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.Sun, 17 Aug 2014 19:13:57 +0200Create an alternative: W(E8) act on positive roots to get some rootshttps://ask.sagemath.org/question/23811/create-an-alternative-we8-act-on-positive-roots-to-get-some-roots/ W=WeylGroup(['E',8])
R = RootSystem(['E',8]).root_lattice()
alpha = R.simple_roots();alpha
[w for w in W if w.action(alpha[1])==(alpha[1]+alpha[2])]
Output shows : gap: cannot extend the workspace any more!
**Is their any alternative calculation to simplify the above **BiswajitSun, 17 Aug 2014 19:13:57 +0200https://ask.sagemath.org/question/23811/Producing 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?markblunkWed, 04 Jan 2012 15:42:04 +0100https://ask.sagemath.org/question/8606/dual of weyl grouphttps://ask.sagemath.org/question/8217/dual-of-weyl-group/I was wondering if it is possible to, given an element in a Weyl group, produce the corresponding element in the dual Weyl group. As an example, if
`w` in `W = RootSystem(['A', 3]).weight_lattice().weyl_group()`
Then I would like a function f such that
`f(w)` in `RootSystem(['A', 3]).coroot_lattice().weyl_group()`,
with the obvious duality
`<w*x,y> = <x,f(w)*(y)>`,
where x in the weight lattice and y is in the coroot lattice.
thanksmarkblunkSat, 09 Jul 2011 18:29:38 +0200https://ask.sagemath.org/question/8217/