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In gal_reps.py we have
```
sage: EllipticCurve([1,-1,0,-107,-379]).galois_representation().image_type(7) # long time
'The image is a group of order 36.'
```
as doctest. I always get a timeout…
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In 4.4.4 the following code produces a number field which is Galois over the rationals but (allegedly) not over an intermediate field.
```
sage: K.=NumberField(x^2+1)
sage: Kt. = K[]
sage: L. = K.e…
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I think it would be sensible to move the functions
enum_projective_rational_field
enum_projective_finite_field
enum_affine_rational_field
enum_affine_finite field
from their current posit…
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The attached patch contains some simple code which will return the element of the Galois group of a number field corresponding to complex conjugation (at a specified complex place, or the "default" …
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The file ell_rational_field.py is huge and should be split up further. This is especially important for the documentation, currently it is not very user-friendy to find a function in the reference.
…
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```
sage: Q. = NumberField(x^2+1)
sage: complex(i)
0.99999999999999967j
```
It should give `1j` instead.
CC: @burcin
Component: **number fields**
Author: **William Stein**
Reviewer: **Mike Ha…
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```
Currently, if A has an action on B (where B is not an A-module) one
implements either a._l_action_ or b._r_action_. This is because
sometimes it makes sense to put the method on the actor (…
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It would be nice to unify Sage's two ways of handling Galois groups: as abstract transitive groups, and as sets of explicit automorphisms with no group structure. This can be done by using Pari's ga…
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If K is a number field, then K.galois_group() gives a group with very little functionality. One can get an abstract group with more functionality by calling K.galois_group().group(), but it would be…
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It would be great if something like the following worked:
```
sage: F = CyclotomicField(7)
sage: z = F.gen()
sage: G = F.galois_group()
sage: phi = G.random()
sage: z.galois_action(phi)
```
Al…