On Thu, Aug 23, 2012 at 11:16 AM, Chris Smith <[email protected]> wrote: >> I don't know. What I am saying is that I am willing to believe (because it is >> very very often true for most permutation groups) that all elements >> of G can be written in the form a^m1*b^n1*a^m2*b^n2*...*a^mk*b^nk, >> for some m1, ..., mk, n1, ..., nk. > > Yes, that's what I see. So to generate the 31 permutations for the > dodecahedron I define a top face rotation, f0, and a front face > rotation, f1, and then, for example, face 2 rotation is equivalent to > doing f0*f1*f0**4. > >> Sage or Gap or, now Sympy. ( I'm not sure if Aleksander ever >> finished correctly implementing the disjoint cycle notation. If not, Sage >> or Gap would probably be easist.) > > Do you mean cyclic notation, like ((123)(465)) ?
Yes. > > We have that, but I think it uses the unconventional R to L rather > than L to R convention: > >>>> p=Permutation >>>> p([[1,2],[0],[3]])*p([[2,3],[0],[1]] > ... ) > Permutation([0, 2, 3, 1]) >>>> _.cyclic_form > [[1, 2, 3], [0]] > > > http://en.wikipedia.org/wiki/Cycle_notation says that the answer of > the above should be (132) not (123) (which is what SymPy gives when > the order of multiplication is reversed). > Actually, that is very bad I think. If it doesn't follow standard conventions and notations, people will not use it. > ... >> them. So, I think the answer to your question might follow from what >> is known theoretically from Douglas' work. I'll try to look up those papers >> as soon as I get the time and let you know. > > If it's easy to put your hands on it, thanks. > I looked at them today. Sorry, but it is much more complicated than I thought. In fact, I don't think I can answer your question using Douglas' results. Sounds like you don't really need his results anyway, so I guess it isn't a big deal. > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
