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, 25 Feb 2017 17:08:32 -0600Producing subgroups of Weyl groupshttps://ask.sagemath.org/question/8606/producing-subgroups-of-weyl-groups/Let W be a Weyl group, e.g.
W = RootSystem('[A, 4]').weight_lattice().weyl_group
Given some elements $S \subset W$, I would like to produce the subgroup generated by $S$. It seems like there are methods in SAGE to do this when W is an abstract group, but I can't see how to do it when $W$ is a Weyl group. Any suggestions?Wed, 04 Jan 2012 08:42:04 -0600https://ask.sagemath.org/question/8606/producing-subgroups-of-weyl-groups/Answer by dan_fulea for <p>Let W be a Weyl group, e.g.
W = RootSystem('[A, 4]').weight_lattice().weyl_group</p>
<p>Given some elements $S \subset W$, I would like to produce the subgroup generated by $S$. It seems like there are methods in SAGE to do this when W is an abstract group, but I can't see how to do it when $W$ is a Weyl group. Any suggestions?</p>
https://ask.sagemath.org/question/8606/producing-subgroups-of-weyl-groups/?answer=36732#post-id-36732There is no general answer to be good enough for special choices of $S$.
Using the general group methods the following is working:
# W = RootSystem('[A, 4]').weight_lattice().weyl_group # does not work
W = RootSystem( [ 'A', 4 ] ).weight_lattice().weyl_group()
some_elements = [ W.random_element() for _ in range( 3 ) ]
G = W.subgroup( some_elements )
G . order()
# G.list()[:10]
We simply want, ask for and get the W.subgroup generated by the specified elements.Sat, 25 Feb 2017 17:08:32 -0600https://ask.sagemath.org/question/8606/producing-subgroups-of-weyl-groups/?answer=36732#post-id-36732