#20749: Use PARI nfeltup() for inclusion of base field into relative number
field
-------------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: number fields | Resolution:
Keywords: relative number | Merged in:
field pari | Reviewers: Stephan Ehlen
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 9f1d90be8d3f05b6d5de8ee75e36e6d17ad52095
u/pbruin/20749-pari_nfeltup | Stopgaps:
Dependencies: |
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Comment (by pbruin):
The only remaining problem (after applying #20759 [non-essential], this
branch and the above PARI patch) seems to be that the following is still
too slow:
{{{
sage: K.<zeta22> = CyclotomicField(22)
sage: x = polygen(K)
sage: f = x^9 + (zeta22^9 - zeta22^6 + zeta22^4 + 1)*x^8 + (2*zeta22^8 +
4*zeta22^7 - 6*zeta22^5 - 205*zeta22^4 - 6*zeta22^3 + 4*zeta22 + 2)*x^7 +
(181*zeta22^9 - 354*zeta22^8 + 145*zeta22^7 - 253*zeta22^6 + 145*zeta22^5
- 354*zeta22^4 + 181*zeta22^3 + 189*zeta22 - 189)*x^6 + (902*zeta22^9 +
13116*zeta22^8 + 902*zeta22^7 - 500*zeta22^5 - 322*zeta22^4 - 176*zeta22^3
+ 176*zeta22^2 + 322*zeta22 + 500)*x^5 + (13196*zeta22^9 + 548*zeta22^8 +
9176*zeta22^7 - 17964*zeta22^6 + 8512*zeta22^5 - 8512*zeta22^4 +
17964*zeta22^3 - 9176*zeta22^2 - 548*zeta22 - 13196)*x^4 + (17104*zeta22^9
+ 23456*zeta22^8 + 8496*zeta22^7 - 8496*zeta22^6 - 23456*zeta22^5 -
17104*zeta22^4 + 39680*zeta22^2 + 283184*zeta22 + 39680)*x^3 +
(118736*zeta22^9 - 118736*zeta22^8 - 93520*zeta22^6 + 225600*zeta22^5 +
66496*zeta22^4 + 373744*zeta22^3 + 66496*zeta22^2 + 225600*zeta22 -
93520)*x^2 + (342176*zeta22^9 + 388928*zeta22^8 + 4800*zeta22^7 -
234464*zeta22^6 - 1601152*zeta22^5 - 234464*zeta22^4 + 4800*zeta22^3 +
388928*zeta22^2 + 342176*zeta22)*x + 431552*zeta22^9 - 1830400*zeta22^8 -
1196800*zeta22^7 - 1830400*zeta22^6 + 431552*zeta22^5 + 1196096*zeta22^3 -
12672*zeta22^2 + 12672*zeta22 - 1196096
sage: L.<a> = K.extension(f)
sage: %prun a*zeta22
}}}
Apparently several push-outs of number fields are constructed, which are
apparently different from `L` (most of the time is spent in two calls to
the PARI function `nf_rnfeq`). This is probably a separate issue from
this ticket.
--
Ticket URL: <http://trac.sagemath.org/ticket/20749#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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