On Mar 16, 9:12 am, Rob Beezer <goo...@beezer.cotse.net> wrote: > Stabilizers of permutation groups, and most likely some other > subgroups of permutation groups, do not know much about their > ancestry.
They are subgroups. Thus their domain must be the domain of the parent group, full stop. That's a particular case of the restriction of a representation. Doing it any other way would create untold headaches. I In the example below, all the elements of the stabilizer > fix 4 by definition, and so the stabilizer considers itself a subgroup > of the symmetric group on 3 symbols, as seen when it reports its > degree to be 3. But then the calculation of the orbits "leaves out" > the singleton orbit [4] that I would have expected to see in this > scenario. > > sage: D = DihedralGroup(4) > sage: S = D.stabilizer(4) > sage: S.degree() > 3 > sage: sage: S.orbits() > [[1, 3], [2]] this is a nightmare... Dima > > Some permutation groups carry an attribute "_deg", but if it is not > set, then it is inferred as the "largest moved point." This is the > mechanism that explains why 4 gets bypassed above. It seems that GAP > never gets too concerned about this notion of the degree of a > permutation group, and the GAP command computing the orbit allows one > to explicitly provide the set of points. But as called from Sage, > there is no information in the stabilizer about where it came from, so > simply a best guess for degree gets passed along to GAP. > > I can fix the stabilizer, but I am wondering if something more > systematic is called for - consistently setting _deg in subgroup > creation, or earlier in general group creation, and with less reliance > on the largest moved point as a best guess. As this is perhaps > different from the GAP philosophy (which I do not claim to know well) > maybe there is a good reason for not being so careful? Maybe there > are times when it is important to scrunch down the degree as happened > above? > > Thoughts? > > Rob -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
