What is the proper Sage construct for working with cyclic group $\mathbb{Z} / n \mathbb{Z}$ ? I cannot see any in group theory manual page. Yes, we have Integers(n), but it cannot be asked like a group about, say, subgroup().
You can use the method CyclicPermutationGroup(n). This will create a cyclic group of given order. Then you can apply all the usual group-theory methods, e.g.
sage: G = CyclicPermutationGroup(8)
sage: G.is_cyclic()
True
sage: genG = G.gen()
sage: genG
(1,2,3,4,5,6,7,8)
One problem is, that the elements are now represented as permutations and not in the "usual way" as integers $0,...,n-1$. However, if you want the element in $G$ which corresponds to $i \in \mathbb{Z}_n$ you can use genG^i.
Asked: 2020-07-29 21:16:41 +0100
Seen: 803 times
Last updated: Jul 30 '20
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.