")
Wall time: 909 ms
sage: %time r2 = p1.composed_sum(p2, "BFSS", "+")
Wall time: 84.2 ms
sage: r1 == r2
True
}}}
The same example with `n=4` took 113s with "resultant", 1.3s with "BFSS".
Replacing ``composed_sum`` with ``composed_product``, for `n=2`
"resultant" took 0.08s, "BFSS" 0.03s;
for `n=4` "resultant" took 106s, "BFSS" 0.3s
--
Ticket URL: <http://trac.sagemath.org/ticket/18356#comment:2>
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