Hello, On Thu, Mar 26, 2009 at 12:09 PM, David Joyner <[email protected]> wrote: > On Thu, Mar 26, 2009 at 12:41 AM, [email protected] > <[email protected]> wrote: >> >> Hello, >> >> I've been trying to use Sage to play around with representation >> theory, but I'm running into trouble when dealing with characters. In >> particular, I can't seem to build any character with complex values. >> So, for example, I'm trying to build the irreducible characters for a >> cyclic subgroup of order 3 in A_4. >> >> H = AlternatingGroup(4) >> g = H.list()[1] >> K = H.subgroup([g]) >> >> # All integers works great >> c = K.character([1,1,1]) >> >> # It doesn't seem to work with elements coming from anywhere else >> # for example >> zeta2 = e^((I*pi*2)/3) >> c = K.character([1,zeta2,zeta2**2]) >> >> # Or from an other source; >> k.<z> = NumberField(x^2+x+1) >> zeta2 = k.roots_of_unity()[3] >> c = K.character([1,zeta2,zeta2**2]) >> >> Both of these will both produce errors. >> >> I'm using Sage 3.4. Any ideas?
> It seems to be an issue with the conversion between > Sage's elements of CyclotomicField(3) and GAP's version > of that field. > > Franco, do you know? Yes, it must be exactly that. If you start with the gap version of that field element, then one can create the character without any problems: sage: H = AlternatingGroup(4) sage: g = H.list()[1] sage: K = H.subgroup([g]) sage: z = gap.E(3) sage: c = K.character([1, z, z**2]) sage: c Character of Subgroup of AlternatingGroup(4) generated by [(2,3,4)] sage: [c(k) for k in K] [1, zeta3, -zeta3 - 1] Take care, Franco -- --~--~---------~--~----~------------~-------~--~----~ 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/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
