ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 16 May 2020 21:37:12 -0500PARI Group Labellinghttps://ask.sagemath.org/question/51427/pari-group-labelling/I have a Galois group that I'm tying to determine:
f = x^5 - 792*x^4 + 71280*x^3 + 39517632*x^2 - 7519640832*x + 314605513728
d = 3
A = -9504*d^2
B = 365904*d^3
K.<a> = NumberField(f)
R.<y> = K[]
g = y^2 - a^3 - A*a - B
L.<z> = NumberField(y^2 - a^3-A*a-B)
G = L.galois_group()
I have a couple of issues: When I type `G[1]`, it says
GaloisGroup_v1 is not subscriptable
The second is the output for `G` says
[10,-1,1,'C(10)=5[x]2']
I know this is the PARI label and the last entry is the GAP 4 label. But for the life of me I cannot find anywhere where it explicitly tells me what `C(10)=5[x]2` means.Sat, 16 May 2020 12:56:09 -0500https://ask.sagemath.org/question/51427/pari-group-labelling/Answer by slelievre for <p>I have a Galois group that I'm tying to determine:</p>
<pre><code>f = x^5 - 792*x^4 + 71280*x^3 + 39517632*x^2 - 7519640832*x + 314605513728
d = 3
A = -9504*d^2
B = 365904*d^3
K.<a> = NumberField(f)
R.<y> = K[]
g = y^2 - a^3 - A*a - B
L.<z> = NumberField(y^2 - a^3-A*a-B)
G = L.galois_group()
</code></pre>
<p>I have a couple of issues: When I type <code>G[1]</code>, it says </p>
<pre><code>GaloisGroup_v1 is not subscriptable
</code></pre>
<p>The second is the output for <code>G</code> says </p>
<pre><code>[10,-1,1,'C(10)=5[x]2']
</code></pre>
<p>I know this is the PARI label and the last entry is the GAP 4 label. But for the life of me I cannot find anywhere where it explicitly tells me what <code>C(10)=5[x]2</code> means.</p>
https://ask.sagemath.org/question/51427/pari-group-labelling/?answer=51431#post-id-51431Forwarding this answer received from Alexander Hulpke:
> The names (for degrees up to 15) are from the paper:
>
> - Conway; Hulpke; McKay. On Transitive Permutation Groups.
> [DOI:10.1112/S1461157000000115](https://doi.org/10.1112/S1461157000000115)
>
> Basically they describe the particular permutation action,
> not just the abstract isomorphism type. The group in the
> question is abstractly a C(10) (cyclic), but the [x]
> (brackets indicate permutational actions)
> indicates that it is the product action of C(5) with C(2)
> on 10 points (not the intransitive action on 7 points).
-----
[Related notes.]
The Sage documentation page:
- [Sage documentation: PARI Groups](http://doc.sagemath.org/html/en/reference/groups/sage/groups/pari_group.html)
points to the PARI documentation page:
- [PARI documentation: polgalois(T)](http://pari.math.u-bordeaux.fr/dochtml/html/General_number_fields.html#polgalois)
Note that it is after a previous similar question here:
- [Ask Sage question: What is a PARI group?](https://ask.sagemath.org/question/40369)
that the link to the PARI documentation was added in Sage:
- [Sage Trac ticket 24452: Add link in "PARI groups" doc page to PARI doc](https://trac.sagemath.org/ticket/24452)
There is an open ticket to make it easier to extract information about a PARI group:
- [Sage Trac ticket 24469: Make extracting information about a PARI group less painful](https://trac.sagemath.org/ticket/24469)Sat, 16 May 2020 21:37:12 -0500https://ask.sagemath.org/question/51427/pari-group-labelling/?answer=51431#post-id-51431