expose pari's galois and finer number field interfaces

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

I would like to use pari's galois computations (such as nfgaloisconj) and finer number field functions (such as nfroots). The interface (in sage.libs.pari.gen) needs to be upgraded.

Component: number theory

Keywords: pari number field nf galois

Issue created by migration from https://trac.sagemath.org/ticket/4724

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

comment:3

A valuable improvement would be to use polisirreducible and nfroots for polynomials defined over number fields.

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

comment:4

This is a step in the right direction -- exposes nfgaloisconj and nfroots, and adds automorphisms/updates embeddings to be much faster for number fields.

Try it with a large degree number field -- you couldn't compute K.embeddings(K) for suff. large K, but now you can.

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

Attachment: 4724-ncalexan-pari-galois-functions.patch.gz

[JohnCremona]

comment:5

This looks really really useful, great code! But it needs to be rebased to 3.4: at present the patch does not merge.

[JohnCremona]

comment:6

Nick, did you get the message about rebasing this? John

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

comment:7

Yes I got messages about this but it is not a priority for me. I will try to rebase it sometime soon.

[aghitza]

replaces the previous patch

[aghitza]

comment:8

Attachment: 4724_rebased.patch.gz

All I did was rebase Nick's patch against 3.4.1.rc2. (ok, I also rest-ified a couple of his docstrings.)

One issue was that the original patch seems to have had a lot of things in double. This is now fixed, hence the difference in size.

The code looks good to me and is nicely documented. Positive review.

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:9

Merged in Sage 3.4.1.rc3.

Cheers,

Michael