Eliminate use of Gp in number_field.py

[jdemeyer]

The file sage/rings/number_field/number_field.py uses the GP interpreter for some computations. It is probably more efficient to use the PARI library instead.

Dependencies: #9898, #9753, #4836, #10012

Component: number fields

Keywords: pari gp number field

Author: Jeroen Demeyer

Reviewer: John Cremona

Merged: sage-4.6.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/10002

[jdemeyer]

Attachment: 10002_remove_gp.patch.gz

[JohnCremona]

Reviewer: John Cremona

[JohnCremona]

Author: Jeroen Demeyer

[JohnCremona]

comment:3

Applies fine to 4.6.1.alpha0.

It's a great idea to remove use of gp interpreter wherever possible. And since one of my to-do items is to handle S-unit groups (and S-class groups) as well as we do unit and class groups, and this will help, I am all in favour -- thanks!

I tested all sage/rings/number_fields and sage/schemes/elliptic_curves (since 2-descent code uses S-units), and all pass.

[jdemeyer]

Merged: sage-4.6.1.alpha2