Opened 4 years ago

Closed 3 years ago

#26817 closed defect (fixed)

GaloisGroup_subgroup.fixed_field() should always return an embedding

Reported by: pbruin Owned by:
Priority: minor Milestone: sage-9.0
Component: number fields Keywords: Galois group
Cc: davidloeffler Merged in:
Authors: Peter Bruin Reviewers: David Roe
Report Upstream: N/A Work issues:
Branch: 2b26bc4 (Commits, GitHub, GitLab) Commit: 2b26bc454ddbf132ab5c41ef90b86d713735a1ad
Dependencies: Stopgaps:

Status badges

Description

Currently, GaloisGroup_subgroup.fixed_field() does not return an embedding of the fixed field into the ambient field if the subgroup is trivial:

sage: K.<a> = NumberField(x^6 - 6*x^4 + 9*x^2 + 23)
sage: G = K.galois_group()
sage: H = G.subgroup([g for g in G if g.order().divides(3)])
sage: H.fixed_field()
(Number Field in a0 with defining polynomial x^2 + 207, Ring morphism:
   From: Number Field in a0 with defining polynomial x^2 + 207
   To:   Number Field in a with defining polynomial x^6 - 6*x^4 + 9*x^2 + 23
   Defn: a0 |--> 3*a^3 - 9*a)
sage: H = G.subgroup([G.identity()])
sage: H.fixed_field()
Number Field in a with defining polynomial x^6 - 6*x^4 + 9*x^2 + 23

This should be fixed for consistency.

Change History (5)

comment:1 Changed 4 years ago by pbruin

Branch: u/pbruin/26817-GaloisGroup_fixed_field
Cc: davidloeffler added
Commit: 9545ec7da42286552422f245a2d9b4f99393beeb
Status: newneeds_review

This branch fixes the problem by removing two lines that "work around a silly error". David, you seem to be the author of this code; do you remember what this was? Maybe a bug in an old PARI version?

comment:2 Changed 4 years ago by git

Commit: 9545ec7da42286552422f245a2d9b4f99393beeb2b26bc454ddbf132ab5c41ef90b86d713735a1ad

Branch pushed to git repo; I updated commit sha1. New commits:

79e2a58Merge branch 'develop' into ticket/26817-GaloisGroup_fixed_field
2b26bc4Trac 26817: fix doctest

comment:3 Changed 3 years ago by roed

Reviewers: David Roe
Status: needs_reviewpositive_review

Looks good to me. The recent test failures are due to the switch to Python 3 breaking patchbots.

comment:4 Changed 3 years ago by chapoton

Milestone: sage-8.5sage-9.0

comment:5 Changed 3 years ago by vbraun

Branch: u/pbruin/26817-GaloisGroup_fixed_field2b26bc454ddbf132ab5c41ef90b86d713735a1ad
Resolution: fixed
Status: positive_reviewclosed
Note: See TracTickets for help on using tickets.