Opened 4 years ago
Closed 3 years ago
#26816 closed enhancement (fixed)
Specify subgroups of Galois groups using generators
Reported by: | pbruin | Owned by: | |
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Priority: | minor | Milestone: | sage-9.0 |
Component: | number fields | Keywords: | Galois group |
Cc: | Merged in: | ||
Authors: | Peter Bruin | Reviewers: | David Roe |
Report Upstream: | N/A | Work issues: | |
Branch: | 1c199f4 (Commits, GitHub, GitLab) | Commit: | 1c199f427f90c4013742fcef77bd3077e7893bf6 |
Dependencies: | Stopgaps: |
Description (last modified by )
It should be possible to construct a subgroup of the Galois group of a number field from a set of generators, just as for permutation groups. This is already supported to some extent, but the list of elements of such a subgroup is wrong.
sage: R.<x> = QQ[] sage: f = x^6 - 6*x^4 + 9*x^2 + 23 sage: K.<a> = NumberField(f) sage: G = K.galois_group() sage: list(G) [(), (1,2,3)(4,5,6), (1,3,2)(4,6,5), (1,4)(2,6)(3,5), (1,5)(2,4)(3,6), (1,6)(2,5)(3,4)] sage: g = G[1] sage: h = G[3]
Before:
sage: list(G.subgroup([])) [] sage: list(G.subgroup([g])) [(1,2,3)(4,5,6)] sage: list(G.subgroup([h])) [(1,4)(2,6)(3,5)] sage: list(G.subgroup([g,h])) [(1,2,3)(4,5,6), (1,4)(2,6)(3,5)]
After:
sage: list(G.subgroup([])) [()] sage: list(G.subgroup([g])) [(), (1,2,3)(4,5,6), (1,3,2)(4,6,5)] sage: list(G.subgroup([h])) [(), (1,4)(2,6)(3,5)] sage: list(G.subgroup([g,h])) [(), (1,2,3)(4,5,6), (1,3,2)(4,6,5), (1,4)(2,6)(3,5), (1,5)(2,4)(3,6), (1,6)(2,5)(3,4)]
There is one user-visible change: the special case where applying subgroup()
to the list of all elements of G
returns G
itself has been removed. Besides simplifying the code, this has the advantage that the object returned by subgroup()
now always has type GaloisGroup_subgroup
, and in particular has a method fixed_field()
.
Change History (5)
comment:1 Changed 4 years ago by
Branch: | → u/pbruin/26816-GaloisGroup_subgroup |
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Commit: | → eed989369d086451145434d9e9b49841ce745332 |
Description: | modified (diff) |
Status: | new → needs_review |
comment:2 Changed 4 years ago by
Commit: | eed989369d086451145434d9e9b49841ce745332 → 1c199f427f90c4013742fcef77bd3077e7893bf6 |
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comment:3 Changed 3 years ago by
Reviewers: | → David Roe |
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Status: | needs_review → positive_review |
Looks good to me. Recent patchbot failures due to transition to Python 3.
comment:4 Changed 3 years ago by
Milestone: | sage-8.5 → sage-9.0 |
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comment:5 Changed 3 years ago by
Branch: | u/pbruin/26816-GaloisGroup_subgroup → 1c199f427f90c4013742fcef77bd3077e7893bf6 |
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Resolution: | → fixed |
Status: | positive_review → closed |
Branch pushed to git repo; I updated commit sha1. New commits:
Merge branch 'develop' into ticket/26816-GaloisGroup_subgroup