Local solubility of conics over number fields

[mstreng]

Use Hilbert symbols to test local solubility of conics over number fields.

Apply attachment: 10742.2.patch

Depends on #10621
Depends on #9334
Depends on #11455

CC: @sagetrac-florian

Component: number fields

Keywords: conic hilbert symbol number field

Author: Marco Streng

Reviewer: Florian Bouyer

Merged: sage-5.3.rc0

Issue created by migration from https://trac.sagemath.org/ticket/10742

[mstreng]

This is the difference between the first two patches of #10621. It contains the local solubility code, but also reverses some fixes of #10621. Select good parts from this patch and make it into a new patch.

[mstreng]

Dependencies: #10621, #9334

[mstreng]

Changed work issues from wait for the pari bug of #9334 to be resolved to write a patch

[mstreng]

comment:1

Attachment: trac_10742_do_not_apply.patch.gz

[mstreng]

Changed dependencies from #10621, #9334 to #10621, #9334, #11455

[mstreng]

Attachment: 10742.patch.gz

[mstreng]

Changed work issues from write a patch to none

[mstreng]

comment:3

apply 10742.patch

[mstreng]

Work Issues: wait for the problem with #11455 to be fixed, then rebase if necessary

[mstreng]

comment:5

With this patch on 5.0.prealpha1, all tests pass. Applies cleanly on top of the new version of #11455, so no rebase was necessary.

[mstreng]

Changed work issues from wait for the problem with #11455 to be fixed, then rebase if necessary to none

[mstreng]

comment:7

does not apply due to new changes in #11455

[mstreng]

rebase

[mstreng]

comment:8

Attachment: 10742.2.patch.gz

testing now; apply 10742.2.patch

[mstreng]

comment:9

all tests pass, please review!

[sagetrac-florian]

comment:10

It passed all test (including long) and the documents turned out fine. I've played around with it and it works.

[sagetrac-florian]

Reviewer: Florian Bouyer

[jdemeyer]

Merged: sage-5.3.rc0