> < ^ Date: Wed, 25 Jul 2001 09:12:05 +0200
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
< ^ Subject: Re: Character Value

Dear GAP Forum,

just a short remark to the recent question about
evaluating group characters at group elements.

In the section "Arithmetic Operations for Class Functions"
of the GAP Reference Manual,
it is stated that applying the powering operator `^'
to a group element and a class function yields the value
of the class function at this element.

In the example used in the discussion, this looks as follows.

gap> G:= SL(2,8);;
gap> g:=[ [ Z(2^3)^6, Z(2^3)^6 ], [ Z(2^3)^6, Z(2^3)^5 ] ];;
gap> chi:= Irr(G)[3];
Character( CharacterTable( SL(2,8) ), 
[ 7, -1, 1, E(9)^2+E(9)^4+E(9)^5+E(9)^7, -E(9)^2-E(9)^7, -E(9)^4-E(9)^5,
  0,  0, 0 ] )
gap> g^chi;

Of course the computation involves the check in which class of the group
the given element lies.
So this is not more efficient than the straightforward method
Alexander had described in his reply.
It just saves a bit of typing.

Kind regards,

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