#20756: sign is slow (if not wrong) for number field elements
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: number fields | Resolution:
Keywords: days74 | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/20756 | 31e8874e03c35a6e1f9f0076d8fe7f2937d0177b
Dependencies: | Stopgaps:
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Description changed by vdelecroix:
Old description:
> {{{
> sage: R.<x> = ZZ[]
> sage: p = R.random_element(degree=20) + x**21
> sage: r = p.roots(AA, False)
> sage: K.<a> = NumberField(p, embedding=r[0])
> sage: %time sign(a)
> CPU times: user 1.34 s, sys: 0 ns, total: 1.34 s
> Wall time: 1.33 s
> -1
> sage: b = continued_fraction(a).convergent(20) - a
> sage: sign(b)
> sgn(3^(1/100) - 179093512558/177136737587)
> sage: %time sign(b)
> CPU times: user 8.35 s, sys: 20 ms, total: 8.37 s
> Wall time: 8.32 s
> sgn(3^(1/100) - 179093512558/177136737587)
> }}}
New description:
{{{
sage: x = polygen(ZZ)
sage: K.<a> = NumberField(x^100 - 3, embedding=AA(3)**(1/100))
sage: %time sign(a)
CPU times: user 1.34 s, sys: 0 ns, total: 1.34 s
Wall time: 1.33 s
1
sage: b = continued_fraction(a).convergent(20) - a
sage: sign(b)
sgn(-1/1495877943276*(1/4)^(1/5)*(-(sqrt(5) - I*sqrt(-2*sqrt(5) + 10) +
1)*(-3^(1/4))^(1/5))^(1/5)*(373969485819*sqrt(5) -
373969485819*I*sqrt(-2*sqrt(5) + 10) + 373969485819) +
378100611523/373969485819)
}}}
With the branch applied
{{{
sage: %time sign(a)
CPU times: user 4 ms, sys: 0 ns, total: 4 ms
Wall time: 4.65 ms
1
sage: b = continued_fraction(a).convergent(20) - a
sage: %time sign(b)
CPU times: user 4 ms, sys: 0 ns, total: 4 ms
Wall time: 6.02 ms
-1
}}}
--
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Ticket URL: <http://trac.sagemath.org/ticket/20756#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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