Support character(group, values)?

[joschmitt]

I would like to have an exported version of the function Oscar.class_function(::Oscar.GAPGroup, ::Vector{<:QQAbElem}) without the need to work in the abelian closure on the user side. So something like character(::GAPGroup, ::Vector{<:FieldElem}). Is there any reason against this?

CC @ThomasBreuer

[ThomasBreuer]

Defining a class functions over a field F requires to define how F embeds into a suitable cyclotomic field.
Several such embeddings are possible, we have to make sure that the choices are compatible.

[fingolfin]

@joschmitt Would you expect this function to perform input validation? I.e. should it check that the given vector actually defines a character? This problem does not exist for class_function, of course.

[joschmitt]

I think it should check the input, yes. We can also call it class_function. I guess, I haven't really thought about this very well.

[thofma]

The interface will be awkward, since one has to construct the character table first to get the right order for the conjugacy classes. But then I could have called class_funtion(::GAPGroupCharacterTable, values) directly.

[joschmitt]

Yeah, so all of this answers my question why the function does not exist.