Softwares which compute all non-isomorphic quivers in a mutation class

Question

Let $Q$ be a quiver. The mutation class of $Q$ consists of all quivers which can be obtained from $Q$ by a sequence of mutations. Are there some softwares which compute all non-isomorphic quivers in a the mutation class of a given quiver? Thank you very much.

Answer 1

This can be done in sage. See the method "mutation_class" described here. Below is an example of computing the mutation class of the a directed triangle. See the second link and/or A compendium on the cluster algebra and quiver package in sage by Musiker and Stump for more information on how to compute with cluster algebras and quivers in sage.

sage: Q = ClusterQuiver(DiGraph([[0,1],[1,2],[2,0]]))

sage: C = Q.mutation_class()

sage: for R in C:

....: print R.digraph().edges()

....: print

....:

[(0, 2, (1, -1)), (1, 0, (1, -1)), (2, 1, (1, -1))]

[(0, 2, (1, -1)), (2, 1, (1, -1))]

[(0, 1, (1, -1)), (0, 2, (1, -1))]

[(0, 2, (1, -1)), (1, 2, (1, -1))]