For the specific case you mentioned, wouldn't it be easier to make
.automorphisms() return a group? This way you can also work with relative
fields.
On Sunday, October 15, 2017 at 12:25:11 PM UTC-4, John Cremona wrote:
>
> Extracting information about a Galois group is more painful than it
> sh
The pari option essentially just identifies which group it is from a list,
and gives back some very basic data about the group. This is not always
easy to extract (see https://trac.sagemath.org/ticket/24469). If you want
to do more, for example use group elements as automorphisms of the field,
y
Hi David,
On 2018-04-13, David Loeffler wrote:
> On 13 April 2018 at 12:25, Sanketh wrote:
>
>> This is probably obvious but why is type='gap' not standard for Galois
>> groups?
>>
>
> Because Pari is *vastly* faster. E.g. see this example, where Pari beats
> Gap by a factor of 100:
>
> sage: K.
Yup. Also, sage seems to have better support for gap groups. For instance,
sage: L. = NumberField(x^5 - x + 1)
> sage: L.galois_group(type='gap').group().is_abelian()
> False
> sage: L.galois_group(type='pari').group().is_abelian()
>
The difference is the time to fire up GAP.
Once GAP is started, there is not much difference
in time between computing with type='pari' or type='gap'.
$ sage -q
sage: K. = NumberField(x^5 - x - 1)
sage: %time K.galois_group(type='pari')
CPU times: user 3.5 ms, sys: 831 µs, total: 4.33 ms
Wall tim
On 13 April 2018 at 12:25, Sanketh wrote:
> This is probably obvious but why is type='gap' not standard for Galois
> groups?
>
Because Pari is *vastly* faster. E.g. see this example, where Pari beats
Gap by a factor of 100:
sage: K. = NumberField(x^5 - x - 1)
sage: time _=K.galois_group(type='p
This is probably obvious but why is type='gap' not standard for Galois
groups?
On Sunday, October 15, 2017 at 12:25:11 PM UTC-4, John Cremona wrote:
>
> Extracting information about a Galois group is more painful than it
> should be. After
>
> sage: K. = CyclotomicField(5)
> sage: G = K.galo
Sorry to reply almost three months later. I opened #24469 for that,
with a link to this discussion.
https://trac.sagemath.org/ticket/24469
Sun 2017-10-15 16:25:11 UTC, John Cremona:
>
> Extracting information about a Galois group is more painful than it
> should be. After
>
> sage: K. =
