On Thu, Mar 26, 2009 at 8:25 PM, Franco Saliola <sali...@gmail.com> wrote:
> Hello,
>
> On Thu, Mar 26, 2009 at 12:09 PM, David Joyner <wdjoy...@gmail.com> wrote:
>> On Thu, Mar 26, 2009 at 12:41 AM, jerome.p.lefeb...@gmail.com
>> <jerome.p.lefeb...@gmail.com> 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]
I created a ticket for the issue.
http://trac.sagemath.org/sage_trac/ticket/5618
Franco
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