What is the proper Sage construct for working with cyclic group Z/nZ ? 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∈Zn you can use genG^i.
Asked: 4 years ago
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Last updated: Jul 30 '20
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