#9400: modify the NumberField constructor to pass in optional integer B such
that
all the internal pari routines will replace the discriminant by its gcd
with B, making some things massively faster.
-----------------------------+----------------------------------------------
Reporter: was | Owner: davidloeffler
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.5
Component: number fields | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
Comment(by was):
Example of what this makes possible:
{{{
~wstein/bin/sagedb
----------------------------------------------------------------------
| Sage Version 4.4.4, Release Date: 2010-06-23 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: R.<x> = QQ[]
sage: f = (x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 -
2023*x^14 +
....: 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 +
6954*x^8 -
....: 74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 +
....: 960*x + 148)
sage: K.<a> = NumberField(f^2+2, maximize_at_primes=[2])
sage: K.degree()
40
sage: time z = K.factor(2)
CPU times: user 0.59 s, sys: 0.01 s, total: 0.60 s
Wall time: 0.60 s
sage: time k = z[0][0].residue_field()
CPU times: user 1.68 s, sys: 0.03 s, total: 1.71 s
Wall time: 1.98 s
sage: time k(a^3+3)
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
abar^3 + 1
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9400#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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