#12186: Faster norm calculations
-----------------------------+----------------------------------------------
Reporter: MvanBeek | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.8
Component: number fields | Keywords: sd35
Work_issues: | Upstream: N/A
Reviewer: | Author: Monique van Beek
Merged: | Dependencies:
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Comment(by mstreng):
The patch speeds up the case where the subfield is QQ, but ignores the
case where K is a number field isomorphic to QQ, which is more likely to
happen in practice, as the {{{subfields}}} method always returns such
number fields.
Without patch:
{{{
sage: x = var('x')
sage: K1.<a1> = CyclotomicField(11)
sage: K2.<a2> = K1.extension(x^2 - 3)
sage: K3.<a3> = K2.extension(x^2 + 1)
sage: t=a1+6*a2+a3*a1
sage: %time t.norm()
Wall time: 0.08 s
46593592840125350650995659797233874763776
sage: CPU times: user 0.10 s, sys: 0.00 s, total: 0.10 s
sage: %time t.norm(QQ)
CPU times: user 3.82 s, sys: 0.04 s, total: 3.86 s
Wall time: 3.85 s
46593592840125350650995659797233874763776
sage: K = NumberField(x-1,'a')
sage: %time t.norm(K)
CPU times: user 11.28 s, sys: 0.14 s, total: 11.42 s
Wall time: 11.43 s
46593592840125350650995659797233874763776
sage: K.degree()
1
sage: K is QQ
False
}}}
Patch speeds up the second one to match the first, but leaves the third
one as it is.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12186#comment:7>
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