ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 16 Apr 2019 11:04:47 +0200group algebrahttps://ask.sagemath.org/question/46218/group-algebra/Can anyone help in writing code to find the list of idempotent and primitive elements of a group algebra?
The examples goes like this. Let $p$ be an odd prime such that $\bar2$ generates $U(Z_{p^2})$ and let $G =(\text{ideal generated by }a) ∗ (\text{ideal generated by }b)$ an abelian group, with $o(a)=p^2$ and $o(b)=p$.
Then $F_2G$ has four inequivalent minimal codes, namely, the ones generated by the idempotents:
$$e_0 = \hat{G}$$
$$e_1=\hat{b}−\widehat{(\text{ideal generated by }a)∗ (\text{ideal generated by }b)}$$
$$e_2=\widehat{a−G}$$
$$e_3=\widehat{(\text{ideal generated by }a_p)∗ (\text{ideal generated by }b)}−\hat{G}$$bandanaTue, 16 Apr 2019 11:04:47 +0200https://ask.sagemath.org/question/46218/Get vector from abelian grouphttps://ask.sagemath.org/question/32436/get-vector-from-abelian-group/ I want to represent the Cayley graph of an abelian group (let's say $A=Z_5^2$) is a way that the element $g=a^i b^j$ is in the position $[i,j]$. I need a method `.pos()`such that:
A= groups.presentation.FGAbelian([n,n]);
g=A[2]
---> g = a*b*a^-1
g.pos()
---> [0,1]
How could I do that?
MLainzThu, 04 Feb 2016 02:30:48 +0100https://ask.sagemath.org/question/32436/Get abelian group element powers.https://ask.sagemath.org/question/32435/get-abelian-group-element-powers/ I have the abelian group (let's say, $Z_5^2$). I want to represent its Cayley graph as a grid, in which the element $a^i b^j$ occupies the $[i,j]$ position in the plane. For that, I need would need a method `.pos()`. which did the following.
A = groups.presentation.FGAbelian([n,n]);
e=A[2]
-->e=a*b*a^-1
e.pos()
--> [0,1]
How can I create something like that?MLainzThu, 04 Feb 2016 02:22:33 +0100https://ask.sagemath.org/question/32435/