> 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)) ? 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). > Incidently, Jesse Douglas, who solved Plateau's problem (a problem > in differential geometry which arose in the study of how soap film > forms a minimal > surface when the boundary is some closed wire loop) and got one of > the two first Fields Medals for his work, turned to researching finite > groups as he got older. He apparently classified the finite groups > which do have the property mentioned in your question above. > I think they are all published in the PNAS and on the web, but I have not read > 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. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
